Journal articles: 'INTUITIONISTIC FUZZY SET'

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Jeon, Joung Kon, Young Bae Jun, and Jin Han Park. "Intuitionistic fuzzy alpha-continuity and intuitionistic fuzzy precontinuity." International Journal of Mathematics and Mathematical Sciences 2005, no. 19 (2005): 3091–101. http://dx.doi.org/10.1155/ijmms.2005.3091.

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A characterization of intuitionistic fuzzyα-open set is given, and conditions for an IFS to be an intuitionistic fuzzyα-open set are provided. Characterizations of intuitionistic fuzzy precontinuous (resp.,α-continuous) mappings are given.

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Szmidt, Eulalia, and Janusz Kacprzyk. "A Fuzzy Set Corresponding to an Intuitionistic Fuzzy Set." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 06, no. 05 (October 1998): 427–35. http://dx.doi.org/10.1142/s0218488598000343.

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We propose a new approach to find a fuzzy set which corresponds to a given intuitionistic fuzzy set (Atanassov, 1986) in a certain sense. This will help extend a huge array of fuzzy properties, models, etc. available to the case of intuitionistic fuzzy sets.

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Pratama, Dian. "STRUKTUR IMAGE DAN PRE-IMAGE HOMOMORFISMA PADA TRANSLASI RING FUZZY INTUITIONISTIK." Jurnal Ilmiah Matematika dan Pendidikan Matematika 11, no. 1 (May 18, 2020): 59. http://dx.doi.org/10.20884/1.jmp.2020.12.1.1937.

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A set that is characterized by membership function and a non-membership function with the sum of both at intervals of 0 to 1 is called intuitionistik fuzzy set.. When it’s applied in ring’s theory, it will called intuitionistic fuzzy ring. In this research,if the topics is membership fuction and non-membership function then there are translates operator. This operator only changes the values of the membership and non-membership function while the properties are fixed. This journal discussed the structure of image ad pre-image homomorphism of translates on intuitionistic fuzzy rings. The result obtained that the structure of image and pre-image is also intuitionistic fuzzy rings. Full Article

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Bashir, Maruah, Abdul Razak Salleh, and Shawkat Alkhazaleh. "Possibility Intuitionistic Fuzzy Soft Set." Advances in Decision Sciences 2012 (March 13, 2012): 1–24. http://dx.doi.org/10.1155/2012/404325.

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Possibility intuitionistic fuzzy soft set and its operations are introduced, and a few of their properties are studied. An application of possibility intuitionistic fuzzy soft sets in decision making is investigated. A similarity measure of two possibility intuitionistic fuzzy soft sets has been discussed. An application of this similarity measure in medical diagnosis has been shown.

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Mandal, Debabrata. "A Hesitant Intuitionistic Fuzzy Set Approach to Study Ideals of Semirings." International Journal of Fuzzy System Applications 10, no. 3 (July 2021): 1–17. http://dx.doi.org/10.4018/ijfsa.2021070101.

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The classical set theory was extended by the theory of fuzzy set and its several generalizations, for example, intuitionistic fuzzy set, interval valued fuzzy set, cubic set, hesitant fuzzy set, soft set, neutrosophic set, etc. In this paper, the author has combined the concepts of intuitionistic fuzzy set and hesitant fuzzy set to study the ideal theory of semirings. After the introduction and the priliminary of the paper, in Section 3, the author has defined hesitant intuitionistic fuzzy ideals and studied several properities of it using the basic operations intersection, homomorphism and cartesian product. In Section 4, the author has also defined hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals of a semiring and used these to find some characterizations of regular semiring. In that section, the author also has discussed some inter-relations between hesitant intuitionistic fuzzy ideals, hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals, and obtained some of their related properties.

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Roh, Eun Hwan, Eunsuk Yang, and Young Bae Jun. "Intuitionistic Fuzzy Ordered Subalgebras in Ordered BCI-algebras." European Journal of Pure and Applied Mathematics 16, no. 3 (July 30, 2023): 1342–58. http://dx.doi.org/10.29020/nybg.ejpam.v16i3.4832.

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In this paper, we apply the concept of an intuitionistic fuzzy set to ordered subalgebras in ordered BCI-algebras in the sense of intuitionistic fuzzy point. We introduce the notion of an intuitionistic fuzzy (ordered) subalgebra in ordered BCI-algebras, and investigate some related properties. We provide relations between an intuitionistic fuzzy ordered subalgebra and an intuitionistic fuzzy subalgebra. We give characterizations of an intuitionistic fuzzy (ordered) subalgebra. Finally, we provide relations between a $q_{(t,s)}$-level set of intuitionistic fuzzy set and an intuitionistic fuzzy ordered subalgebra.

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Balamurugan, Manivannan, Nazek Alessa, Karuppusamy Loganathan, and M. Sudheer Kumar. "Bipolar Intuitionistic Fuzzy Soft Ideals of BCK/BCI-Algebras and Its Applications in Decision-Making." Mathematics 11, no. 21 (October 28, 2023): 4471. http://dx.doi.org/10.3390/math11214471.

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In this paper, we merge the concepts of soft set theory and a bipolar intuitionistic fuzzy set. A bipolar intuitionistic fuzzy soft ideal in a BCK-algebra is defined as a soft set over the set of elements in the BCK-algebra, with each element associated with an intuitionistic fuzzy set. This relationship captures degrees of uncertainty, hesitancy, and non-membership degrees within the context of BCK-algebras. We investigate basic operations on bipolar intuitionistic fuzzy soft ideals such as union, intersection, AND, and OR. The intersection, union, AND, and OR of two bipolar intuitionistic fuzzy soft ideals is a bipolar intuitionistic fuzzy soft ideal. We also demonstrate how to use a bipolar intuitionistic fuzzy soft set to solve a problem involving decision making. Finally, we provide a general approach for handling decision-making problems using a bipolar intuitionistic fuzzy soft set.

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Jana, Chiranjibe, and Madhumangal Pal. "Application of Bipolar Intuitionistic Fuzzy Soft Sets in Decision Making Problem." International Journal of Fuzzy System Applications 7, no. 3 (July 2018): 32–55. http://dx.doi.org/10.4018/ijfsa.2018070103.

