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Journal articles on the topic 'Fuzzy set theory'

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Published: 4 June 2021
Last updated: 9 June 2025

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1

Lehmann, Ingo, Richard Weber, and Hans Jürgen Zimmermann. "Fuzzy set theory." Operations-Research-Spektrum 14, no. 1 (March 1992): 1–9. http://dx.doi.org/10.1007/bf01783496.

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2

Zimmermann, H. J. "Fuzzy set theory." Wiley Interdisciplinary Reviews: Computational Statistics 2, no. 3 (April 16, 2010): 317–32. http://dx.doi.org/10.1002/wics.82.

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3

Barr, Michael. "Fuzzy Set Theory and Topos Theory." Canadian Mathematical Bulletin 29, no. 4 (December 1, 1986): 501–8. http://dx.doi.org/10.4153/cmb-1986-079-9.

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AbstractThe relation between the categories of Fuzzy Sets and that of Sheaves is explored and the precise connection between them is explicated. In particular, it is shown that if the notion of fuzzy sets is further fuzzified by making equality (as well as membership) fuzzy, the resultant categories are indeed toposes.
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4

Takeuti, Gaisi, and Satoko Titani. "Fuzzy logic and fuzzy set theory." Archive for Mathematical Logic 32, no. 1 (January 1992): 1–32. http://dx.doi.org/10.1007/bf01270392.

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5

Radu, C., and R. Wilkerson. "Using fuzzy set theory." IEEE Potentials 14, no. 5 (1996): 33–35. http://dx.doi.org/10.1109/45.481510.

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6

Anjan, Mukherjee1 and Ajoy Kanti Das2. "On Fuzzy Soft Multi Set and Its Application in Information Systems." International Journal of Computer-Aided technologies (IJCAx) 2, no. 3 (August 17, 2023): 29. https://doi.org/10.5281/zenodo.8256282.

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Research on information and communication technologies have been developed rapidly since it can be applied easily to several areas like computer science, medical science, economics, environments, engineering, among other. Applications of soft set theory, especially in information systems have been found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with respect to these newly defined operations. In this paper, we extend their work and study some more basic properties of their defined operations. Also, we define some basic supporting tools in information system also application of fuzzy soft multi sets in information system are presented and discussed. Here we define the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy soft multi set is a fuzzy multi valued information system.
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7

Anjan, Mukherjee1 and Ajoy Kanti Das2. "On Fuzzy Soft Multi Set and Its Application in Information Systems." International Journal of Computer-Aided Technologies (IJCAx) 02, Jul (July 31, 2015): 01–18. https://doi.org/10.5121/ijcax.2015.2303.

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Research on information and communication technologies have been developed rapidly since it can be applied easily to several areas like computer science, medical science, economics, environments, engineering, among other. Applications of soft set theory, especially in information systems have been found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with respect to these newly defined operations. In this paper, we extend their work and study some more basic properties of their defined operations. Also, we define some basic supporting tools in information system also application of fuzzy soft multi sets in information system are presented and discussed. Here we define the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy soft multi set is a fuzzy multi valued information system.
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8

Hajek, P., and Z. Hanikova. "Interpreting lattice-valued set theory in fuzzy set theory." Logic Journal of IGPL 21, no. 1 (July 18, 2012): 77–90. http://dx.doi.org/10.1093/jigpal/jzs023.

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9

GAO, XIAOYU, Q. S. GAO, Y. HU, and L. LI. "A PROBABILITY-LIKE NEW FUZZY SET THEORY." International Journal of Pattern Recognition and Artificial Intelligence 20, no. 03 (May 2006): 441–62. http://dx.doi.org/10.1142/s0218001406004697.

