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Journal articles on the topic 'Vague Set'

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Author: Grafiati

Published: 6 September 2023

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1

Wang, Chao, Qi Hai Zhou, and Yan Li. "Transforming Model from Vague Set to Fuzzy Set Based on the DWCO Operator." Applied Mechanics and Materials 66-68 (July 2011): 2317–22. http://dx.doi.org/10.4028/www.scientific.net/amm.66-68.2317.

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In the research on transforming vague set to fuzzy set, it is the key question to carry on the judgment to the vague-degree's tendentiousness. Vague set's vague-degree expresses one kind of indefinite degree, therefore the question transforming vague set to fuzzy set may regard as the venture decision under the definite condition. When the policy-maker carries on the venture decision, the policy-maker's risk preferences decided by the subjective and objective condition is a very essential policy-making parameter. In this paper, introduce the risk-income balancing weight into the transforming model, thus enable reflect the policy-maker's risk preferences well in the transforming result. In addition, decompose the value of fuzzy set's membership degree into the following two parts: the value of vague set's real membership degree, the weighting sum of the risk value and the tendency value.

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2

Yan, Ruixia, Jinliang Liu, and Bingxue Yao. "The connections of vague set and rough set." Kybernetes 41, no. 9 (October 12, 2012): 1318–22. http://dx.doi.org/10.1108/03684921211275351.

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3

Wang, Chang. "Vague parameterized vague soft set theory and its decision making." Journal of Intelligent & Fuzzy Systems 33, no. 4 (September 22, 2017): 2341–50. http://dx.doi.org/10.3233/jifs-17423.

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4

Zhang, Kun, Mei Yi Chen, and Zhuang Li. "Similarity Measure of Vague Set Based on Uncertainty." Applied Mechanics and Materials 602-605 (August 2014): 3850–53. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.3850.

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According to the experimental analysis, this work found out the defect of the formula for similarity measure between current Vague values, and redefined the similarity measure between Vague values. Therefore, a new formula subject to the new definition was put forward according to data mining and uncertainty of Vague value.

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5

Alhazaymeh, Khaleed, and Nasruddin Hassan. "Vague soft set relations and functions." Journal of Intelligent & Fuzzy Systems 28, no. 3 (2015): 1205–12. http://dx.doi.org/10.3233/ifs-141403.

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6

Al-Quran, Ashraf, and Nasruddin Hassan. "Neutrosophic vague soft expert set theory." Journal of Intelligent & Fuzzy Systems 30, no. 6 (April 30, 2016): 3691–702. http://dx.doi.org/10.3233/ifs-162118.

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7

Alhazaymeh, Khaleed, and Nasruddin Hassan. "Generalized interval-valued vague soft set." Applied Mathematical Sciences 7 (2013): 6983–88. http://dx.doi.org/10.12988/ams.2013.310575.

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8

Alhazaymeh, Khaleed, and Nasruddin Hassan. "Possibility interval-valued vague soft set." Applied Mathematical Sciences 7 (2013): 6989–94. http://dx.doi.org/10.12988/ams.2013.310576.

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9

Singh, Prem Kumar. "Complex vague set based concept lattice." Chaos, Solitons & Fractals 96 (March 2017): 145–53. http://dx.doi.org/10.1016/j.chaos.2017.01.019.

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10

Ramya Swetha, R., T. Anitha, and V. Amarendra Babu. "Vague Separation." International Journal of Engineering & Technology 7, no. 3.34 (September 1, 2018): 654. http://dx.doi.org/10.14419/ijet.v7i3.34.19407.

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In this paper we are introducing VT1 space, vague haussdorff space (VT2) and then we derive every vague subspace of VT1 space is VT1 and also for VT2. And also we derive the Cartesian product of two vague closed sets is also vague closed set in the vague product topological space X x Y .Finally we define Vague limit point, Vague isolated point, Vague adherent point, Vague perfect, Vague derived set, vague exterior and also derive some theorems on this .

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11

Zhang, Hai Dong, and Yan Ping He. "Aximatics for Rough Set Model Based on Vague Relations." Advanced Materials Research 282-283 (July 2011): 283–86. http://dx.doi.org/10.4028/www.scientific.net/amr.282-283.283.