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This article describes how recently, a paper by D. Ezhilmaran and K. Sankar called Morphism of bipolar intuitionistic fuzzy graphs, has introduced bipolar intuitionistic fuzzy sets and morphism of bipolar intuitionistic fuzzy graphs. By using this concept, the authors of this article have combined a bipolar intuitionistic fuzzy set and a soft set. They introduce the notion of bipolar intuitionistic fuzzy soft set and study their basic properties. Also, presented in this article are the basic operations on bipolar intuitionistic fuzzy soft sets, extended unions, and the intersection of two bipolar intuitionistic fuzzy soft sets. An application of bipolar intuitionistic fuzzy soft set provides into a decision-making problem and a general algorithm to solve this decision making problem.

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Singh, Shiva Raj, Surendra Singh Gautam, and Abhishekh . "An Intuitionistic Fuzzy Soft Set Theoretic Approach to Decision Making Problems." MATEMATIKA 34, no. 1 (May 28, 2018): 49–58. http://dx.doi.org/10.11113/matematika.v34.n1.890.

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In general most of real life problem of decision making involve imprecise parameters. In recent past the major emphasis of research workers in this area have been to develop the reliable models to deal with such imprecision and vagueness effectively. Several theories have been developed such as fuzzy set theory, interval valued fuzzy set, intuitionistic fuzzy set, and interval valued intuitionistic fuzzy set, rough set and soft set. The primary objectives of all the above developed theories are to deal with various kinds of uncertainty, imprecision and vagueness but unfortunately every theory has certain limitations. In the present paper we briefly introduced the notion of soft set, fuzzy soft set and intuitionistic fuzzy soft set. We extend the Jurio et al construction method of converting fuzzy set into intuitionistic fuzzy set to fuzzy soft set into intuitionistic fuzzy soft set. Here we consider a problem of decision making in fuzzy soft set and presented a method to generalize it into intuitionistic fuzzy soft set based decision making problem for modelling the problem in a better way. In the process we used the construction method and score function of intuitionistic fuzzy number.

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Wijaya, Ongky Denny, Abdul Rouf Alghofari, Noor Hidayat, and Mohamad Muslikh. "The Properties of Intuitionistic Anti Fuzzy Module t-norm and t-conorm." CAUCHY 7, no. 2 (March 11, 2022): 207–19. http://dx.doi.org/10.18860/ca.v7i2.13351.

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Zadeh have introduced fuzzy set in 1965 and Atanassov have introduced intuitionistic fuzzy set in 1986 in theirs paper. Now, many of researcher connecting intuitionistic fuzzy set with algebraic structure. We interested to combine some concepts over intuitionistic fuzzy set, module of a ring, t-norm, t-conorm, and intuitionistic anti fuzzy. In this paper, we discusses about intuitionistic anti fuzzy module t-norm and t-conorm (IAFMTC) and their properties with respect to module homomorphism, maps, pre-image, and anti-image from intuitionistic fuzzy sets. We have investigate all properties of IAFMTC.

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Zhang, Haidong, Lan Shu, and Shilong Liao. "Intuitionistic Fuzzy Soft Rough Set and Its Application in Decision Making." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/287314.

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The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. In this paper, we present concepts of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets, and investigate some properties of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets in detail. Furthermore, classical representations of intuitionistic fuzzy soft rough approximation operators are presented. Finally, we develop an approach to intuitionistic fuzzy soft rough sets based on decision making and a numerical example is provided to illustrate the developed approach.

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Gosain, Anjana, and Sonika Dahiya. "An effective fuzzy clustering algorithm with outlier identification feature." Journal of Intelligent & Fuzzy Systems 41, no. 1 (August 11, 2021): 2417–28. http://dx.doi.org/10.3233/jifs-201858.

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DKIFCM (Density Based Kernelized Intuitionistic Fuzzy C Means) is the new proposed clustering algorithm that is based on outlier identification, kernel functions, and intuitionist fuzzy approach. DKIFCM is an inspiration from Kernelized Intuitionistic Fuzzy C Means (KIFCM) algorithm and it addresses the performance issue in the presence of outliers. It first identifies outliers based on density of data and then clusters are computed accurately by mapping the data to high dimensional feature space. Performance and effectiveness of various algorithms are evaluated on synthetic 2D data sets such as Diamond data set (D10, D12, and D15), and noisy Dunn data set as well as on high dimension real-world data set such as Fisher-Iris, Wine, and Wisconsin Breast Cancer Data-set. Results of DKIFCM are compared with results of other algorithms such as Fuzzy-C-Means (FCM), Intuitionistic FCM (IFCM), Kernel-Intuitionistic FCM (KIFCM), and density-oriented FCM (DOFCM), and the performance of proposed algorithm is found to be superior even in the presence of outliers and noise. Key advantages of DKIFCM are outlier identification, robustness to noise, and accurate centroid computation.

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Alshehri, Noura, and Muhammad Akram. "Intuitionistic Fuzzy Planar Graphs." Discrete Dynamics in Nature and Society 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/397823.

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Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomorphism between intuitionistic fuzzy planar graphs.

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Hidayahningrum, Syafitri, Noor Hidayat, and Marjono Marjono. "An η-Intuitionistic Fuzzy Rings Structure." JTAM (Jurnal Teori dan Aplikasi Matematika) 7, no. 1 (January 12, 2023): 231. http://dx.doi.org/10.31764/jtam.v7i1.11833.

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In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuzzy ring is a structure which is built with combinating the definition of fuzzy ring, intuitionistic fuzzy set, and η-intuitionistic fuzzy set. The η-intuitionistic fuzzy set is characterized by any value η∈[0,1], where the degree of membership μ_(A^η ) (k) is obtained based on the averaging operator of the degree of membership μ_A (k) and the value of η∈[0,1]. While the degree of non membership ν_(A^η ) (k) is obtained based on the averaging operator of the degree of non membership ν_A (k) and the value of 1-η∈[0,1]. In its development, new concepts were obtained, namely the η-intuitionistic fuzzy ideal and its properties related to the sum and product operation of η-intuitionistic fuzzy ideals. Furthermore, the η-intuitionistic fuzzy ideals concept can be developed into an η-intuitionistic fuzzy quotient ring, η-intuitionistic fuzzy homomorphism, and its properties on the next research.

