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WEI, GUI-WU. "UNCERTAIN LINGUISTIC HYBRID GEOMETRIC MEAN OPERATOR AND ITS APPLICATION TO GROUP DECISION MAKING UNDER UNCERTAIN LINGUISTIC ENVIRONMENT." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 02 (April 2009): 251–67. http://dx.doi.org/10.1142/s021848850900584x.
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In this paper, we propose an uncertain linguistic hybrid geometric mean (ULHGM) operator, which is based on the uncertain linguistic weighted geometric mean (ULWGM) operator and the uncertain linguistic ordered weighted geometric (ULOWG) operator proposed by Xu [Z. S. Xu, "An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations", Decision Support Systems41 (2006) 488–499] and study some desirable properties of the ULHGM operator. We have proved both ULWGM and ULOWG operators are the special case of the ULHGM operator. The ULHGM operator generalizes both the ULWGM and ULOWG operators, and reflects the importance degrees of both the given arguments and their ordered positions. Based on the ULWGM and ULHGM operators, we propose a practical method for multiple attribute group decision making with uncertain linguistic preference relations. Finally, an illustrative example demonstrates the practicality and effectiveness of the proposed method.
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Selvaraj, Jeevaraj, Prakash Gatiyala, and Sarfaraz Hashemkhani Zolfani. "Trapezoidal Intuitionistic Fuzzy Power Heronian Aggregation Operator and Its Applications to Multiple-Attribute Group Decision-Making." Axioms 11, no. 11 (October 25, 2022): 588. http://dx.doi.org/10.3390/axioms11110588.
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Decision-making problems involve imprecise and incomplete information that can be modelled well using intuitionistic fuzzy numbers (IFNs). Various IFNs are available in the literature for modelling such problems. However, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used. It is mainly because of the flexibility in capturing the incompleteness that occurs in the data. Aggregation operators play a vital role in real-life decision-making problems (modelled under an intuitionistic fuzzy environment). Different aggregation operators are available in the literature for better decision-making. Various aggregation operators are introduced in the literature as a generalization to the conventional aggregation functions defined on the set of real numbers. Each aggregation operator has a specific purpose in solving the problems effectively. In recent years, the power average (PA) operator has been used to reduce the effect of biased data provided by decision-makers. Similarly, the Heronian mean (HM) operator has a property that considers the inter-relationship among various criteria available in the decision-making problem. In this paper, we have considered both the operators (HM, PA) to introduce a new aggregation operator (on the set of TrIFNs), which takes advantage of both properties of these operators. In this study, firstly, we propose the idea of a trapezoidal intuitionistic fuzzy power Heronian aggregation (TrIFPHA) operator and a trapezoidal intuitionistic fuzzy power weighted Heronian aggregation (TrIFPWHA) operator by combining the idea of the Heronian mean operator and power average operator in real numbers. Secondly, we study different mathematical properties of the proposed aggregation operators by establishing a few essential theorems. Thirdly, we discuss a group decision-making algorithm for solving problems modelled under a trapezoidal intuitionistic fuzzy environment. Finally, we show the applicability of the group decision-making algorithm by solving a numerical case problem, and we compare the proposed method’s results with existing methods.
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Chen, Chung-Chuan, Seyyed Mohammad Tabatabaie, and Ali Mohammadi. "Chaotic Cosine Operator Functions Generated by Group Actions." Iranian Journal of Science and Technology, Transactions A: Science 44, no. 2 (March 26, 2020): 465–72. http://dx.doi.org/10.1007/s40995-020-00850-2.
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Park, Jin Han, Jong Jin Seo, Young Chel Kwun, and Ja Hong Koo. "An Approach Based on Power Generalized Aggregation Operator to Decision Making." Advanced Materials Research 542-543 (June 2012): 198–203. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.198.
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The power average (PA) operator and power generalized mean (PGM) operator, proposed by Yager [15], are the nonlinear weighted aggregation tools whose weighting vectors depend on input arguments. In this paper, we study the power generalized mean (PGM) operator and its weighted form, and develop a power ordered weighted generalized mean (POWGM) operator, and study some properties of these operators. The relationship between the PGM operator and other existing operators is also discussed. Moreover, we utilize the weighted PGM operator to develop an approach to group decision making.
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Rong, Yuan, Yi Liu, and Zheng Pei. "Novel Multiple Attribute Group Decision-Making Methods Based on Linguistic Intuitionistic Fuzzy Information." Mathematics 8, no. 3 (March 2, 2020): 322. http://dx.doi.org/10.3390/math8030322.
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As an effective technique to qualitatively depict assessment information, a linguistic intuitionistic fuzzy number (LIFN) is more appropriate to portray vagueness and indeterminacy in actual situations than intuitionistic fuzzy number (IFN). The prominent feature of a Muirhead mean (MM) operator is that it has the powerful ability to capture the correlations between any input-data and MM operator covers other common operators by assigning the different parameter vectors. In the article, we first analyze the limitations of the existing ranking approaches of LIFN and propose a novel ranking approach to surmount these limitations. Secondly, we propound several novel MM operators to fuse linguistic intuitionistic fuzzy (LIF) information, such as the LIF Muirhead mean (LIFMM) operator, the weighted LIF Muirhead mean (WLIFMM) operator and their dual operators, the LIFDMM operator and the WLIFDMM operator. Subsequently, we discuss several desirable properties along with exceptional cases of them. Moreover, two novel multiple attribute group decision-making approaches are developed based upon these operators. Ultimately, the effectuality and practicability of the propounded methods are validated through dealing with a global supplier selection issue, and the comparative analysis and the merits of the presented approaches are demonstrated by comparing them with existing approaches.
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Fahmi, Aliya, Fazli Amin, Saleem Abdullah, and Muhammad Shakeel. "Power Average Operators of Trapezoidal Cubic Fuzzy Numbers and Application to Multi-attribute Group Decision Making." Journal of Intelligent Systems 29, no. 1 (December 24, 2019): 1643–61. http://dx.doi.org/10.1515/jisys-2018-0122.
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Abstract Trapezoidal cubic fuzzy numbers (TzCFNs) are an extraordinary cubic fuzzy set on a real number set. TzCFNs are useful for dealing with well-known quantities in decision data and decision making problems themselves. This paper is about multi-attribute group decision making problems in which the attribute values are stated with TzCFNs, which are solved by developing a new decision method based on power average operators of TzCFNs. The new operation laws for TzCFNs are given. Hereby, the power average operator of real numbers is extended to four kinds of power average operators of TzCFNs, involving the power average operator of TzCFNs, the weighted power average operator of TzCFNs, the power ordered weighted average operator of TzCFNs, and the power hybrid average operator of TzCFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TzCFNs. Applying the hybrid average operator of TzCFNs, the specific general evaluation standards of alternatives are then combined into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method.
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Urbański, Aleksander. "Entropy of a Convolution Operator." Open Systems & Information Dynamics 11, no. 01 (March 2004): 79–85. http://dx.doi.org/10.1023/b:opsy.0000024758.63038.dd.