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This paper presents a general framework for the study of rough set approximation operators in vague environment in which both constructive and axiomatic approaches are used. In constructive approach, by means of a vague relation defined by us, a new pair of vague rough approximation operators is ﬁrst deﬁned. Also some properties about the approximation operators are then discussed. In axiomatic approach, an operator-oriented characterization of vague rough sets is proposed, that is, vague rough approximation operators are defined by axioms.

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12

Wang, Jian Hong, and Lei Liu. "Modeling Fuzzy Decision Fusion Based on Vague Set." Applied Mechanics and Materials 197 (September 2012): 7–12. http://dx.doi.org/10.4028/www.scientific.net/amm.197.7.

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As a further generalization of fuzzy set theory, the vague set theory can overcome the shortcomings of fuzzy set by describing the membership from two sides of both TRUE and FALSE, rather than only by a single membership value. Since vague sets can provide more information than fuzzy sets, it is superior in mathematical analysis of system with uncertainty. Thus, vague set is more powerful in the describing and processing of uncertain, inaccurate, even conflicting information. In this paper, a new method vague set-based is proposed to deal with fuzzy decision fusion problem. Compared with traditional fuzzy decision fusion method- such as fuzzy comprehensive evaluation, the new method is more efficient and powerful to fulfill decision fusion with uncertain and inaccurate information. Generally, the new method is the same with group decision fusion and soft fusion.

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13

Chinnadurai, V., G. Thirumurugan, and A. Arulselvam. "CUBIC VAGUE SOFT SET AND ITS APPLICATION." Advances in Mathematics: Scientific Journal 9, no. 4 (July 3, 2020): 1569–75. http://dx.doi.org/10.37418/amsj.9.4.11.

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14

Vervaat, Wim. "Narrow and vague convergence of set functions." Statistics & Probability Letters 6, no. 5 (April 1988): 295–98. http://dx.doi.org/10.1016/0167-7152(88)90002-8.

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15

Sakr, Hanan H., Abdisalam Hassan Muse, Mohamed S. Mohamed, and Saieed F. Ateya. "Applications on Bipolar Vague Soft Sets." Journal of Mathematics 2023 (March 31, 2023): 1–25. http://dx.doi.org/10.1155/2023/5467353.

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The purpose of this research is to interpolate bipolarity into the definition of the vague soft set. This gives a new more applicable, flexible, and generalized extension of the soft set, the fuzzy soft set, or even the vague soft set, which is the bipolar vague soft set. In addition, types of bipolar vague soft sets, as well as some new related concepts and operations are established with examples. Moreover, properties of bipolar vague soft sets including absorption, commutative, associative, distributive, and De Morgan’s laws are discussed in detail. Furthermore, a bipolar vague soft set-designed decision-making algorithm is provided generalizing Roy and Maji method. This allows making more effective decisions to choose the optimal alternative. Finally, an applied problem is introduced with a comparative analysis to illustrate how the proposed algorithm works more successfully than the previous models for problems that contain uncertain ambiguous data.

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16

Zhang, Qinghua, Jin Wang, Guoyin Wang, and Hong Yu. "The approximation set of a vague set in rough approximation space." Information Sciences 300 (April 2015): 1–19. http://dx.doi.org/10.1016/j.ins.2014.12.023.

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17

Bourahla, Mustapha. "Using Rough Set Theory for Reasoning on Vague Ontologies." International Journal of Intelligent Systems and Applications 14, no. 4 (August 8, 2022): 21–36. http://dx.doi.org/10.5815/ijisa.2022.04.03.

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Web ontologies can contain vague concepts, which means the knowledge about them is imprecise and then query answering will not possible due to the open world assumption. A concept description can be very exact (crisp concept) or exact (fuzzy concept) if its knowledge is complete, otherwise it is inexact (vague concept) if its knowledge is incomplete. In this paper, we propose a method based on the rough set theory for reasoning on vague ontologies. With this method, the detection of vague concepts will insert into the original ontology new rough vague concepts where their description is defined on approximation spaces to be used by extended Tableau algorithm for automatic reasoning. A prototype of Tableau's extended algorithm is developed and tested on examples where encouraging results are given by this method to demonstrate that unlike other methods, it is possible to answer queries even in the presence of incomplete information.