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In this paper, the reasons for the shortcoming of Zadeh's fuzzy set theory — it cannot correctly reflect different kinds of fuzzy phenomenon in the natural world — are discussed. In addition, the proof of the error of Zadeh's fuzzy set theory — it incorrectly defined the set complement that cannot exist in Zadeh's fuzzy set theory — is proposed. This error of Zadeh's fuzzy set theory causes confusion in thinking, logic and conception. It causes the seriously mistaken belief that logics of fuzzy sets necessarily go against classical and normal thinking, logic and conception. Two new fuzzy set theories, C-fuzzy set theory and probability-like fuzzy set theory, the N-fuzzy set theory, are proposed. The two are equivalent, and both overcome the error and shortcoming of Zadeh's fuzzy set theory, and they are consistent with normal, natural and classical thinking, logic and concepts. The similarities of N-fuzzy set theory with probability theory are also examined.
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10

Soni, Manjula. "Fuzzy Set Theory in Sociology." International Journal for Research in Applied Science and Engineering Technology V, no. IX (September 30, 2017): 1148–51. http://dx.doi.org/10.22214/ijraset.2017.9165.

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11

Maiers, J., and Y. S. Sherif. "Applications of fuzzy set theory." IEEE Transactions on Systems, Man, and Cybernetics SMC-15, no. 1 (January 1985): 175–89. http://dx.doi.org/10.1109/tsmc.1985.6313408.

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12

Nakamura, K. "Fuzzy set and possibility theory." Proceedings of the IEEE 73, no. 2 (1985): 382. http://dx.doi.org/10.1109/proc.1985.13157.

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13

Toth, Herbert. "From fuzzy-set theory to fuzzy set-theory: Some critical remarks on existing concepts." Fuzzy Sets and Systems 23, no. 2 (August 1987): 219–37. http://dx.doi.org/10.1016/0165-0114(87)90060-1.

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14

Tilahun, Gebrie Yeshiwas. "Fuzzy Set Theory Applied on Autometrized Algebra." F1000Research 14 (February 4, 2025): 159. https://doi.org/10.12688/f1000research.161249.1.

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This paper introduces fuzzy subalgebras of autometrized algebras and studies their properties. Also, we present fuzzy ideals of autometrized algebras and provide examples to illustrate our findings. We examine the homomorphisms of both the images and the inverse images of fuzzy subalgebras and ideals. Furthermore, we introduce fuzzy congruences on autometrized algebras. We prove that in normal autometrized algebra, the set of all fuzzy ideals is in one-to-one correspondence with the set of all fuzzy congruences.
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15

Atiqe, Ur Rahman, Saeed Muhammad, and Zahid Saba. "Application in decision making based on fuzzy parameterized hypersoft set theory." Asia Mathematika 5, no. 1 (April 26, 2021): 19–27. https://doi.org/10.5281/zenodo.4721481.

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Hypersoft set is the generalization of the soft set as it converts single attribute function to multi-attribute function. The core purpose of this study is to make the existing literature regarding fuzzy parameterized soft set in line with the need for multi-attribute function. We first conceptualize the fuzzy parameterized hypersoft set along with some of its fundamentals. Then we propose a decision-making-based algorithm with the help of this theory. Moreover, an illustrative example is presented which depicts its validity for successful application to the problems involving vagueness and uncertainties.
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16

Shi, Fu-Gui. "(L,M)-Fuzzyσ-Algebras". International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/356581.

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The notion of (L,M)-fuzzyσ-algebras is introduced in the lattice value fuzzy set theory. It is a generalization of Klement's fuzzyσ-algebras. In our definition of (L,M)-fuzzyσ-algebras, eachL-fuzzy subset can be regarded as anL-measurable set to some degree.
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17

W. Sitnicki, Maksym, Valeriy Balan, Inna Tymchenko, Viktoriia Sviatnenko, and Anastasiia Sychova. "Measuring the commercial potential of new product ideas using fuzzy set theory." Innovative Marketing 17, no. 2 (June 17, 2021): 149–63. http://dx.doi.org/10.21511/im.17(2).2021.14.