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The concept of the entropy of a doubly stochastic operator was introduced in 1999 by Ghys, Langevin, and Walczak. The idea was developed further by Kamiński and de Sam Lazaro, who also conjectured that the entropy of a convolution operator determined by a probability measure on a compact abelian group is equal to zero. We prove that this is true when the group is connected and the convolution operator is determined by a measure absolutely continuous with respect to the normalized Haar measure. Our result provides also a characterization of the set of doubly stochastic operators with non-zero entropy.
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Oliva-Maza, J. "On Lie group representations and operator ranges." Proceedings of the American Mathematical Society 149, no. 10 (July 21, 2021): 4317–29. http://dx.doi.org/10.1090/proc/15554.
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In this paper, Lie group representations on Hilbert spaces are studied in relation with operator ranges. Let R \mathcal {R} be an operator range of a Hilbert space H \mathcal {H} . Given the set Λ \Lambda of R \mathcal {R} -invariant operators, and given a Lie group representation ρ : G → GL ( H ) \rho :G\rightarrow \text {GL}(\mathcal {H}) , we discuss the induced semigroup homomorphism ρ ~ : ρ − 1 ( Λ ) → B ( R ) \widetilde {\rho }: \rho ^{-1}(\Lambda ) \rightarrow \mathcal {B(R)} for the operator range topology on R \mathcal {R} . In one direction, we work under the assumption ρ − 1 ( Λ ) = G \rho ^{-1} (\Lambda ) = G , so ρ ~ : G → B ( R ) \widetilde {\rho }:G\rightarrow \mathcal {B}(\mathcal {R}) is in fact a group representation. In this setting, we prove that ρ ~ \widetilde {\rho } is continuous (and smooth) if and only if the tangent map d ρ d\rho is R \mathcal {R} -invariant. In another direction, we prove that for the tautological representations of unitary or invertible operators of an arbitrary infinite-dimensional Hilbert space H \mathcal {H} , the set ρ − 1 ( Λ ) \rho ^{-1}(\Lambda ) is neither a group for a large set of nonclosed operator ranges R \mathcal {R} nor closed for all nonclosed operator ranges R \mathcal {R} . Both results are proved by means of explicit counterexamples.
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Khameneh, Azadeh, and Adem Kiliçman. "m-Polar Fuzzy Soft Weighted Aggregation Operators and Their Applications in Group Decision-Making." Symmetry 10, no. 11 (November 13, 2018): 636. http://dx.doi.org/10.3390/sym10110636.
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Aggregation operators are important tools for solving multi-attribute group decision-making (MAGDM) problems. The main challenging issue for aggregating data in a MAGDM problem is how to develop a symmetric aggregation operator expressing the decision makers’ behavior. In the literature, there are some methods dealing with this difficulty; however, they lack an effective approach for multi-polar inputs. In this study, a new aggregation operator for m-polar fuzzy soft sets (M-pFSMWM) reflecting different agreement scenarios within a group is presented to proceed MAGDM problems in which both attributes and experts have different weights. Moreover, some desirable properties of M-pFSMWM operator, such as idempotency, monotonicity, and commutativity (symmetric), that means being invariant under any permutation of the input arguments, are studied. Further, m-polar fuzzy soft induced ordered weighted average (M-pFSIOWA) operator and m-polar fuzzy soft induced ordered weighted geometric (M-pFSIOWG) operator, which are extensions of IOWA and IOWG operators, respectively, are developed. Two algorithms are also designed based on the proposed operators to find the final solution in MAGDM problems with weighted multi-polar fuzzy soft information. Finally, the efficiency of the proposed methods is illustrated by some numerical examples. The characteristic comparison of the proposed aggregation operators shows the M-pFSMWM operator is more adaptable for solving MAGDM problems in which different cases of agreement affect the final outcome.
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Wang, Weize, and Xinwang Liu. "SOME HESITANT FUZZY GEOMETRIC OPERATORS AND THEIR APPLICATION TO MULTIPLE ATTRIBUTE GROUP DECISION MAKING." Technological and Economic Development of Economy 20, no. 3 (June 9, 2014): 371–90. http://dx.doi.org/10.3846/20294913.2013.877094.
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Hesitant fuzzy set (HFS), a generalization of fuzzy set (FS), permits the membership degree of an element of a set to be represented as several possible values between 0 and 1. In this paper, motivated by the extension principle of HFs, we export Einstein operations on FSs to HFs, and develop some new aggregation operators, such as the hesitant fuzzy Einstein weighted geometric operator, hesitant fuzzy Einstein ordered weighted geometric operator, and hesitant fuzzy Einstein hybrid weighted geometric operator, for aggregating hesitant fuzzy elements. In addition, we discuss the correlations between the proposed aggregation operators and the existing ones respectively. Finally, we apply the hesitant fuzzy Einstein weighted geometric operator to multiple attribute group decision making with hesitant fuzzy information. Some numerical examples are given to illustrate the proposed aggregation operators.
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Park, Jin Han, and Eun Jin Park. "Generalized Fuzzy Bonferroni Harmonic Mean Operators and Their Applications in Group Decision Making." Journal of Applied Mathematics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/604029.
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The Bonferroni mean (BM) operator is an important aggregation technique which reflects the correlations of aggregated arguments. Based on the BM and harmonic mean operators, H. Sun and M. Sun (2012) developed the fuzzy Bonferroni harmonic mean (FBHM) and fuzzy ordered Bonferroni harmonic mean (FOBHM) operators. In this paper, we study desirable properties of these operators and extend them, by considering the correlations of any three aggregated arguments instead of any two, to develop generalized fuzzy weighted Bonferroni harmonic mean (GFWBHM) operator and generalized fuzzy ordered weighted Bonferroni harmonic mean (GFOWBHM) operator. In particular, all these operators can be reduced to aggregate interval or real numbers. Then based on the GFWBHM and GFOWBHM operators, we present an approach to multiple attribute group decision making and illustrate it with a practical example.
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Fishel, B. "Generalized translations associated with an unbounded self-adjoint operator." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 3 (May 1986): 519–28. http://dx.doi.org/10.1017/s030500410006446x.
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Delsarte [2], Povzner [9], Levitan [8], Leblanc [7], Dunford and Schwartz [3] (p. 1626) and Hutson and Pym [5] have discussed generalized translation operators (GTO) ‘associating with a differential operator’. The latter authors have also considered the topic in an abstract setting-the GTO ‘associates’ with a compact operator in a normed space. GTO are to have properties generalizing those of the translation operators defined by members of a group on a vector space E of functions defined on the group:(πεE, s and t are group elements). In the case of a locally compact topological group the integration spaces E = L1,L2,L∞, for a Haar measure of the group, are of especial interest.
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Akram, Muhammad, Rabia Bibi, and Mohammed M. Ali Al-Shamiri. "A Decision-Making Framework Based on 2-Tuple Linguistic Fermatean Fuzzy Hamy Mean Operators." Mathematical Problems in Engineering 2022 (July 6, 2022): 1–29. http://dx.doi.org/10.1155/2022/1501880.