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18

Alhazaymeh, Khaleed, Yousef Al-Qudah, Nasruddin Hassan, and Abdul Muhaimin Nasruddin. "Cubic Vague Set and its Application in Decision Making." Entropy 22, no. 9 (August 31, 2020): 963. http://dx.doi.org/10.3390/e22090963.

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From the hybrid nature of cubic sets, we develop a new generalized hybrid structure of cubic sets known as cubic vague sets (CVSs). We also define the concept of internal cubic vague sets (ICVSs) and external cubic vague sets (ECVSs) with examples and discuss their interesting properties, including ICVSs and ECVSs under both P and R-Order. Moreover, we prove that the R and R-intersection of ICVSs (or ECVSs) need not be an ICVS (or ECVS). We also derive the different conditions for P-union (P-intersection, R and R-intersection) operations of both ICVSs (ECVSs) to become an ICVS (ECVS). Finally, we introduce a decision-making based on the proposed similarity measure of the CVSs domain and a numerical example is given to elucidate that the proposed similarity measure of CVSs is an important concept for measuring entropy in the information/data. It will be shown that the cubic vague set has the novelty to accurately represent and model two-dimensional information for real-life phenomena that are periodic in nature.

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19

Qin, Xiaoyan, Yi Liu, and Yang Xu. "Vague Congruences and Quotient Lattice Implication Algebras." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/197403.

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The aim of this paper is to further develop the congruence theory on lattice implication algebras. Firstly, we introduce the notions of vague similarity relations based on vague relations and vague congruence relations. Secondly, the equivalent characterizations of vague congruence relations are investigated. Thirdly, the relation between the set of vague filters and the set of vague congruences is studied. Finally, we construct a new lattice implication algebra induced by a vague congruence, and the homomorphism theorem is given.

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20

Shijian, Gao, and Yu Jiankun. "Mining Spatial Co-location Patterns from Vague Set." Journal of Physics: Conference Series 1437 (January 2020): 012009. http://dx.doi.org/10.1088/1742-6596/1437/1/012009.

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21

Yatabe, Shunsuke, and Hiroyuki Inaoka. "On Evans's Vague Object from Set Theoretic Viewpoint." Journal of Philosophical Logic 35, no. 4 (March 21, 2006): 423–34. http://dx.doi.org/10.1007/s10992-005-9022-7.

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22

Wang, Hai Feng, Hong E. Ren, Kun Zhang, and Hong Xu Wang. "Mining Methods Based on Vague Optimization Evaluation." Advanced Materials Research 659 (January 2013): 128–33. http://dx.doi.org/10.4028/www.scientific.net/amr.659.128.

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Method based on vague optimization evaluation is vague pattern recognition. There are six detailed steps of application. The first, Set up Techno-economic indicator system. Secondly set up preparative optimization scheme sets. Thirdly set up optimal scheme in theory. It is made up of each Techno-economic indicator optimal data. Fourthly transform techno-economic input data into vague data. The fifth, Calculating similarly measures. Similarity measures will be evaluated between preparative optimization scheme vague sets and optimal scheme in theory. The last is vague optimization evaluation. The weight of each preparative optimization scheme is given. The data of weighted similarity measures by the weight factors are obtained. And applying them we obtain the good and bad sort of vague optimization scheme. The new similarity measures formula between vague sets is given. The formula is indispensable in the method of vague optimization evaluation. Application examples show that the Vague optimization evaluation method to the conclusion is reliable.

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23

Mishra, Jaydev, and Sharmistha Ghosh. "Uncertain Query Processing using Vague Set or Fuzzy Set: Which One Is Better?" International Journal of Computers Communications & Control 9, no. 6 (October 11, 2014): 730. http://dx.doi.org/10.15837/ijccc.2014.6.500.

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24

Zhang, Qinghua, Yu Xiao, and Guoyin Wang. "A new method for measuring fuzziness of vague set (or intuitionistic fuzzy set)." Journal of Intelligent & Fuzzy Systems 25, no. 2 (2013): 505–15. http://dx.doi.org/10.3233/ifs-2012-0571.