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The stage of selecting creative ideas that have the prospect of further commercial use and can be used to create new products, services, or startups is one of the most complex and important stages of the innovation process. It is essential to take into account expert opinions and evaluations, often vague and ambiguous. The study aims to develop a methodological approach to measure the commercial potential of new product ideas based on fuzzy set theory and fuzzy logic. To this end, three calculation schemes are developed: the first two are based on fuzzy multicriteria analysis using Fuzzy SAW and Fuzzy TOPSIS methods, respectively; the third is based on building a logical-linguistic model with fuzzy expert knowledge bases and applying fuzzy inference using the Mamdani algorithm. Fuzzy numbers in triangular form with triangular membership functions are used to present linguistic estimates of experts and fuzzy data; the CoA (Center of Area) method is used to dephase the obtained values. For practical application of the proposed algorithm, the model is used as an Excel framework containing a general set of input expert information in the form of linguistic estimates and fuzzy data, a set of calculations using three schemes, and a set of defuzzification of the obtained results. The framework allows for simulation modeling depending on the modification of the list of defined evaluation criteria and their partial criteria, and adjustments to expert opinions. The developed methodological approach is suggested for the initial stages of the innovation process to facilitate the assessment of creative ideas and improve their implementation. AcknowledgmentThis scientific paper is published with the support of the International Visegrad Fund.
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18

DESCHRIJVER, GLAD, and CHRIS CORNELIS. "REPRESENTABILITY IN INTERVAL-VALUED FUZZY SET THEORY." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, no. 03 (June 2007): 345–61. http://dx.doi.org/10.1142/s0218488507004716.

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Interval-valued fuzzy set theory is an increasingly popular extension of fuzzy set theory where traditional [0,1]-valued membership degrees are replaced by intervals in [0,1] that approximate the (unknown) membership degrees. To construct suitable graded logical connectives in this extended setting, it is both natural and appropriate to "reuse" ingredients from classical fuzzy set theory. In this paper, we compare different ways of representing operations on interval-valued fuzzy sets by corresponding operations on fuzzy sets, study their intuitive semantics, and relate them to an existing, purely order-theoretical approach. Our approach reveals, amongst others, that subtle differences in the representation method can have a major impact on the properties satisfied by the generated operations, and that contrary to popular perception, interval-valued fuzzy set theory hardly corresponds to a mere twofold application of fuzzy set theory. In this way, by making the mathematical machinery behind the interval-valued fuzzy set model fully transparent, we aim to foster new avenues for its exploitation by offering application developers a much more powerful and elaborate mathematical toolbox than existed before.
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19

Atiqe, Ur Rahman, Saeed Muhammad, and Abd El-Wahed Khalifa Hamiden. "Decision making application based on parameterization of fuzzy hypersoft set with fuzzy setting." Italian Journal of Pure and Applied Mathematics 48 (October 13, 2022): 1033–48. https://doi.org/10.5281/zenodo.7477708.

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Fuzzy soft set is considered as an apt parameterization tool to deal with vagueness and uncertainties. There are many situations when attributes need to be further classified into attribute-valued disjoint sets. Such situations are not tackled by the existing fuzzy soft-like structures. Hypersoft set, an extension of soft set, employs multi-argument approximate function which addresses the inadequacy of existing structures for attribute-valued disjoint sets. In this study, theory of fuzzy parameterized fuzzy hypersoft set is characterized and some of its essential properties are discussed. In order to cope with the decision making problems, an algorithm is proposed which employs the fuzzy decision set of fuzzy parameterized fuzzy hypersoft set for dealing with decision making problems under uncertain scenarios. The proposed algorithm is validated with the help of a numerical example.
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20

Bhattacharyya, Surajit. "FUZZY SET THEORY---------- SOME USEFUL DISCUSSIONS AND INVESTIGATIONS." International Journal of Research -GRANTHAALAYAH 9, no. 8 (August 31, 2021): 125–49. http://dx.doi.org/10.29121/granthaalayah.v9.i8.2021.4124.