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Aggregation operators are useful tools for approaching situations in the realm of multiattribute decision-making (MADM). Among the most valuable aggregation strategies, the Hamy mean (HM) operator is designed to capture the correlations among integral parameters. In this article, a series of Hamy-inspired operators are used to combine 2-tuple linguistic Fermatean fuzzy (2TLFF) information. The new 2TLFF aggregation operators that are born from this adaptation include the 2-tuple linguistic Fermatean fuzzy Hamy mean (2TLFFHM) operator, 2-tuple linguistic Fermatean fuzzy weighted Hamy mean (2TFFWHM) operator, 2-tuple linguistic Fermatean fuzzy dual Hamy mean (2TLFFDHM) operator, and 2-tuple linguistic Fermatean fuzzy weighted Hamy mean (2TLFFWDHM) operator. Furthermore, various essential theorems are stated, and special cases of these operators are thoroughly examined. Then, a renewed multiattribute group decision-making (MAGDM) technique based on the suggested aggregation operators is provided. A practical example corroborates the usefulness and implementability of this technique. Finally, the merits of the proposed MAGDM method are demonstrated by comparing it with existing approaches, namely, it can deal with MAGDM problems by considering interactions among multiple attributes based on the 2TLFFWHM operator.
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UI, HARUO, and N. AIZAWA. "q-ANALOGUE OF BOSON COMMUTATOR AND THE QUANTUM GROUPS SUq(2) AND SUq(1, 1)." Modern Physics Letters A 05, no. 04 (February 10, 1990): 237–42. http://dx.doi.org/10.1142/s0217732390000287.
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We propose a defining set of commutation relations to a q-analogue of boson operator; [Formula: see text], [Formula: see text] and [N, aq]=−aq, which contracts to the Heisenberg algebra of boson operators in the limit of q=1. Here, N is the number operator, [N]q being its q-analogue operator. By making use of this set, we construct a new realization of the “noncompact” quantum group SUq(1, 1) in addition to that of the SUq(2) recently proposed by Biedenharn. The explicit form of the number operator is given in terms of aq and [Formula: see text] and its positive definiteness is proved. A uniqueness of our commutators is also discussed. It is shown that the quantum group SUq(2) appears as a true symmetry group of a q-analogue of the two-dimensional harmonic oscillator and the SUq(1, 1) as its dynamical group.
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Chen, Chung-Chuan. "Disjoint topological transitivity for cosine operator functions on groups." Filomat 31, no. 8 (2017): 2413–23. http://dx.doi.org/10.2298/fil1708413c.
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In this paper, we study finite sequences of operators, generated by the powers of weighted translations on discrete groups, and give sufficient conditions for such sequences to be disjoint topologically transitive and mixing in terms of the group elements and weights. The sequences of operators are cosine operator functions. Moreover, we also obtain necessary conditions for cosine operator functions to be disjoint transitive and mixing.
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Tan, Ruipu, Wende Zhang, and Shengqun Chen. "Some Generalized Single Valued Neutrosophic Linguistic Operators and Their Application to Multiple Attribute Group Decision Making." Journal of Systems Science and Information 5, no. 2 (June 8, 2017): 148–62. http://dx.doi.org/10.21078/jssi-2017-148-15.
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Abstract This paper proposes a group decision making method based on entropy of neutrosophic linguistic sets and generalized single valued neutrosophic linguistic operators. This method is applied to solve the multiple attribute group decision making problems under single valued neutrosophic liguistic environment, in which the attribute weights are completely unknown. First, the attribute weights are obtained by using the entropy of neutrosophic linguistic sets. Then three generalized single valued neutrosophic linguistic operators are introduced, including the generalized single valued neutrosophic linguistic weighted averaging (GSVNLWA) operator, the generalized single valued neutrosophic linguistic ordered weighted averaging (GSVNLOWA) operator and the generalized single valued neutrosophic linguistic hybrid averaging (GSVNLHA) operator, and the GSVNLWA and GSVNLHA operators are used to aggregate information. Furthermore, similarity measure based on single valued neutrosophic linguistic numbers is defined and used to sort the alternatives and obtain the best alternative. Finally, an illustrative example is given to demonstrate the feasibility and effectiveness of the developed method.
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Peng, Ding-Hong, Tie-Dan Wang, Chang-Yuan Gao, and Hua Wang. "Multigranular Uncertain Linguistic Prioritized Aggregation Operators and Their Application to Multiple Criteria Group Decision Making." Journal of Applied Mathematics 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/857916.
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We investigate multiple criteria group decision-making problems in which there are priority relationships between the decision elements (criteria and experts), and decision information provided by decision makers takes the form of multigranular uncertain linguistic information. Firstly, some operational laws and possibility degree of multi-granular uncertain linguistic variables are introduced. Then, some new linguistic aggregation operators based on the prioritized aggregation operator, such as the multigranular uncertain linguistic prioritized weighted average (MULPWA) operator and the multigranular uncertain linguistic prioritized ordered weighted average (MULPOWA) operator, are developed and their desirable properties are studied. The prominent characteristics of these proposed operators are that they can aggregate directly the uncertain linguistic variables whose values form the linguistic term sets with different granularities and convey the prioritization phenomenon among the aggregated arguments. Furthermore, based on the MULPWA and MULPOWA operators, an approach to deal with multiple criteria group decision-making problems under multi-granular uncertain linguistic environments is developed. Finally, a practical example is provided to illustrate the multiple criteria group decision-making process.
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Chen, Chung-Chuan, Seyyed Tabatabaie, and Ali Mohammadi. "Dynamics of weighted translations generated by group actions." Filomat 34, no. 7 (2020): 2131–39. http://dx.doi.org/10.2298/fil2007131c.
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In this paper, we consider actions of locally compact groups on measure spaces, and give a sufficient and necessary condition for weighted translations on such spaces to be chaotic. Moreover, some dynamical properties for certain cosine operator functions, generated by translations, are proved as well.
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Baranetskij, Ya O., P. I. Kalenyuk, L. I. Kolyasa, and M. I. Kopach. "The nonlocal problem for the differential-operator equation of the even order with the involution." Carpathian Mathematical Publications 9, no. 2 (January 2, 2018): 109–19. http://dx.doi.org/10.15330/cmp.9.2.109-119.
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In this paper, the problem with boundary nonself-adjoint conditions for a differential-operator equations of the order $2n$ with involution is studied. Spectral properties of operator of the problem is investigated.
By analogy of separation of variables the nonlocal problem for the differential-operator equation of the even order is reduced to a sequence $ \{L_{k}\}_{k=1}^{\infty}$ of operators of boundary value problems for ordinary differential equations of even order. It is established that each element $L_{k}$, of this sequence, is an isospectral perturbation of the self-adjoint operator $L_{0,k}$ of the boundary value problem for some linear differential equation of order 2n.
We construct a commutative group of transformation operators whose elements reflect the system $V(L_{0,k})$ of the eigenfunctions of the operator $L_{0,k}$ in the system $V(L_{k})$ of the eigenfunctions of the operators $L_{k}$. The eigenfunctions of the operator $L$ of the boundary value problem for a differential equation with involution are obtained as the result of the action of some specially constructed operator on eigenfunctions of the sequence of operators $L_{0,k}.$
The conditions under which the system of eigenfunctions of operator $L$ the studied problem is a Riesz basis is established.