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Seo, Young Joo, Hee Sik Kim, Young Bae Jun, and Sun Shin Ahn. "Multipolar Intuitionistic Fuzzy Hyper BCK-Ideals in Hyper BCK-Algebras." Mathematics 8, no. 8 (August 16, 2020): 1373. http://dx.doi.org/10.3390/math8081373.

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In 2020, Kang et al. introduced the concept of a multipolar intuitionistic fuzzy set of finite degree, which is a generalization of a k-polar fuzzy set, and applied it to a BCK/BCI-algebra. The specific purpose of this study was to apply the concept of a multipolar intuitionistic fuzzy set of finite degree to a hyper BCK-algebra. The notions of the k-polar intuitionistic fuzzy hyper BCK-ideal, the k-polar intuitionistic fuzzy weak hyper BCK-ideal, the k-polar intuitionistic fuzzy s-weak hyper BCK-ideal, the k-polar intuitionistic fuzzy strong hyper BCK-ideal and the k-polar intuitionistic fuzzy reflexive hyper BCK-ideal are introduced herein, and their relations and properties are investigated. These concepts are discussed in connection with the k-polar lower level set and the k-polar upper level set.

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Yunianti, Dwi Nur, Noor Hidayat, Raden Sulaiman, and Abdul Rouf Alghofari. "Some Properties of Operations in the Collection of Intuitionistic Fuzzy Sets : A Novel Approach." European Journal of Pure and Applied Mathematics 16, no. 4 (October 30, 2023): 2198–207. http://dx.doi.org/10.29020/nybg.ejpam.v16i4.4939.

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In this paper, we introduce collection of intuitionistic fuzzy sets as a new concept of intuitionistic fuzzy sets. In ordinary, universal set in intuitionistic fuzzy sets is classical set. So in this paper, we generalize the universal set as a collection or family of intuitionistic fuzzy sets. We also present intersection and union operation on collection of of intuitionistic fuzzy sets and show that the operations hold commutative, assosiative, idempotent, and De Morgan’s laws properties.

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Thumbakara, Rajesh K. "On Intuitionistic Fuzzy Filters of Intuitionistic Fuzzy Coframes." Journal of Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/793824.

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Frame theory is the study of topology based on its open set lattice, and it was studied extensively by various authors. In this paper, we study quotients of intuitionistic fuzzy filters of an intuitionistic fuzzy coframe. The quotients of intuitionistic fuzzy filters are shown to be filters of the given intuitionistic fuzzy coframe. It is shown that the collection of all intuitionistic fuzzy filters of a coframe and the collection of all intutionistic fuzzy quotient filters of an intuitionistic fuzzy filter are coframes.

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Kang, Kyung Tae, Seok-Zun Song, and Young Bae Jun. "Multipolar Intuitionistic Fuzzy Set with Finite Degree and Its Application in BCK/BCI-Algebras." Mathematics 8, no. 2 (February 2, 2020): 177. http://dx.doi.org/10.3390/math8020177.

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When events occur in everyday life, it is sometimes advantageous to approach them in two directions to find a solution for them. As a mathematical tool to handle these things, we can consider the intuitionistic fuzzy set. However, when events are complex and the key to a solution cannot be easily found, we feel the need to approach them for hours and from various directions. As mathematicians, we wish we had the mathematical tools that apply to these processes. If these mathematical tools were developed, we would be able to apply them to algebra, topology, graph theory, etc., from a close point of view, and we would be able to apply these research results to decision-making and/or coding theory, etc., from a distant point of view. In light of this view, the purpose of this study is to introduce the notion of a multipolar intuitionistic fuzzy set with finite degree (briefly, k-polar intuitionistic fuzzy set), and to apply it to algebraic structure, in particular, a BCK/BCI-algebra. The notions of a k-polar intuitionistic fuzzy subalgebra and a (closed) k-polar intuitionistic fuzzy ideal in a BCK/BCI-algebra are introduced, and related properties are investigated. Relations between a k-polar intuitionistic fuzzy subalgebra and a k-polar intuitionistic fuzzy ideal are discussed. Characterizations of a k-polar intuitionistic fuzzy subalgebra/ideal are provided, and conditions for a k-polar intuitionistic fuzzy subalgebra to be a k-polar intuitionistic fuzzy ideal are provided. In a BCI-algebra, relations between a k-polar intuitionistic fuzzy ideal and a closed k-polar intuitionistic fuzzy ideal are discussed. A characterization of a closed k-polar intuitionistic fuzzy ideal is considered, and conditions for a k-polar intuitionistic fuzzy ideal to be closed are provided.

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Guangpeng Ta and Zengtai Gong. "The Shadowed Set, Intuitionistic Fuzzy Set and their Three-way Decision." Journal of Mathematics and Informatics 22 (2022): 09–22. http://dx.doi.org/10.22457/jmi.v22a02206.

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The theory of three-way decision provides an effective tool for decision-making under uncertainty and incomplete information when a two-way decision is difficult to make. In this paper, we try to transform an intuitionistic fuzzy set into a pessimistic shadowed set or an optimistic shadowed set by using two intuitionistic fuzzy parameters and the classical shadowed set. Accordingly, the pessimistic three-way decision or the optimistic three-way decision of intuitionistic fuzzy set are investigated by means of the proposed shadowed sets. In addition, a method to calculate the thresholds by the minimum cost principle is proposed and some examples are given for illustrating the validity of the method.

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Muhiuddin, G., D. Al-Kadi, K. P. Shum, and A. M. Alanazi. "Generalized Ideals of BCK/BCI-Algebras Based on Fuzzy Soft Set Theory." Advances in Fuzzy Systems 2021 (January 23, 2021): 1–10. http://dx.doi.org/10.1155/2021/8869931.

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In the present paper, using Lukaswize triple-valued logic, we introduce the notion of α , β -intuitionistic fuzzy soft ideal of BCK / BCI -algebras, where α and β are the membership values between an intuitionistic fuzzy soft point and intuitionistic fuzzy set. Moreover, intuitionistic fuzzy soft ideals with thresholds are introduced, and their related properties are investigated.

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Xin, Xiaolong, Rajab Borzooei, Mahmood Bakhshi, and Young Jun. "Intuitionistic Fuzzy Soft Hyper BCK Algebras." Symmetry 11, no. 3 (March 19, 2019): 399. http://dx.doi.org/10.3390/sym11030399.