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25

Liu, Peide. "MULTI‐ATTRIBUTE DECISION‐MAKING METHOD RESEARCH BASED ON INTERVAL VAGUE SET AND TOPSIS METHOD." Technological and Economic Development of Economy 15, no. 3 (September 30, 2009): 453–63. http://dx.doi.org/10.3846/1392-8619.2009.15.453-463.

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This paper proposed a method to resolve the multi‐attribute decision‐making problem using TOPSIS method based on attribute weights and attribute values are all interval vague value. Firstly, based on the operation rules of the interval Vague value, the interval Vague attribute value is made by weighted operation, and the ideal and negative ideal solutions are calculated based on the score function. Then the distance of interval Vague value is defined, as well as the distance between each project and the ideal, and negative ideal solutions. The relative adjacent degree is calculated by TOPSIS method, then the order of the projects is confirmed according to the relative adjacent degree. Finally, a case is used to show the process of the method this paper proposed and the validity of this method is proved. Santrauka Straipsnyje siūlomas daugiakriterinės sprendimo priėmimo problemos sprendimas TOPSIS metodu, kai kriterijų reikšmingumai ir reikšmės yra intervaliniai dydžiai. Iš pradžių, naudojantis procedūromis, nustatomos svertinės intervalinių dydžių reikšmės, paskui apskaičiuojami idealiai teigiamas ir idealiai negiamas sprendiniai. Toliau nustatomi intervalų dydžiai, apskaičiuojami atstumai tarp kiekvienos alternatyvos ir idealiai teigiamo ir idealiai neigiamo sprendinių. TOPSIS metodu apskaičiuojami santykiniai atstumai iki minėtų idealių sprendinių ir alternatyvos išrikuojamos į eilę. Galiausiai konkrečiu pavyzdžiu demonstruojamas skaičiavimo procesas ir patvirtinamas siūlomo metodo pagrįstumas.

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26

Feng, Lin, Tianrui Li, Da Ruan, and Shirong Gou. "A vague-rough set approach for uncertain knowledge acquisition." Knowledge-Based Systems 24, no. 6 (August 2011): 837–43. http://dx.doi.org/10.1016/j.knosys.2011.03.005.

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27

Zhang, Qingchuan, Guangping Zeng, Chaoen Xiao, and Yang Yue. "A rule conflict resolution method based on Vague set." Soft Computing 18, no. 3 (July 2, 2013): 549–55. http://dx.doi.org/10.1007/s00500-013-1075-x.

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28

Selvachandran, Ganeshsree, and Abdul Razak Salleh. "RINGS AND IDEALS IN A VAGUE SOFT SET SETTING." Far East Journal of Mathematical Sciences (FJMS) 99, no. 2 (December 31, 2015): 279–300. http://dx.doi.org/10.17654/ms099020279.

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29

Ghorbani, Shokoofeh. "Vague Filters of Residuated Lattices." Journal of Discrete Mathematics 2014 (September 10, 2014): 1–9. http://dx.doi.org/10.1155/2014/120342.

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Notions of vague filters, subpositive implicative vague filters, and Boolean vague filters of a residuated lattice are introduced and some related properties are investigated. The characterizations of (subpositive implicative, Boolean) vague filters is obtained. We prove that the set of all vague filters of a residuated lattice forms a complete lattice and we find its distributive sublattices. The relation among subpositive implicative vague filters and Boolean vague filters are obtained and it is proved that subpositive implicative vague filters are equivalent to Boolean vague filters.

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30

Wang, Lihui, Desheng Sun, Qingya Liu, and Le Yu. "Matching area selection of an underwater terrain navigation database with fuzzy multi-attribute decision making method." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 233, no. 4 (November 21, 2018): 1133–40. http://dx.doi.org/10.1177/1475090218812517.

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Selecting suitable underwater terrain navigation matching areas is a prerequisite for building an underwater terrain navigation database, which is important for vehicles operating underwater. By using information features to evaluate underwater terrain matching areas, vague sets are proposed to evaluate matching performance. Mathematical models of matching area features are built and topographic factor eigenvalues are obtained. With the topographic factor eigenvalues, fuzzy relationships between factor sets and judge sets are calculated. Vague set uses membership functions and non-membership functions to define the influence of topographic factor eigenvalues on matching suitability. Simulation results demonstrate that vague set theory can overcome the deficiency of single value in fuzzy sets and define the effect of geographic characteristics for matching performance. Based on vague set method, selection rules for terrain navigation matching areas in underwater terrain database are put forward.