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Faizi, Shahzad, Wojciech Sałabun, Nisbha Shaheen, Atiq ur Rehman, and Jarosław Wątróbski. "A Novel Multi-Criteria Group Decision-Making Approach Based on Bonferroni and Heronian Mean Operators under Hesitant 2-Tuple Linguistic Environment." Mathematics 9, no. 13 (June 24, 2021): 1489. http://dx.doi.org/10.3390/math9131489.
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Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.
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Chen, Chung-Chuan. "Recurrence of Cosine Operator Functions on Groups." Canadian Mathematical Bulletin 59, no. 4 (December 1, 2016): 693–704. http://dx.doi.org/10.4153/cmb-2016-011-2.
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AbstractIn this note, we study the recurrence and topologically multiple recurrence of a sequence of operators on Banach spaces. In particular, we give a sufficient and necessary condition for a cosine operator function, induced by a sequence of operators on the Lebesgue space of a locally compact group, to be topologically multiply recurrent.
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Feng, Min, Peide Liu, and Yushui Geng. "A Method of Multiple Attribute Group Decision Making Based on 2-Tuple Linguistic Dependent Maclaurin Symmetric Mean Operators." Symmetry 11, no. 1 (January 1, 2019): 31. http://dx.doi.org/10.3390/sym11010031.
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Aiming at multiple attribute group decision making (MAGDM) problems, especially the attribute values of 2-tuple linguistic numbers and the interrelationships between each attribute needing to be considered, this paper proposes a new method of analysis. Firstly, we developed a few new aggregation operators, like the 2-tuple linguistic dependent weighted Maclaurin symmetric mean (2TLDWMSM) operator, the 2-tuple linguistic dependent weighted generalized Maclaurin symmetric mean (2TLDWGMSM) operator, and the 2-tuple linguistic dependent weighted geometric Maclaurin symmetric mean (2TLDWGeoMSM) operator. In the above operators, Maclaurin symmetric mean (MSM) operators can take the relationships between each attribute into account and dependent operators can mitigate the unfair parameters’ impact on the overall outcome, in which those ‘‘incorrect’’ and ‘‘prejudiced’’ parameters are distributed with low weights. Next, a method used by the 2TLDWMSM, 2TLDWGMSM, and 2TLDWGeoMSM operators for MAGDM is introduced. Finally, there is an explanative example to confirm the proposed approach and explain its availability and usefulness.
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Zeiler, F. A., B. Unger, Q. Zhu, J. Xiao, A. W. Kirkpatrick, A. H. Kramer, E. M. Aleassa, and L. M. Gillman. "A Unique Model for ONSD Part II: Inter/Intra-operator Variability." Canadian Journal of Neurological Sciences / Journal Canadien des Sciences Neurologiques 41, no. 4 (July 2014): 430–35. http://dx.doi.org/10.1017/s0317167100018448.
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Objective:To evauluate our novel ultrasound model for measurement of optic nerve sheath diameter (ONSD) and determine the intra- and inter-operator variability associated with this technique.Methods:We conducted ten measurements of ONSD per model amongst eight different models with a single experienced operator to examine intra-operator variability. Similarly, we had seven different operators measure the OSND twice in eight different models, in order to determine inter-operator variability analyzed with a three level linear statistical model.Results:For intra-operator variability, the intra-cluster correlation coefficients for the experienced and novice operators were 0.643 and 0.453 respectively. This displayed improvement in intra-operator variability with experience. The inter-cluster correlation coefficient was 0 for the group of novice operators, indicating negligible difference amongst multiple operators in measuring any given model of ONSD. A strong, statistically significant, linear relationship between the actual model disc size and the ultrasound ONSD measures was identified, implying the reliability of the images produced by our novel model.Conclusions:Utilizing a novel model for ONSD ultrasonography, we have determined the intraoperator reliability of ONSD measurement to be moderate, with no appreciable difference amongst multiple operators. Improvement in measurement reliability has been demonstrated between expert and novice operators with our model, indicating the potential benefit of simulation platforms for teaching the technique of ONSD ultrasound.
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Tasora, Alessandro. "GROUP ALGEBRA FOR ROBOTIC APPLICATIONS BY MEANS OF OPERATOR OVERLOADING." MM Science Journal 2011, no. 03 (September 20, 2011): 252–59. http://dx.doi.org/10.17973/mmsj.2011_10_201107.
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Bozzo, Giancarlo, Elisabetta Bonerba, Roberta Barrasso, Rocco Roma, Francesco Luposella, Nicola Zizzo, and Giuseppina Tantillo. "Evaluation of the Occurrence of False Aneurysms During Halal Slaughtering and Consequences on the Animal’s State of Consciousness." Animals 10, no. 7 (July 13, 2020): 1183. http://dx.doi.org/10.3390/ani10071183.
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This study evaluated the occurrence of false aneurysms and reflexes in bovines, associated with the point along the neck where the cut was performed. The survey was carried out on a total of 1200 male beef cattle, belonging mainly to the Charolais and Limousin breeds, aged between twelve and twenty-four months. In the slaughterhouse, three operators, identified by convention as Operator C4, Operator C2, and Operator C1, performed the Halal slaughtering. Each operator carried out the slaughter of 400 animals and, on the basis of his own professional training, performed the cutting of the vessels at different points along the neck: Operator C4 between the third and fourth cervical vertebrae; Operator C2 at the level of the second cervical vertebra; and Operator C1 at the first cervical vertebra. The occurrence of false aneurysms was assessed on the basis of the different cutting site used by the three operators. Then, the evaluation of consciousness indicators, that is, rhythmic breathing and eye response, closely related to a slow bleeding process and to a delayed loss of brain function, was carried out 90 s post-bleeding. The group of cattle slaughtered by Operator C4 had a prevalence of false aneurysms of 10.25%. Conversely, the other two groups of cattle slaughtered by Operators C2 and C1 showed false aneurysm formation in 7.25% of each case. Further, 37.5% of the animals (18 for Operator C4, 17 for Operator C2, and 16 for Operator C1) with signs of consciousness 90 s after sticking were consequent to the onset of false aneurysms and, more precisely, they were owing to a late second cut of the vessel carried out by the operator, when false aneurysms occurred. The results of the research showed that the cutting point chosen by the operator is a key element in determining the onset of false aneurysms.
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Liu, Hu-Chen, Qing-Lian Lin, and Jing Wu. "Dependent Interval 2-Tuple Linguistic Aggregation Operators and Their Application to Multiple Attribute Group Decision Making." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22, no. 05 (October 2014): 717–35. http://dx.doi.org/10.1142/s0218488514500366.