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Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets, and presented an application of fuzzy soft sets in a decision-making problem. Maji et al. also introduced the notion of intuitionistic fuzzy soft sets in the paper [P.K. Maji, R. Biswas and A.R. Roy, Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics, 9 (2001), no. 3, 677–692]. The aim of this manuscript is to apply the notion of intuitionistic fuzzy soft set to hyper BCK algebras. The notions of intuitionistic fuzzy soft hyper BCK ideal, intuitionistic fuzzy soft weak hyper BCK ideal, intuitionistic fuzzy soft s-weak hyper BCK-ideal and intuitionistic fuzzy soft strong hyper BCK-ideal are introduced, and related properties and relations are investigated. Characterizations of intuitionistic fuzzy soft (weak) hyper BCK ideal are considered. Conditions for an intuitionistic fuzzy soft weak hyper BCK ideal to be an intuitionistic fuzzy soft s-weak hyper BCK ideal are provided. Conditions for an intuitionistic fuzzy soft set to be an intuitionistic fuzzy soft strong hyper BCK ideal are given.

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Davvaz, Bijan, Fatema F. Kareem, and Wisam K. Awad. "Cubic intuitionistic structures of a semigroup in KU-algebra." Mathematica Montisnigri 56 (2023): 63–75. http://dx.doi.org/10.20948/mathmontis-2023-56-7.

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An intuitionistic fuzzy set was exhibited by Atanassov in 1986 as a generalization of the fuzzy set. So, we introduce cubic intuitionistic structures on a KU-semigroup as a generalization of the fuzzy set of a KU-semigroup. A cubic intuitionistic k-ideal and some related properties are introduced. Also, a few characterizations of a cubic intuitionistic k-ideal are discussed and new cubic intuitionistic fuzzy sets in a KU-semigroup are defined.

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DESCHRIJVER, GLAD, and ETIENNE E. KERRE. "CLASSES OF INTUITIONISTIC FUZZY T-NORMS SATISFYING THE RESIDUATION PRINCIPLE." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11, no. 06 (December 2003): 691–709. http://dx.doi.org/10.1142/s021848850300248x.

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Intuitionistic fuzzy sets constitute an extension of fuzzy sets: while fuzzy sets give a degree to which an element belongs to a set, intuitionistic fuzzy sets give both a membership degree and a non-membership degree. The only constraint on those two degrees is that the sum must be smaller than or equal to 1. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In the fuzzy case a t-norm satisfies the residuation principle if and only if it is left-continuous. Deschrijver, Cornelis and Kerre proved that for intuitionistic fuzzy t-norms the equivalence between the residuation principle and intuitionistic fuzzy left-continuity only holds for t-representable t-norms.1 In this paper we construct particular subclasses of intuitionistic fuzzy t-norms that satisfy the residuation principle but that are not t-representable and we show that a continuous intuitionistic fuzzy t-norm [Formula: see text] satisfying the residuation principle is t-representable if and only if [Formula: see text].

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Al-Sharoa, Doaa. "(α1, 2, β1, 2)-complex intuitionistic fuzzy subgroups and its algebraic structure." AIMS Mathematics 8, no. 4 (2023): 8082–116. http://dx.doi.org/10.3934/math.2023409.

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<abstract> <p>A complex intuitionistic fuzzy set is a generalization framework to characterize several applications in decision making, pattern recognition, engineering, and other fields. This set is considered more fitting and coverable to Intuitionistic Fuzzy Sets (IDS) and complex fuzzy sets. In this paper, the abstraction of (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$) complex intuitionistic fuzzy sets and (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroups were introduced regarding to the concept of complex intuitionistic fuzzy sets. Besides, we show that (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroup is a general form of every complex intuitionistic fuzzy subgroup. Also, each of (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy normal subgroups and cosets are defined and studied their relationship in the sense of the commutator of groups and the conjugate classes of group, respectively. Furthermore, some theorems connected the (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroup of the classical quotient group and the set of all (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy cosets were studied and proved. Additionally, we expand the index and Lagrange's theorem to be suitable under (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroups.</p> </abstract>

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Derseh, Beza Lamesgin, Berhanu Assaye Alaba, and Yohannes Gedamu Wondifraw. "t-Intuitionistic Fuzzy Structures on PMS-Ideals of a PMS-Algebra." International Journal of Mathematics and Mathematical Sciences 2022 (September 23, 2022): 1–13. http://dx.doi.org/10.1155/2022/5101293.

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In this article, we apply the concept of a t -intuitionistic fuzzy set to PMS-ideals in PMS-algebras. The notion of the t -intuitionistic fuzzy PMS-ideal of PMS-algebra is introduced, and several related properties are studied. The relationships between a t -intuitionistic fuzzy PMS-ideal and a t -intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, as well as the relationships between an intuitionistic fuzzy PMS-ideal and a t -intuitionistic fuzzy PMS-ideal are discussed in detail. A condition for an intuitionistic fuzzy set to be a t -intuitionistic fuzzy PMS-ideal is provided. The t -intuitionistic fuzzy PMS-ideals of PMS-algebra are described using their α , β level cuts. The homomorphism of a t -intuitionistic fuzzy PMS-ideal of a PMS-algebra is studied, and its homomorphic image and inverse image are explored. The Cartesian product of any two t -intuitionistic fuzzy PMS-ideals is discussed, and some related results are derived. The Cartesian product of the t -intuitionistic fuzzy PMS-ideals is also characterized using its α , β level cuts. The strongest t -intuitionistic fuzzy PMS-relation in a PMS-algebra is defined. Finally, the relationships between the strongest t -intuitionistic fuzzy PMS-relation and t -intuitionistic fuzzy PMS-ideal are studied.

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Pratama, Dian. "IMAGE DAN PRE-IMAGE TRANSLASI PADA GRUP FUZZY INTUITIONISTIK." Jurnal Ilmiah Matematika dan Pendidikan Matematika 8, no. 2 (December 30, 2016): 41. http://dx.doi.org/10.20884/1.jmp.2016.8.2.2886.