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31

Wang, Chang, and Yaya Li. "Topological Structure of Vague Soft Sets." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/504021.

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We introduce vague soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of vague soft open sets, vague soft closed sets, vague soft interior, vague soft closure, and vague soft boundary are introduced and their basic properties and relations are investigated. Furthermore, with the help of examples they established that some properties of topological spaces and soft topological spaces do not hold in vague soft topological spaces. Vague soft connectedness and vague soft compactness are also studied.

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32

BHUTANI, KIRAN R., and JOHN N. MORDESON. "SIMILARITY RELATIONS, VAGUE GROUPS, AND FUZZY SUBGROUPS." New Mathematics and Natural Computation 02, no. 03 (November 2006): 195–208. http://dx.doi.org/10.1142/s1793005706000488.

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We define vague groups in terms of similarity relations rather than fuzzy equalities. This yields a bijection between the set of all right-invariant similarity relations on a group and the set of all fuzzy subgroups of the group. Under this bijection, right-invariant and left-invariant similarity relations correspond to normal fuzzy subgroups. We show how this bijection allows for the transfer of results between vague groups and fuzzy subgroups. In particular, certain numerical invariants that characterize fuzzy subgroups of an Abelian group can be used to characterize vague groups.

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33

Xu, Ke Hu, Jin Yu Chen, De Peng Kong, and Pu Fan. "Research on Vague Set of Target Threat Information Fusion Algorithm." Applied Mechanics and Materials 599-601 (August 2014): 1671–78. http://dx.doi.org/10.4028/www.scientific.net/amm.599-601.1671.

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Information fusion technology is one of the most active research areas currently, which is affected by the fact that the computer can only handle quantitative information and the result cannot reflect the actual feature of the target sometimes. This paper makes use of advantages of the vague set in dealing with uncertain information process to establish the target threat sequencing model based on vague set and take both quantitative and qualitative information of target into account. Using the improved scoring function, this paper comes up with the target threat sequence steps based on extreme score function method to provide a better data supporting for the decision-making function of information fusion technology.

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34

Afzal, Farkhanda, Arif Mehmood, Samer Al Ghour, Mudasar Zafar, Hamzah Sakidin, and Saeed Gul. "Characterization of Bipolar Vague Soft S -Open Sets." Journal of Function Spaces 2022 (May 5, 2022): 1–13. http://dx.doi.org/10.1155/2022/5964872.

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This paper concerns the study of the concept of bipolar vague soft s -open set, bipolar vague soft s-interior, bipolar vague soft s-closer, and bipolar vague soft s-exterior in bipolar vague soft topological spaces. By using such concepts, some results are addressed in bipolar vague soft topological spaces. The engagements among these results are also addressed by using bipolar vague soft s -open sets.

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35

Mehmood, Arif, Samer Al Ghour, Saleem Abdullah, Choonkil Park, and Jung Rye Lee. "A new approach to vague soft toplogical structures concerning soft points." Journal of Intelligent & Fuzzy Systems 42, no. 3 (February 2, 2022): 1483–99. http://dx.doi.org/10.3233/jifs-210828.

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This paper concerns the study of the notion of vague soft β-open set and vague soft separation axioms in vague soft topological spaces. By using such notions and that of the vague soft pints, we study the separation axioms βi (with i = 0, 1, 2, 3, 4) in vague soft topological spaces. We give some peculiar examples about them and we prove some relationships between them. The relationship of βi (with i = , 1, 2, 3, 4) spaces with the closer of vague soft β-open set by means of soft points, vague soft countable spaces and their relationship with βi (with i = , 1, 2) spaces by means of soft points are addressed. In continuation, vague soft topological, vague soft inverse topological spaces properties, Bolzano Weirstrass Property(BVP) and its topological characteristics, compact spaces and sequentially compact spaces and their relationship with separation axioms by means soft points are addressed in vague soft topological spaces.

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36

Yousef, Al-Qudah, Khaleed Alhazaymeh, Nasruddin Hassan, Hamza Qoqazeh, Mohammad Almousa, and Mohammad Alaroud. "Transitive Closure of Vague Soft Set Relations and its Operators." INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS 22, no. 1 (March 31, 2022): 59–68. http://dx.doi.org/10.5391/ijfis.2022.22.1.59.