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Consider the various types of uncertain preference information provided by the decision makers and the importance of determining the associated weights for the aggregation operator, the multiple attribute group decision making (MAGDM) methods based on some dependent interval 2-tuple linguistic aggregation operators are proposed in this paper. Firstly some operational laws and possibility degree of interval 2-tuple linguistic variables are introduced. Then, we develop a dependent interval 2-tuple weighted averaging (DITWA) operator and a dependent interval 2-tuple weighted geometric (DITWG) operator, in which the associated weights only depend on the aggregated interval 2-tuple arguments and can relieve the influence of unfair arguments on the aggregated results by assigning low weights to them. Based on the DITWA and the DITWG operators, some approaches for multiple attribute group decision making with interval 2-tuple linguistic information are proposed. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approaches.
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Kawamura, Hiroyuki, Tsuneo Uematsu, Yoshiaki Yasui, and Jiro Kodaira. "Renormalization of Twist-Four Operators in QCD Bjorken and Ellis–Jaffe Sum Rules." Modern Physics Letters A 12, no. 02 (January 20, 1997): 135–43. http://dx.doi.org/10.1142/s0217732397000133.
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The QCD effects of twist-four operators on the first moment of nucleon spin-dependent structure function g1(x,Q2) are studied in the framework of operator product expansion and renormalization group method. We investigate the operator mixing through renormalization of the twist-four operators including those proportional to the equation of motion by evaluating off-shell Green's functions in the usual covariant gauge as well as in the background gauge. Through this procedure we extract the one-loop anomalous dimension of the spin-1 and twist-four operator which determines the logarithmic correction to the 1/Q2 behavior of the contribution from the twist-four operators to the first moment of g1(x,Q2).
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He, Z., and M. W. Wong. "Wavelet multipliers and signals." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 40, no. 4 (April 1999): 437–46. http://dx.doi.org/10.1017/s0334270000010523.
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AbstractThe Schatten-von Neumann property of a pseudo-differential operator is established by showing that the pseudo-differential operator is a multiplier defined by means of an admissible wavelet associated to a unitary representation of the additive group Rn on the C*-algebra of all bounded linear operators from L2(Rn) into L2(Rn). A bounded linear operator on L2(R) arising in the Landau, Pollak and Slepian model in signal analysis is shown to be a wavelet multiplier studied in this paper.
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Hassler, Curt C., Shawn T. Grushecky, and Chris B. LeDoux. "The Effects of Group Selection Harvest Size on Logging Productivity." Northern Journal of Applied Forestry 17, no. 2 (June 1, 2000): 51–56. http://dx.doi.org/10.1093/njaf/17.2.51.
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Abstract Because increasing demands are being placed on industry to harvest timber by aesthetically, economically, and ecologically acceptable means, we investigated the effects of a ground-based group selection harvest on logging productivity. Results show that size of opening had little or no effect on skidding productivity. However, significant skidder operator differences existed. Some skidder operators consistently, in shorter periods of time, loaded their machine with larger payloads resulting in larger turn volumes. Group selection unit size, skidder operator, and utilization level had no statistically significant impact on delay times. Results also suggest that additional time spent training skidder operators to hook larger payloads faster could pay dividends in increased daily production and improvements in logging profitability. North. J. Appl. For. 17(2):51-56.
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Qi, Xiao-wen, Chang-yong Liang, and Junling Zhang. "Some Generalized Dependent Aggregation Operators with Interval-Valued Intuitionistic Fuzzy Information and Their Application to Exploitation Investment Evaluation." Journal of Applied Mathematics 2013 (2013): 1–24. http://dx.doi.org/10.1155/2013/705159.
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We investigate multiple attribute group decision making (MAGDM) problems with arguments taking the form of interval-valued intuitionistic fuzzy numbers. In order to relieve influence of unfair arguments, a Gaussian distribution-based argument-dependent weighting method and a hybrid support-function-based argument-dependent weighting method are devised by, respectively, measuring support degrees of arguments indirectly and directly, based on which the Gaussian generalized interval-valued intuitionistic fuzzy ordered weighted averaging operator (Gaussian-GIIFOWA) and geometric operator (Gaussian-GIIFOWG), the power generalized interval-valued intuitionistic fuzzy ordered weighted averaging (P-GIIFOWA) operator and geometric (P-GIIFOWA) operator are proposed to generalize a wide range of aggregation operators for decision makers to flexibly choose in decision modelling. And some desirable properties of the proposed operators are also analyzed. Further, application of an approach integrating proposed operators to exploitation investment evaluation of tourist spots has shown the effectiveness and practicality of developed methods; experimental results also verify the properties of proposed operators.
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Lei, Fan, Guiwu Wei, and Xudong Chen. "Some self-evaluation models of enterprise’s credit based on some probabilistic double hierarchy linguistic aggregation operators." Journal of Intelligent & Fuzzy Systems 40, no. 6 (June 21, 2021): 11809–28. http://dx.doi.org/10.3233/jifs-202922.
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Probabilistic double hierarchy linguistic term set (PDHLTS) can not only express the complex linguistic information that the probabilistic linguistic term set (PLTS) cannot express, but also reflect the frequency or importance of linguistic term set (LTS)that cannot be reflected by the double hierarchy linguistic term set (DHLTS). It is an effective tool to deal with multiple attribute group decision making (MAGDM) problems. Therefore, in this paper, we propose several aggregation operators which can aggregate PDHLTS information and apply them to MAGDM problems. Firstly, the basic notion of PDHLTS is reviewed, and the distance formula and algorithm of PDHLTS are defined; then, extant weighted averaging (WA) operator, weighted geometric(WG) operator and power weighted averaging (PWA) operator, power weighted geometric(PWG) operator to PDHLTS, and establish probability double hierarchy linguistic weighted averaging (PDHLWA) operator, probability double hierarchy linguistic weighted geometric (PDHLWG) operator, probability double hierarchy linguistic power weighted averaging (PDHLPWA) operator, probability double hierarchy linguistic power weighted geometric (PDHLPWG) operator; in addition, The idempotency, boundedness and monotonicity of these aggregation operators are studied; what’s more, those aggregation operators are proposed to establish the enterprise credit self-evaluation model; Finally, compared with the available probabilistic double hierarchy linguistic MAGDM methods, the defined model is proved to be scientific and effective.
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Sagala, Irwan Pernandi, Delfitri Munir, Andriana Yunita Murni Rambe, and Taufik Ashar. "The Difference of Olfactory Functions in The Workers of The Gas Station by Using Sniffin’ Stickstest in Medan City." Sumatera Medical Journal 1, no. 1 (October 1, 2018): 49–55. http://dx.doi.org/10.32734/sumej.v1i1.446.
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Introduction: Chronic exposure of volatile substances can cause the impaired olfactory function. Objectives: In order to identify the difference of olfactory function in the workers of the Gas Station in Medan city. Methods: Analytical research with cross- sectional approach. The research subjects were 80 persons consisting of 40 gas station operators and 40 non-operators who fulfilled the inclusion and exclusion criteria. The applied statistical analysis was Mann Whitney, Fisher's Exact, Chi Square, T independent, Spearman with 95% confidence level. Results: Proportion of the impaired olfactory function in the gas station operator group by 77.5% and non-operator group by 0%. Significant correlation was obtained between age, duration of work with the impaired olfactory function (p = 0,047, p = 0,001). The gas station operators will suffer the impaired olfactory function if they work for 3.89 years. Conclusions: There were differences of olfactory functions in the gas station workers by using Sniffin 'Sticks Test in Medan city.