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A intuitionistic fuzzy set in is set gives a membership function and a non-membership function (the complement of membership function) for each with the sum worth one. When it’s applied in group’s theory, it will called intuitionistic fuzzy group with conditions membership function is fuzzy subgroup and non-membership function is anti-fuzzy subgroup. In this research, the operator will be given a fuzzy set is called fuzzy translation operator. This operator is a mapping imposed on membership functions (fuzzy subset) to interval [ 0,1]. This research will discuss the properties homomorphism of translation on intuitionistic fuzzy groups. These properties is the structure of the image and pre-image homomorphism of translation on intuitionistic fuzzy group. We obtain that image and pre-image of translation on intuitionistic fuzzy (normal) groups is also intuitionistic fuzzy (normal) groups.

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BUSTINCE, H., and P. BURILLO. "PERTURBATION OF INTUITIONISTIC FUZZY RELATIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 01 (February 2001): 81–103. http://dx.doi.org/10.1142/s0218488501000648.

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In this paper we present a way of perturbing reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relations afterward obtaining the perturbation of another reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relation. To do so we study the main properties of an operator that allows us to go from an intuitionistic fuzzy set to another also intuitionistic fuzzy set, we then apply this operator to intuitionistic fuzzy relations with different properties and we study the conditions there must be for the new intuitionistic fuzzy relation to maintain the original properties.

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Mostafavi, Marzieh. "Z_2-graded intuitionistic L-fuzzy q-deformed quantum subspaces of A_q." Notes on Intuitionistic Fuzzy Sets 28, no. 2 (June 9, 2022): 93–112. http://dx.doi.org/10.7546/nifs.2022.28.2.93-112.

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In this paper, assuming that ⟨L, ≤〉 is a lattice set with a few specific conditions, intuitionistic L-fuzzy subalgebras, intuitionistic L-fuzzy subcoalgebras and intuitionistic L-fuzzy left (right) coideals are defined and the properties of intuitionistic L-fuzzy subcoalgebras under homomorphisms of coalgebras are investigated. Duality of intuitionistic L-fuzzy subalgebras and duality of intuitionistic L-fuzzy subcoalgebras are also discussed. Intuitionistic L-fuzzy subbialgebras as well as intuitionistic L-fuzzy Hoph subalgebras are studied. Intuitionistic L-fuzzy quantum subsets of k_q[x, y] are established and also Z2-graded intuitionistic L-fuzzy q-deformed quantum subspaces of A_q are introduced.

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Ebrahimnejad, Ali, Amal Kumar Adak, and Ezzatallah Baloui Jamkhaneh. "Eigenvalue of Intuitionistic Fuzzy Matrices Over Distributive Lattice." International Journal of Fuzzy System Applications 8, no. 1 (January 2019): 1–18. http://dx.doi.org/10.4018/ijfsa.2019010101.

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In this article, the concepts of intuitionistic fuzzy complete and complete distributive lattice are introduced and the relative pseudocomplement relation of intuitionistic fuzzy sets is defined. The concepts of intuitionistic fuzzy eigenvalue and eigenvector of an intuitionistic fuzzy matrixes are presented and proved that the set of intuitionistic fuzzy eigenvectors of a given intuitionistic fuzzy eigenvalue form an intuitionistic fuzzy subspace. Also, the authors obtain an intuitionistic fuzzy maximum matrix of a given intuitionistic fuzzy eigenvalue and eigenvector and give some properties of an intuitionistic fuzzy maximum matrix. Finally, the invariant of an intuitionistic fuzzy matrix over a distributive lattice is given with some properties.

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Sen, Dilip Kumar, Saurav Datta, and S. S. Mahapatra. "Sustainable supplier selection in intuitionistic fuzzy environment: a decision-making perspective." Benchmarking: An International Journal 25, no. 2 (March 5, 2018): 545–74. http://dx.doi.org/10.1108/bij-11-2016-0172.

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Purpose The purpose of this paper is to attempt supplier selection considering economic, environmental and social sustainability issues. Design/methodology/approach Subjective human judgment bears some kind of vagueness and ambiguity; fuzzy set theory has immense potential to overcome this. Owing to the advantage of intuitionistic fuzzy numbers set over classical fuzzy numbers set; three decision-making approaches have been applied here in intuitionistic fuzzy setting (namely, intuitionistic-TOPSIS, intuitionistic-MOORA and intuitionistic-GRA) to facilitate supplier selection in sustainable supply chain. Findings The stated objective of this research “to verify application potential of different decision support systems (in intuitionistic fuzzy setting) in the context of sustainable supplier selection” has been carried out successfully. A case empirical research has been conducted by applying three different decision-making approaches: intuitionistic fuzzy-TOPSIS, intuitionistic fuzzy-MOORA and intuitionistic fuzzy-GRA to an empirical data set of sustainable supplier selection problem. The ranking orders thus obtained through exploration of aforesaid three approaches have been explored and compared. Originality/value As compared to generalized fuzzy numbers, intuitionistic fuzzy numbers exhibit a membership degree, a non-membership degree and the extent of hesitation; a better way to capture inconsistency, incompleteness and imprecision of human judgment. Application potential of aforesaid three decision support approaches has been demonstrated in this reporting for a case sustainable supplier selection.

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Lee, Jeong-Gon, Mohammad Fozouni, Kul Hur, and Young Bae Jun. "A p-Ideal in BCI-Algebras Based on Multipolar Intuitionistic Fuzzy Sets." Mathematics 8, no. 6 (June 17, 2020): 993. http://dx.doi.org/10.3390/math8060993.

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In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar intuitionistic fuzzy p-ideal is found to be k-polar intuitionistic fuzzy ideal, and an example to show that the converse is not true is provided. The notions of p-ideals and k-polar ( ∈ , ∈ ) -fuzzy p-ideal in BCI-algebras are used to study the characterization of k-polar intuitionistic p-ideal. The concept of normal k-polar intuitionistic fuzzy p-ideal is introduced, and its characterization is discussed. The process of eliciting normal k-polar intuitionistic fuzzy p-ideal using k-polar intuitionistic fuzzy p-ideal is provided.

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Derseh, Beza Lamesgin, Yohannes Gedamu Wondifraw, and Berhanu Assaye Alaba. "On t-Intuitionistic Fuzzy PMS-Subalgebras of a PMS Algebra." International Journal of Fuzzy System Applications 12, no. 1 (February 10, 2023): 1–22. http://dx.doi.org/10.4018/ijfsa.317103.