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37

Hong, Dug Hun, and Chang-Hwan Choi. "Multicriteria fuzzy decision-making problems based on vague set theory." Fuzzy Sets and Systems 114, no. 1 (August 2000): 103–13. http://dx.doi.org/10.1016/s0165-0114(98)00271-1.

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38

Beaubouef, Theresa, Frederick E. Petry, and Roy Ladner. "Spatial data methods and vague regions: A rough set approach." Applied Soft Computing 7, no. 1 (January 2007): 425–40. http://dx.doi.org/10.1016/j.asoc.2004.11.003.

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39

P., John Robinson, and Henry Amirtharaj E.C. "A Short Primer on the Correlation Coefficient of Vague Sets." International Journal of Fuzzy System Applications 1, no. 2 (April 2011): 55–69. http://dx.doi.org/10.4018/ijfsa.2011040105.

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Intuitionistic fuzzy sets and vague sets are generalizations of the concept of fuzzy sets. Various researchers have studied the vagueness of data through vague sets, and it was later demonstrated that vague sets are indeed intuitionistic fuzzy sets. Since its entry in the literature, vague set theory has received increased attention. Many real life problems involve information in the form of vague values, due to the increasing complexity of the socio-economic environment and the vagueness of the inherent subjective nature of human thinking. Instead of using point-based membership as in fuzzy sets, interval-based membership is used in a vague set. This paper presents a detailed comparison between vague sets and intuitionistic fuzzy sets, from various perspectives of algebraic properties, graphical representations, and practical applications. Methods of calculating the correlation coefficient of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are already found in the literature. This paper defines the correlation coefficient of vague sets through simple examples.

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40

Zhang, Hai Dong, and Yan Ping He. "Representations of Vague Approximation Operators." Advanced Materials Research 282-283 (July 2011): 287–90. http://dx.doi.org/10.4028/www.scientific.net/amr.282-283.287.

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As a suitable mathematical model to handle partial knowledge in data bases, rough set theory is emerging as a powerful theory and has been found its successive applications in the fields of artificial intelligence such as pattern recognition, machine learning, etc. In the paper, a vague relation is ﬁrst deﬁned, which is the extension of fuzzy relation. Then a new pair of lower and upper generalized rough approximation operators based on the vague relation is ﬁrst proposed by us. Finally, the representations of vague rough approximation operators are presented.

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41

De, Soumitra, and Jaydev Mishra. "A New Approach of Functional Dependency in a Neutrosophic Relational Database Model." Asian Journal of Computer Science and Technology 8, no. 2 (May 5, 2019): 44–48. http://dx.doi.org/10.51983/ajcst-2019.8.2.2142.

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In order to model the imprecise and uncertain information, different classical relational data model have been studied in literature using vague set theory. However, neutrosophic set, as a generalized vague set, has more powerful ability to process fuzzy information than vague set. In this paper, we have proposed a neutrosophic relational database model and have defined a new kind of neutrosophic functional dependency (called  -nfd) based on the -equality of tuples and the similarity measure of neutrosophic sets. Next, we present a set of sound neutrosophic inference rules which are similar to Armstrong’s axioms for the classical case. Finally, partial  -nfdand neutrosophic key have been studied with the new notion of  -nfdand also tested.

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42

Wang, Lihui, Le Yu, Nan Qiao, and Desheng Sun. "Analysis and Simulation of Geomagnetic Map Suitability Based on Vague Set." Journal of Navigation 69, no. 5 (April 18, 2016): 1114–24. http://dx.doi.org/10.1017/s0373463316000199.

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An evaluation method named vague set is proposed to describe the suitability of a geomagnetic map. It is based on the Fuzzy Decision Making (FDM) method, and overcomes the FDM model's shortcomings that favouring and opposing content cannot be taken into account simultaneously. The membership function and non-membership function are used to define the influence of the geomagnetic map parameters on map suitability, including standard deviation, information entropy, roughness and slope variance. The weight of each geomagnetic map parameter is calculated by establishing an optimisation model. Vague set data are divided into four types after classification, and Weighted Score Function Values (WSFVs) of matching areas are obtained by using the Weighted Score Function (WSF) method. Then, WSFV of each matching area are compared to select an optimal area. Simulation results demonstrate that geomagnetic map suitability is positively proportional to the function value, and matching error is negatively proportional to the WSFV of the matching area.