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GUIVARC’H, Y., and EMILE LE PAGE. "On spectral properties of a family of transfer operators and convergence to stable laws for affine random walks." Ergodic Theory and Dynamical Systems 28, no. 2 (April 2008): 423–46. http://dx.doi.org/10.1017/s0143385707001010.
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AbstractWe consider a random walk on the affine group of the real line, we denote by P the corresponding Markov operator on $\mathbb {R}$, and we study the Birkhoff sums associated with its trajectories. We show that, depending on the parameters of the random walk, the normalized Birkhoff sums converge in law to a stable law of exponent α∈ ]0,2[ or to a normal law. The corresponding analysis is based on the spectral properties of two families of associated transfer operators Pt,Tt. The operator Pt is a Fourier operator and is considered here as a perturbation of the Markov operator P=P0 of the random walk. The operator Tt is related to Pt by a symmetry of Heisenberg type and is also considered as a perturbation of the Markov operator T0=T. We prove that these operators have an isolated dominant eigenvalue which has an asymptotic expansion involving fractional powers of t. The parameters of this expansion have simple expressions in terms of tails and moments of the stationary measures of P and T.
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P., John Robinson, and Henry AmirtharajE C. "Extended TOPSIS with Correlation Coefficient of Triangular Intuitionistic Fuzzy Sets for Multiple Attribute Group Decision Making." International Journal of Decision Support System Technology 3, no. 3 (July 2011): 15–41. http://dx.doi.org/10.4018/jdsst.2011070102.
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This paper extends the technique for order preference by similarity to ideal solution (TOPSIS) for solving multi-attribute group decision making (MAGDM) problems under triangular intuitionistic fuzzy sets by using its correlation coefficient. In situations where the information or the data is of the form of triangular intuitionistic fuzzy numbers (TIFNs), some arithmetic aggregation operators have to be defined, namely the triangular intuitionistic fuzzy ordered weighted averaging (TIFOWA) operator and the triangular intuitionistic fuzzy hybrid aggregation (TIFHA) operator. An extended TOPSIS model is developed to solve the MAGDM problems using a new type of correlation coefficient defined for TIFNs based on the triangular intuitionistic fuzzy weighted arithmetic averaging (TIFWAA) operator and the TIFHA operator. With an illustration this proposed model of MAGDM with the correlation coefficient of TIFNs is compared with the other existing methods.
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Markin, Marat V. "On the non-hypercyclicity of scalar type spectral operators and collections of their exponentials." Demonstratio Mathematica 53, no. 1 (January 1, 2020): 352–59. http://dx.doi.org/10.1515/dema-2020-0030.
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Abstract Generalizing the case of a normal operator in a complex Hilbert space, we give a straightforward proof of the non-hypercyclicity of a scalar type spectral operator A in a complex Banach space as well as of the collection { e t A } t ≥ 0 {\{{e}^{tA}\}}_{t\ge 0} of its exponentials, which, under a certain condition on the spectrum of the operator A, coincides with the C 0 {C}_{0} -semigroup generated by A. The spectrum of A lying on the imaginary axis, we also show that non-hypercyclic is the strongly continuous group { e t A } t ∈ ℝ {\{{e}^{tA}\}}_{t\in {\mathbb{R}}} of bounded linear operators generated by A. From the general results, we infer that, in the complex Hilbert space L 2 ( ℝ ) {L}_{2}({\mathbb{R}}) , the anti-self-adjoint differentiation operator A ≔ d d x A:= \tfrac{\text{d}}{\text{d}x} with the domain D ( A ) ≔ W 2 1 ( ℝ ) D(A):= {W}_{2}^{1}({\mathbb{R}}) is non-hypercyclic and so is the left-translation strongly continuous unitary operator group generated by A.
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Khan, Qaisar, Harish Garg, Hizbullah Khattak, Abdulhakim A. Al-Babtain, I. Elbatal, and Mohammed Elgarhy. "A Novel MAGDM Approach Based on Cubic q -Rung Orthopair Fuzzy Power Generalized Maclaurin Symmetric Mean Operator." Journal of Function Spaces 2022 (August 5, 2022): 1–33. http://dx.doi.org/10.1155/2022/9056605.
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The cubic q -rung orthopair fuzzy set (Cq-ROFS) is a basic simplification of several fuzzy notions, including fuzzy set (FS), interval valued FS (INVFS), intuitionistic FS (INTFS), q -rung orthopair FS (q-ROFS), and INV q -rung orthopair FS (INVq-ROFS). By the degrees of INVq-ROFS and q-ROFS, Cq-ROFS exposes fuzzy judgement, and this is one of the advanced mathematical tools to handle more complicated assessment information in multiple attribute group decision-making (MAGDM) problems. In this article, firstly, encouraged from power average (PA) operator, generalized MSM operator, and generalized dual MSM operator, two novel aggregation operators (AOs) such as cubic q -rung orthopair fuzzy power generalized Maclaurin symmetric mean (Cq-ROFPWGMSM) operator and cubic q -rung orthopair fuzzy power generalized dual Maclaurin symmetric mean (Cq-ROFPWGDMSM) operator are initiated by merging PA operator with GMSM and GDMSM operators and some core characteristics of these AOs are investigated. Furthermore, some core cases with respect to different general parameters values are also investigated and found that some aggregation operators are special cases of the initiated AOs. Secondly, the weighted form of these newly initiated aggregation operators is also offered. Thirdly, two MAGDM models are offered based on Cq-OFPGWMSM and Cq-ROFPGWDMSM operators. Lastly, a numerical example about the selection of the best assistant professor of the year is taken as an application to show the effectiveness and capability of the initiated approaches. There is also a comparison with existing decision-making models.
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YANG, WEI. "INDUCED CHOQUET INTEGRALS OF 2-TUPLE LINGUISTIC INFORMATION." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21, no. 02 (April 2013): 175–200. http://dx.doi.org/10.1142/s0218488513500104.
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The group decision making problem with inter-dependent or interactive attributes is studied. By using the Choquet integral and the inducing variables, we develop the induced 2-tuple correlated averaging (ITCA) operator, the generalized induced 2-tuple correlated averaging (GITCA) operator and the quasi-arithmetic induced 2-tuple correlated averaging (QITCA) operator. The characteristics of the proposed operators are that the evaluation values of decision makers are in linguistic arguments, the correlations among the elements can be reflected and the ordering of the arguments is based on other associated variables instead of their own values. The properties of these operators are studied and new multiple attribute decision making method based on the new operators is proposed. Finally, architecture material supplier selection problem is provided to illustrate the feasibility and efficiency of the proposed method.
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Moalla, Nedra, and Wafa Selmi. "Some essential spectra of unbounded operator matrices pencils with non-diagonal domain and application." Filomat 36, no. 3 (2022): 763–79. http://dx.doi.org/10.2298/fil2203763m.