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In this paper, the authors extend the concept of a t-intuitionistic fuzzy set to PMS-subalgebras of PMS-algebras. The authors define the t-intuitionistic fuzzy PMS-subalgebra of a PMS-algebra and show that any intuitionistic fuzzy PMS-subalgebra of a PMS-algebra is a t-intuitionistic fuzzy PMS-subalgebra. The authors provide the condition for an intuitionistic fuzzy set in a PMS-algebra to be a t-intuitionistic fuzzy PMS-subalgebra. The authors use their (α,β) level cuts to characterize the t-intuitionistic fuzzy PMS-subalgebras of PMS-algebra. The authors investigate whether the homomorphic images and inverse images of t-intuitionistic fuzzy PMS-subalgebras are also t-intuitionistic fuzzy PMS-subalgebras. Furthermore, the authors show that the homomorphic images and inverse images of the nonempty (α,β) level cuts of the t-intuitionistic fuzzy PMS-subalgebras of a PMS-algebra are again PMS-subalgebras of a PMS-algebra. Finally, the authors show that the Cartesian product of the t-intuitionistic fuzzy PMS-subalgebras of a PMS-algebra is itself a t-intuitionistic fuzzy PMS-subalgebra and characterize it in terms of its (α,β) level cuts.

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Van Dinh, Nguyen, and Nguyen Xuan Thao. "Some Measures of Picture Fuzzy Sets and Their Application." Journal of Science and Technology: Issue on Information and Communications Technology 3, no. 2 (December 31, 2017): 35. http://dx.doi.org/10.31130/jst.2017.49.

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To measure the difference of two fuzzy sets (FSs) / intuitionistic sets (IFSs), we can use the distance measure and dissimilarity measure between fuzzy sets/intuitionistic fuzzy set. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set (PFS) is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets, and also provide the formulas for determining these values. We also present an application of dissimilarity measures in the sample recognition problems, can also be considered a decision-making problem.

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He, Xiaorong, and Yingyu Wu. "Global Research Trends of Intuitionistic Fuzzy Set: A Bibliometric Analysis." Journal of Intelligent Systems 28, no. 4 (September 25, 2019): 621–31. http://dx.doi.org/10.1515/jisys-2017-0240.

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Abstract Despite the fast growth of intuitionistic fuzzy publications, only a small part of these groundbreaking researches have significantly impacted the field. The main purpose of this paper was to identify and investigate the 100 most cited publications in the intuitionistic fuzzy field. Topic search based on the keyword “intuitionistic fuzzy” in the Science Citation Index and Social Sciences Citation Index databases was conducted to identify the 100 most cited articles. Bibliometric analysis methods were employed to describe these articles from different angles, such as the citation amount and rate, distribution among journals, institutions and countries/regions, author frequency, and citation distribution over time. This paper provides an insight on the characteristics of the highly cited intuitionistic fuzzy publications. The achievements of this study may provide useful information for researchers in the fields related to intuitionistic fuzzy.

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Sayed, Osama Rashed, Nabil Hasan Sayed, and Gui-Xiu Chen. "Suitable interval-valued intuitionistic fuzzy topological spaces." Journal of Intelligent & Fuzzy Systems 41, no. 1 (August 11, 2021): 879–89. http://dx.doi.org/10.3233/jifs-202757.

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In the present paper, a characterization of the intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy sets and their set-operations are given. By making use of these characterizations, the relationships between the interval-valued intuitionistic fuzzy topology and four fuzzy topologies associated to it are studied. For this reason, some subclasses of the family of interval-valued intuitionistic fuzzy topologies on a set which we call pre-suitable and suitable are introduced. Furthermore, the concepts of homeomorphism functions and compactness in the framework of interval-valued intuitionistic fuzzy topological spaces are introduced and studied.

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Naidu, J. Vadivel, and K. Bharathivelan. "NEW OPERATIONS ON FUZZY ENVIRONMENT." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 01 (January 13, 2023): 3132–37. http://dx.doi.org/10.47191/ijmcr/v11i1.04.

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In this paper we introduce the operations and on interval valued intuitionistic fuzzy soft set and establish some properties of these operators. We also develop a decision making method based on information measure of interval valued intuitionistic fuzzy soft set.

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Kurfia, Mustika Ana, Noor Hidayat, and Corina Karim. "η-Intuitionistic Fuzzy Soft Groups." CAUCHY: Jurnal Matematika Murni dan Aplikasi 7, no. 3 (October 11, 2022): 354–61. http://dx.doi.org/10.18860/ca.v7i3.14555.

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In this research, we present the idea of the intuitionistic fuzzy soft group defined on the intuitionistic fuzzy soft set. The main purpose of this research is to create a new concept, which is an intuitionistic fuzzy group. To achieve this, we combine the concept of intuitionistic fuzzy group and intuitionistic fuzzy soft group. As the main result, we prove the correlation between the intuitionistic fuzzy soft group and intuitionistic fuzzy soft group along with some properties of intuitionistic fuzzy soft groups. Also, we prove some properties of a subgroup of an intuitionistic fuzzy soft group. An intuitionistic fuzzy soft homomorphism is also proved.

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Khan, Muhammad Jabir, Poom Kumam, Peide Liu, Kumam, and Ashraf. "A Novel Approach to Generalized Intuitionistic Fuzzy Soft Sets and Its Application in Decision Support System." Mathematics 7, no. 8 (August 13, 2019): 742. http://dx.doi.org/10.3390/math7080742.

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The basic idea underneath the generalized intuitionistic fuzzy soft set is very constructive in decision making, since it considers how to exploit an extra intuitionistic fuzzy input from the director to make up for any distortion in the information provided by the evaluation experts, which is redefined and clarified by F. Feng. In this paper, we introduced a method to solve decision making problems using an adjustable weighted soft discernibility matrix in a generalized intuitionistic fuzzy soft set. We define the threshold functions like mid-threshold, top-bottom-threshold, bottom-bottom-threshold, top-top-threshold, med-threshold function and their level soft sets of the generalized intuitionistic fuzzy soft set. After, we proposed two algorithms based on threshold functions, a weighted soft discernibility matrix and a generalized intuitionistic fuzzy soft set and also to show the supremacy of the given methods we illustrate a descriptive example using a weighted soft discernibility matrix in the generalized intuitionistic fuzzy soft set. Results indicate that the proposed method is more effective and generalized over all existing methods of the fuzzy soft set.