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43

Bi, Aorui, Shuya Huang, and Xinguo Sun. "Risk Assessment of Oil and Gas Pipeline Based on Vague Set-Weighted Set Pair Analysis Method." Mathematics 11, no. 2 (January 9, 2023): 349. http://dx.doi.org/10.3390/math11020349.

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This study focuses on a risk assessment method for oil and gas pipelines. Oil and gas pipelines are usually constructed in a complex geological environment and are potentially dangerous. Risk assessment is a key step for their safety management. Therefore, the present paper establishes a risk indicator system as the risk assessment foundation, and we propose a risk assessment method to obtain a quantitative assessment result for the pipeline based on set pair analysis (SPA) theory. For the weight values of each indicator in the assessment process, this paper presents a calculation method based on vague sets theory. Then, a pipeline in the Yanchang oilfield was taken as a case study to verify the feasibility of the method, and the final assessment result was 2.911, which meant the pipeline was relatively safe. The method could also obtain the risk level of each indicator, showing that geological conditions, extreme weather, and public safety awareness were particularly unsafe, and service time, pipeline deformation, ground activity, and operation training were relatively unsafe. It is expected that the risk assessment result could provide a reference for pipeline safety management.

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Singh, Karan, Samajh Singh Thakur, and Mangi Lal. "Vague Rough Set Techniques for Uncertainty Processing in Relational Database Model." Informatica 19, no. 1 (January 1, 2008): 113–34. http://dx.doi.org/10.15388/informatica.2008.205.

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Selvachandran, Ganeshsree, and Abdul Razak Salleh. "A vague soft set theoretic approach to multiattribute decision making problems." Applied Mathematical Sciences 8 (2014): 6937–49. http://dx.doi.org/10.12988/ams.2014.48636.

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Bhargavi, Y. "A study on translational invariant vague set of a $$\Gamma $$-semiring." Afrika Matematika 31, no. 7-8 (May 12, 2020): 1273–82. http://dx.doi.org/10.1007/s13370-020-00794-1.

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Chen, Shyi-Ming, and Jiann-Mean Tan. "Handling multicriteria fuzzy decision-making problems based on vague set theory." Fuzzy Sets and Systems 67, no. 2 (October 1994): 163–72. http://dx.doi.org/10.1016/0165-0114(94)90084-1.

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Devos, Filip, Nancy Van Gyseghem, Ria Vandenberghe, and Rita De Caluwe. "Modelling vague lexical time expressions by means of fuzzy set theory*." Journal of Quantitative Linguistics 1, no. 3 (January 1994): 189–94. http://dx.doi.org/10.1080/09296179408590016.

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Shi, Xiaolong, Maryam Akhoundi, A. A. Talebi, and Masome Mojahedfar. "A Study on Regular Domination in Vague Graphs with Application." Advances in Mathematical Physics 2023 (May 20, 2023): 1–9. http://dx.doi.org/10.1155/2023/7098134.

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Vague graphs (VGs), which are a family of fuzzy graphs (FGs), are a well-organized and useful tool for capturing and resolving a range of real-world scenarios involving ambiguous data. In graph theory, a dominating set (DS) for a graph G ∗ = X , E is a subset S of the vertices X such that every vertex not in S is adjacent to at least one member of S . The concept of DS in FGs has received the attention of many researchers due to its many applications in various fields such as computer science and electronic networks. In this paper, we introduce the notion of ϵ 1 , ϵ 2 , 2 -Regular vague dominating set and provide some examples to explain various concepts introduced. Also, some results were discussed. Additionally, the ϵ 1 , ϵ 2 , 2 -Regular strong (weak) and independent strong (weak) domination sets for vague domination set (VDS) were presented with some theorems to support the context.

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Shu Fuhua, 舒服华. "Application of Vague Set in Process Optimization of Laser Quenching of Cr12MoV Steels." Laser & Optoelectronics Progress 54, no. 1 (2017): 011403. http://dx.doi.org/10.3788/lop54.011403.

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