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In this paper, we investigate the stability of some essential spectra of a 2x2 block operator matrices pencil with unbounded entries and with non-diagonal domain (i.e a domain consisting of vectors which satisfy certain relations between their components) by using the resolvent of this kind of matrix operator in terms of the union of the essential spectra of the restriction of its diagonal operators entries. Furthermore, an example of two-group transport operators pencils is presented to illustrate the validity of the main results.
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Choi, Taeseung. "Proper relativistic position operators in 1+1 and 2+1 dimensions." International Journal of Modern Physics A 35, no. 18 (June 17, 2020): 2050084. http://dx.doi.org/10.1142/s0217751x20500840.
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We have revisited the Dirac theory in [Formula: see text] and [Formula: see text] dimensions by using the covariant representation of the parity-extended Poincaré group in their native dimensions. The parity operator plays a crucial role in deriving wave equations in both theories. We studied two position operators, a canonical one and a covariant one that becomes the particle position operator projected onto the particle subspace. In [Formula: see text] dimensions the particle position operator, not the canonical position operator, provides the conserved Lorentz generator. The mass moment defined by the canonical position operator needs an additional unphysical spin-like operator to become the conserved Lorentz generator in [Formula: see text] dimensions. In [Formula: see text] dimensions, the sum of the orbital angular momentum given by the canonical position operator and the spin angular momentum becomes a constant of motion. However, orbital and spin angular momentum do not conserve separately. On the other hand the orbital angular momentum given by the particle position operator and its corresponding spin angular momentum become a constant of motion separately.
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Zhang, Jun Ling, and Jian Wu. "Research on the IAMM and IGMM Operators in Group Decision Making with Intuitionistic Preference Relations." Advanced Materials Research 753-755 (August 2013): 2806–15. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.2806.
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Preference relations are the most common techniques to express decision makers preference information over alternatives or criteria. This paper focus on investigating effective operators for multiple attribute group decision making with intuitionistic fuzzy preference relations. Firstly, we extend arithmetic mean method operator and geometric mean method operator for accommodating intuitionistic fuzzy information to present the intuitionistic arithmetic mean method (IAMM) operator and the intuitionistic geometric mean method (IGMM) operator. Then the compatibility properties of intuitionistic preference relations obtained by IAMM and IGMM are analyzed, we found that aggregation of individual judgments and aggregation of individual priorities provide the same priorities of alternatives, and that if all the individual decision makers have acceptable consensus degree, then the collective preference relations obtained also are of acceptable consensus degree. Finally, the results are verified by an illustrative example carried out in the background of parts supplier selection.
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Liu, Yujia, Jian Wu, and Changyong Liang. "Attitudinal ranking and correlated aggregating methods for multiple attribute group decision making with triangular intuitionistic fuzzy Choquet integral." Kybernetes 44, no. 10 (November 2, 2015): 1437–54. http://dx.doi.org/10.1108/k-02-2014-0040.
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Purpose – The purpose of this paper is to propose novel attitudinal prioritization and correlated aggregating methods for multiple attribute group decision making (MAGDM) with triangular intuitionistic fuzzy Choquet integral. Design/methodology/approach – Based on the continuous ordered weighted average (COWA) operator, the triangular fuzzy COWA (TF-COWA) operator is defined, and then a novel attitudinal expected score function for triangular intuitionistic fuzzy numbers (TIFNs) is investigated. The novelty of this function is that it allows the prioritization of TIFNs by taking account of the expert’s attitudinal character. When the ranking order of TIFNs is determined, the triangular intuitionistic fuzzy correlated geometric (TIFCG) operator and the induced TIFCG (I-TIFCG) operator are developed. Findings – Their use is twofold: first, the TIFCG operator is used to aggregate the correlative attribute value; and second, the I-TIFCG operator is designed to aggregate the preferences of experts with some degree of inter-dependent. Then, a TIFCG and I-TIFCG operators-based approach is presented for correlative MAGDM problems. Finally, the propose method is applied to select investment projects. Originality/value – Based on the TIFCG and I-TIFCG operators, this paper proposes a novel correlated aggregating methods for MAGDM with triangular intuitionistic fuzzy Choquet integral. This method helps to solve the correlated attribute (criteria) relationship. Furthermore, by the attitudinal expected score functions of TIFNs, the propose method can reflect decision maker’s risk attitude in the final decision result.
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Li, Ming-Liang. "An Algorithm for Arranging Operators to Balance Assembly Lines and Reduce Operator Training Time." Applied Sciences 11, no. 18 (September 14, 2021): 8544. http://dx.doi.org/10.3390/app11188544.
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Industry 4.0 is transforming how costs, including labor costs, are managed in manufacturing and remanufacturing systems. Managers must balance assembly lines and reduce the training time of workstation operators to achieve sustainable operations. This study’s originality lies in its use of an algorithm to balance an assembly line by matching operators to workstations so that the line’s workstations achieve the same targeted output rates. First, the maximum output rate of the assembly line is found, and then the number of operators needed at each workstation is determined. Training time is reduced by matching operators’ training and skills to workstations’ skill requirements. The study obtains a robust, cluster algorithm based on the concept of group technology, then forms operator skill cells and determines operator families. Four numerical examples are presented to demonstrate the algorithm’s implementation. The proposed algorithm can solve the problem of arranging operators to balance assembly lines. Managers can also solve the problem of worker absences by assigning more than one operator with the required skillset to each workstation and rearranging them as needed.
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Miller, Kenneth G. "Microlocal regularity on step two nilpotent Lie groups." Proceedings of the Edinburgh Mathematical Society 31, no. 1 (February 1988): 25–39. http://dx.doi.org/10.1017/s0013091500006544.
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A necessary and sufficient condition for a homogeneous left invariant partial differential operator P on a nilpotent Lie group G to be hypoelliptic is that π(P) be injective in π for every nontrivial irreducible unitary representation π of G. This was conjectured by Rockland in [18], where it was also proved in the case of the Heisenberg group. The necessity of the condition in the general case was proved by Beals [2] and the sufficiency by Helffer and Nourrigat [4]. In this paper we present a microlocal version of this theorem when G is step two nilpotent. The operator may be homogeneous with respect to any family of dilations on G, not just the natural dilations. We may also consider pseudodifferential operators as well as partial differential operators.
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Azam, Muhammad, Muhammad Sajjad Ali Khan, and Shilin Yang. "A Decision-Making Approach for the Evaluation of Information Security Management under Complex Intuitionistic Fuzzy Set Environment." Journal of Mathematics 2022 (February 21, 2022): 1–30. http://dx.doi.org/10.1155/2022/9704466.