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Buvaneswari, R., and K. Umamaheswari. "Bondage and non-bondage sets in regular intuitionistic fuzzy graphs." Notes on Intuitionistic Fuzzy Sets 29, no. 3 (November 2023): 318–24. http://dx.doi.org/10.7546/nifs.2023.29.3.318-324.

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The concept of strong edges in domination set and its properties are discussed. The increasing or reducing domination numbers using cardinality are also studied. Bondage $(\alpha(G))$ and non-bondage $(\alpha_K(G))$ sets are defined in regular intuitionistic fuzzy graph. The properties of bondage and non-bondage number of intuitionistic fuzzy graph analyzed. A minimum $2$-bondage set $X$ of an intuitionistic fuzzy graph (IFG) $G$ is a bondage set of regular intuitionistic fuzzy graph in $G$.

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Zhao, Feng, Hao Hao, and Hanqiang Liu. "Robust intuitionistic fuzzy clustering with bias field estimation for noisy image segmentation." Intelligent Data Analysis 26, no. 5 (September 5, 2022): 1403–26. http://dx.doi.org/10.3233/ida-216058.

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The concept of intuitionistic fuzzy set has been found to be highly useful to handle vagueness in data. Based on intuitionistic fuzzy set theory, intuitionistic fuzzy clustering algorithms are proposed and play an important role in image segmentation. However, due to the influence of initialization and the presence of noise in the image, intuitionistic fuzzy clustering algorithm cannot acquire the satisfying performance when applied to segment images corrupted by noise. In order to solve above problems, a robust intuitionistic fuzzy clustering with bias field estimation (RIFCB) is proposed for noisy image segmentation in this paper. Firstly, a noise robust intuitionistic fuzzy set is constructed to represent the image by using the neighboring information of pixels. Then, initial cluster centers in RIFCB are adaptively determined by utilizing the frequency statistics of gray level in the image. In addition, in order to offset the information loss of the image when constructing the intuitionistic fuzzy set of the image, a new objective function incorporating a bias field is designed in RIFCB. Based on the new initialization strategy, the intuitionistic fuzzy set representation, and the incorporation of bias field, the proposed method preserves the image details and is insensitive to noise. Experimental results on some Berkeley images show that the proposed method achieves satisfactory segmentation results on images corrupted by different kinds of noise in contrast to conventional fuzzy clustering algorithms.

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Atanassov, Krassimir T. "Circular intuitionistic fuzzy sets." Journal of Intelligent & Fuzzy Systems 39, no. 5 (November 19, 2020): 5981–86. http://dx.doi.org/10.3233/jifs-189072.

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Hayat, Khizar, Muhammad Ali, Bing-Yuan Cao, Faruk Karaaslan, and Xiao-Peng Yang. "Another View of Aggregation Operators on Group-Based Generalized Intuitionistic Fuzzy Soft Sets: Multi-Attribute Decision Making Methods." Symmetry 10, no. 12 (December 14, 2018): 753. http://dx.doi.org/10.3390/sym10120753.

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In this paper, the existing definition of the group-based generalized intuitionistic fuzzy soft set is clarified and redefined by merging intuitionistic fuzzy soft set over the set of alternatives and a group of intuitionistic fuzzy sets on parameters. In this prospect, two new subsets of the group-based generalized intuitionistic fuzzy soft set are proposed and several operations are contemplated. The two new aggregation operators called generalized group-based weighted averaging and generalized group-based weighted geometric operator are introduced. The related properties of proposed operators are discussed. The recent research is emerging on multi-attribute decision making methods based on soft sets, intuitionistic fuzzy soft sets, and generalized intuitionistic fuzzy soft sets. An algorithm is structured and two case studies of multi-attribute decision makings are considered using proposed operators. Further, we provide the comparison and advantages of the proposed method, which give superiorities over recent major existing methods.

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Liu, Yan, Zhaojun Yang, Jialong He, Lijuan Yu, and Yuan Zhong. "Some Intuitionistic Cubic Fuzzy Muirhead Mean Operators with Their Application to Multicriteria Decision Making." International Journal of Intelligent Systems 2023 (May 9, 2023): 1–21. http://dx.doi.org/10.1155/2023/9891355.

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Intuitionistic cubic fuzzy sets (ICFSs), as a hybrid fuzzy set consisting of interval-valued fuzzy sets and intuitionistic fuzzy sets, can deal with the uncertainty of information in decision problems more comprehensively. Muirhead mean (MM) operators can deal with the correlation between attributes in decision problems more realistically. However, there has been no research on MM operators under intuitionistic cubic fuzzy sets so far. In this study, some new operators are proposed under the intuitionistic cubic fuzzy set. It contains the intuitionistic cubic fuzzy MM (ICFMM) operator, intuitionistic cubic fuzzy weighted MM (ICFWMM) operator, intuitionistic cubic fuzzy dual MM (ICFDMM) operator, and intuitionistic cubic fuzzy dual weighted MM (ICFDWMM) operator. Their proof procedure, properties, and proof of properties are given. Two MCDM decision models based on ICFWMM and ICFDWMM operators are proposed, and the proposed decision models are applied to supplier selection, and the better reliability and accuracy of the proposed decision methods in this study are verified through comparative analysis with existing methods.

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WEI, G. W. "SOME GEOMETRIC AGGREGATION FUNCTIONS AND THEIR APPLICATION TO DYNAMIC MULTIPLE ATTRIBUTE DECISION MAKING IN THE INTUITIONISTIC FUZZY SETTING." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 02 (April 2009): 179–96. http://dx.doi.org/10.1142/s0218488509005802.

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The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy sets", Information and Control8 (1965) 338–356] to deal with fuzziness and uncertainty. In this paper, the dynamic multiple attribute decision making (DMADM) problems with intuitionistic fuzzy information are investigated. The notions of intuitionistic fuzzy variable and uncertain intuitionistic fuzzy variable are defined, and two new aggregation operators called dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator and uncertain dynamic intuitionistic fuzzy weighted geometric (UDIFWG) operator are proposed. Moreover, a procedure based on the DIFWG and IFWG operators is developed to solve the dynamic intuitionistic fuzzy multiple attribute decision making problems where all the decision information about attribute values takes the form of intuitionistic fuzzy numbers collected at different periods, and a procedure based on the UDIFWG and IIWG operators is developed for uncertain dynamic intuitionistic fuzzy multiple attribute decision making problems under interval uncertainty in which all the decision information about attribute values takes the form of interval-valued intuitionistic fuzzy numbers collected at different periods. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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Li, Ya Ya. "Entropy and Distance Measure of Intuitionistic Fuzzy Soft Sets." Advanced Materials Research 1070-1072 (December 2014): 2056–61. http://dx.doi.org/10.4028/www.scientific.net/amr.1070-1072.2056.