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Since intuitionistic fuzzy set only deals with uncertainty but not periodicity, therefore to overcome, this situation complex intuitionistic fuzzy set is a better tool that deals with both uncertainty and periodicity. Also, Bonferroni mean operator has the advantage of considering interrelationships between parameters, but it deals with only the crisp data. Recently, to deal with fuzzy data, many extensions of Bonferroni operators have been developed. Motivated by the CIFS and BM operators, in this paper, we proposed some Dombi Bonferroni mean operators to deal with CIF information. Dombi Bonferroni mean operators are special cases of general T-conorm and T-norm, which have the advantage of good flexibility with a general parameter. We proposed the complex intuitionistic fuzzy Dombi Bonferroni mean (CIFDBM) operator, complex intuitionistic fuzzy Dombi weighted Bonferroni mean (CIFDWBM) operator, complex intuitionistic fuzzy Dombi geometric Bonferroni mean (CIFDGBM) operator, and complex intuitionistic fuzzy Dombi weighted geometric Bonferroni mean (CIFDWGBM) operator. Some properties of the developed operators are discussed in detail, and different cases are investigated. Moreover, a multicriteria group decision-making (MCGDM) method is developed based on the proposed aggregation operators. Finally, a numerical example of information security management evaluation is given in order to demonstrate the application and effectiveness of the proposed approach. A comparative study is also conducted in order to show the advantage of the developed method.
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Decker, Thomas, Dominik Janzing, and Martin Rötteler. "Implementation of group-covariant positive operator valued measures by orthogonal measurements." Journal of Mathematical Physics 46, no. 1 (January 2005): 012104. http://dx.doi.org/10.1063/1.1827924.
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Fegan, H. D., and B. Steer. "First Order Operators on Manifolds With a Group Action." Canadian Journal of Mathematics 48, no. 4 (August 1, 1996): 758–76. http://dx.doi.org/10.4153/cjm-1996-039-6.
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AbstractWe investigate questions of spectral symmetry for certain first order differential operators acting on sections of bundles over manifolds which have a group action. We show that if the manifold is in fact a group we have simple spectral symmetry for all homogeneous operators. Furthermore if the manifold is not necessarily a group but has a compact Lie group of rank 2 or greater acting on it by isometries with discrete isotropy groups, and let D be a split invariant elliptic first order differential operator, then D has equivariant spectral symmetry.
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Dai, Songsong. "Linguistic Complex Fuzzy Sets." Axioms 12, no. 4 (March 28, 2023): 328. http://dx.doi.org/10.3390/axioms12040328.
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Complex fuzzy sets (CFSs) are a suitable tool to manage spatial directional information which includes distance and direction. However, spatial directional information is given by linguistic values. It is very awkward for the CFS to describe this type of spatial directional information. To overcome this limitation, we first propose a novel concept called a linguistic complex fuzzy set (LCFS) to serve as an extension of the CFS. Then we put forward some basic operational laws for LCFSs. After that, we define three operators for LCFSs: the linguistic complex fuzzy weighted averaging (LCFWA) operator, the linguistic amplitude max (Amax) operator and the linguistic amplitude min (Amin) operator. In actual application, we use the LCFWA operator to deal with group decision making when the importance weights of experts are known. For the situation in which the weights of experts are unknown, we develop an Amax-Amin method for group decision making.
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Rong, Yuan, Zheng Pei, and Yi Liu. "Linguistic Pythagorean Einstein Operators and Their Application to Decision Making." Information 11, no. 1 (January 16, 2020): 46. http://dx.doi.org/10.3390/info11010046.
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Linguistic Pythagorean fuzzy (LPF) set is an efficacious technique to comprehensively represent uncertain assessment information by combining the Pythagorean fuzzy numbers and linguistic variables. In this paper, we define several novel essential operations of LPF numbers based upon Einstein operations and discuss several relations between these operations. For solving the LPF numbers fusion problem, several LPF aggregation operators, including LPF Einstein weighted averaging (LPFEWA) operator, LPF Einstein weighted geometric (LPFEWG) operator and LPF Einstein hybrid operator, are propounded; the prominent characteristics of these operators are investigated as well. Furthermore, a multi-attribute group decision making (MAGDM) approach is presented on the basis of the developed operators under an LPF environment. Ultimately, two application cases are utilized to demonstrate the practicality and feasibility of the developed decision approach and the comparison analysis is provided to manifest the merits of it.
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He, Wen, Bapi Dutta, Rosa M. Rodríguez, Ahmad A. Alzahrani, and Luis Martínez. "Induced OWA Operator for Group Decision Making Dealing with Extended Comparative Linguistic Expressions with Symbolic Translation." Mathematics 9, no. 1 (December 23, 2020): 20. http://dx.doi.org/10.3390/math9010020.
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Nowadays, decision making problems have increased their complexity and a single decision maker cannot handle these problems, with a more diverse and comprehensive view of them being necessary, which results in group decision making (GDM) schemes. The complexity of GDM problems is often due to their inherent uncertainty that is not solved just by using a group. Consequently, different methodologies has been proposed to handle it, in which, the use of the fuzzy linguistic approach stands out. Among the multiple fuzzy linguistic modeling approaches, Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) information has been recently introduced, which enhances classical linguistic modeling that is based on single terms by providing linguistic expressions in a continuous linguistic domain. Its application to decision making is quite promising, but it is necessary to develop enough operators to accomplish aggregation processes in the decision solving scheme. So far, just a small number of aggregation operators have been defined for ELICIT information. Hence, this paper aims at providing new aggregation operators for ELICIT information by developing novel OWA based operators, such as the Induced OWA (IOWA) operator in order to avoid the OWA operator needs of reordering its arguments, because ELICIT information does not have an inherent order due to its fuzzy representation. Our proposal not only consists of extending the definition of an IOWA operator for ELICIT information with crisp weights, but it is also proposed a type-1 IOWA operator for ELICIT information in which both weights and arguments are fuzzy as well as the use of ELICIT information constructing the order inducing variable to reorder the arguments. Additionally, the use of ELICIT information in GDM demands the ability to manage majority based decisions that are better represented in the IOWA operator by linguistic quantifiers. Hence, a majority-driven GDM process for ELICIT information is proposed, which it is the first proposal for fulfilling the majority solving process for GDM while using ELICIT information. Eventually, an illustrative example and a brief comparative analysis are presented in order to show the performance of the proposal and its feasibility.
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Wu, Wenying, Zhiwei Ni, Feifei Jin, Jian Wu, Ying Li, and Ping Li. "Investment Selection Based on Bonferroni Mean under Generalized Probabilistic Hesitant Fuzzy Environments." Mathematics 9, no. 1 (January 5, 2021): 107. http://dx.doi.org/10.3390/math9010107.
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In investment selection problems, the existence of contingency and uncertainty may result in the loss of attribute information. Then, how to make proper investment decision-making will be a tricky proposition. In this work, a multiattribute group decision making (MAGDM) method based on the generalized probabilistic hesitant fuzzy Bonferroni mean (GPHFBM) operator is constructed, which enables decision-makers to select the proper parameters in decision-making process. Firstly, the GPHFBM operator is proposed by combining the Bonferroni mean operator and Archimedean norm. Secondly, five excellent properties of the GPHFBM operator are discussed in detail. In view of applications, we further develop some special aggregation operators for GPHFBM with the various values of parameters b, d and additive operators g(t). Finally, we propose a probabilistic hesitant fuzzy MAGDM method based on the GPHFBM operator to analyze the aggregated information. A case study of the investment of social insurance funds is given to depict the validity and reasonability of the proposed method. Ultimately, the company X4 is selected as the investment company with the best comprehensive indicator.