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Molodtsov initiated the concept of soft sets, which can be used as general mathematical tool for dealing with untertainty. An intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. In this paper, we introduce a formula to calculate the entropy of intuitionistic fuzzy soft sets. We also give numerical example to illustrate the application of the entropy. Furthermore, we study the relationship of the entropy and the distance measure of intuitionistic soft fuzzy sets.

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Wu, Mei Hong. "An Intuitionistic Fuzzy Set-Based Model for Intelligent Traditional Chinese Medicine Diagnosis." Key Engineering Materials 480-481 (June 2011): 944–49. http://dx.doi.org/10.4028/www.scientific.net/kem.480-481.944.

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According to the characteristics of Traditional Chinese Medicine, this paper introduces an intuitionistic fuzzy set-based method to realize the intelligent diagnostic decision making. We firstly concentrate on diagnosis of diseases and differentiation of syndromes by modeling medical diagnosis rules via intuitionistic fuzzy relations as well as how to obtain intuitionistic medical knowledge on the basis of intuitionistic fuzzy sets. Subsequently we develop a new approach to point out the final proper diagnosis by largest degree of intuitionistic cognitive fuzzy match between symptoms characteristic for a patient and symptoms indicate the considered illnesses in decision-making process. The new approach allows reaching the intelligent diagnoses reasonably and easily, which benefit TCM syndrome differentiation for the whole diagnosis.

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Chaudhary, Priti, and Tanuj Kumar. "Intuitionistic fuzzy inventory model with quadratic demand rate, time-dependent holding cost and shortages." Journal of Physics: Conference Series 2223, no. 1 (March 1, 2022): 012003. http://dx.doi.org/10.1088/1742-6596/2223/1/012003.

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Abstract In the present work, we studied an inventory model under quadratic demand rate, linearly time-dependent holding cost, constant deterioration rate and allowed shortages. Intuitionistic fuzzy set (IFS) theory is an efficient tool to reduce the uncertainty that occurs due to hesitation, so we studied the considered model under intuitionistic fuzzy set theory. Further, the model is transformed into an intuitionistic fuzzy inventory model by taking the decision variables as triangular intuitionistic fuzzy numbers. To optimize the best inventory policy under the intuitionistic fuzzy environment, the alpha-cut approach is used for the defuzzification of all intuitionistic fuzzy decision variables. Regarding the proposed model, a numerical example is presented to validate the methodology.

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Chuanchao, Zhang. "Generalized dynamic attribute reduction based on similarity relation of intuitionistic fuzzy rough set." Journal of Intelligent & Fuzzy Systems 39, no. 5 (November 19, 2020): 7107–22. http://dx.doi.org/10.3233/jifs-200347.

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In view of the characteristics with big data, high feature dimension, and dynamic for a large-scale intuitionistic fuzzy information systems, this paper integrates intuitionistic fuzzy rough sets and generalized dynamic sampling theory, proposes a generalized attribute reduction algorithm based on similarity relation of intuitionistic fuzzy rough sets and dynamic reduction. It uses dynamic reduction sampling theory to divide a big data set into small data sets and relative positive domain cardinality instead of dependency degree as decision-making condition, and obtains reduction attributes of big intuitionistic fuzzy decision information systems, and achieves the goal of extracting key features and fault diagnosis. The innovation of this paper is that it integrates generalized dynamic reduction and intuitionistic fuzzy rough set, and solves the problem of big data set which cannot be solved by intuitionistic fuzzy rough set. Taking an actual data as an example, the scientificity, rationality and effectiveness of the algorithm are verified from the aspects of stability, diagnostic accuracy, optimization ability and time complexity. Compared with similar algorithms, the advantages of the proposed algorithm for big data processing are confirmed.

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Riaz, Muhammad, Khadija Akmal, Yahya Almalki, and Daud Ahmad. "Cubic Intuitionistic Fuzzy Topology with Application to Uncertain Supply Chain Management." Mathematical Problems in Engineering 2022 (November 16, 2022): 1–22. http://dx.doi.org/10.1155/2022/9631579.

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The concept of the cubic intuitionistic fuzzy set is an effective hybrid model for modeling uncertainties with an intuitionistic fuzzy set and an interval-valued intuitionistic fuzzy set, simultaneously. The primary objective of this study is to develop a topological structure on cubic intuitionistic fuzzy sets with P-order and R-order as well as to define some fundamental characteristics and significant results with illustrations. Taking advantage of topological data analysis with cubic intuitionistic information, novel multicriteria group decision-making methods are developed for an uncertain supply chain management. Algorithms 1 and 2 are proposed for extensions of the weighted product model and the choice value method towards a cubic intuitionistic fuzzy environment, respectively. A comparative analysis is also given to discuss the validity and advantages of the proposed techniques.

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Yusoff, B., A. Kilicman, D. Pratama, and R. Hasni. "Circular q-Rung Orthopair Fuzzy Set and Its Algebraic Properties." Malaysian Journal of Mathematical Sciences 17, no. 3 (September 13, 2023): 363–78. http://dx.doi.org/10.47836/mjms.17.3.08.

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Circular intuitionistic fuzzy sets (CIFS) are a recent extension of intuitionistic fuzzy sets (IFS) that can handle imprecise membership values effectively. However, its representation is limited to the space under the intuitionistic fuzzy interpretation triangle (IFIT). To address this, a new generalization of CIFS called circular q-rung orthopair fuzzy sets (Cq-ROFS) is proposed, extending the IFIT to cover a larger space of imprecision. Several relations and operations, including algebraic operations for Cq-ROFS are proposed. In addition, modal operators and their properties are then investigated.

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Journal articles on the topic 'INTUITIONISTIC FUZZY SET'

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