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In this paper I have discussed some basic but very important theories of fuzzy set theory with numerous examples. I have investigated α-sets, operations of fuzzy numbers, on interval fuzzy sets and also on fuzzy mappings. I have introduced S.Bs. class of fuzzy complements with its increasing and decreasing generators .
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21

Anjan, Mukherjee, Kanti Das Ajoy, and Saha Abhijit. "MORE ON INTERVAL-VALUED INTUITIONISTIC FUZZY SOFT MULTI SETS." Advances in Vision Computing: An International Journal (AVC) 2, no. 2 (June 26, 2015): 01–21. https://doi.org/10.5281/zenodo.3591661.

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In 2013, Mukherje et al. developed the concept of interval-valued intuitionistic fuzzy soft multi set as a mathematical tool for making descriptions of the objective world more realistic, practical and accurate in some cases, making it very promising. In this paper we define some operations in interval-valued intuitionistic fuzzy soft multi set theory and show that the associative, distribution and De Morgan’s type of results hold in interval-valued intuitionistic fuzzy soft multi set theory for the newly defined operations in our way. Also, we define the necessity and possibility operations on interval-valued intuitionistic fuzzy soft multi set theory and study their basic properties and some results.
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22

Lozano, Carmen, and Enriqueta Mancilla-Rendón. "Fuzzy Set Theory Applied to Accounting Sciences." New Mathematics and Natural Computation 16, no. 01 (March 2020): 1–16. http://dx.doi.org/10.1142/s1793005720500015.

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Fuzzy set theory and fuzzy logic have been successfully developed in engineering and mathematics. However, these concepts have found great acceptance in social sciences in recent years since they provide an answer to those problems in the real world that cannot be modeled using classical mathematics. In this paper, we propose a new methodology for accounting science based on fuzzy triangular numbers. The methodology uses Hamming distance between fuzzy triangular numbers and arithmetic operations to evaluate corporate governance of multinational public stock corporations (PSCs) in the telecommunications sector.
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23

Al-Quran, Ashraf Al, Faisal Al Al-Sharqi, Hamiden Abd El Wahed Khalifa, Haifa Alqahtani, and Ali M. A. Bany Awad. "T-Spherical Fuzzy-Valued Neutrosophic Set Theory." International Journal of Neutrosophic Science 23, no. 2 (2024): 104–15. http://dx.doi.org/10.54216/ijns.230209.

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From fuzzy to neutrosophy, multiple hybrid models have been innovated, with each introduced model surpassing its predecessor. Due to the inherent indeterminacy in the world, a more precise form of imprecision is required. As a result, more sophisticated variants of the neutrosophic set have been created. Examples of these amalgamations include fuzzy neutrosophic sets, intuitionistic fuzzy neutrosophic sets, Pythagorean fuzzy neutrosophic sets, neutrosophic vague sets, and neutrosophic rough sets. The main objective of this paper is to present another variant of the neutrosophic set called T-spherical fuzzy-valued neutrosophic set (T-SFVNS). Serving as a generalization of the aforementioned combinations, T-SFVNS allows for the representation of indeterminacy and inconsistency in a more nuanced manner. In this paper, we define the T-SFVNS and Tspherical fuzzy-valued neutrosophic numbers (T-SFVNNs). Additionally, we propose several types of score and accuracy functions to compare the T-SFVNNs. We also present the basic operations of T-SFVNSs and the algebraic operations of T-SFVNNs, supported by proofs and illustrative examples..
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24

Sun, Xiao Chao, Xin Tao Xia, Yan Bin Liu, and Lei Lei Gao. "Evaluation of Rolling Bearing Vibration Using Fuzzy Set Theory and Chaos Theory." Advanced Materials Research 424-425 (January 2012): 338–41. http://dx.doi.org/10.4028/www.scientific.net/amr.424-425.338.

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The optimal fuzzy similarity coefficient based on the phase space is proposed to evaluate the rolling bearing vibration acceleration generated by wear on the surface of the ring raceway. The phase space of the time series of the rolling bearing vibration acceleration is reconstructed via the chaos theory, the fuzzy similarity relation between the phase trajectories is established by the fuzzy set theory, and then the optimal fuzzy similarity coefficient is obtained through a reasonable choice of the embedding dimension and the delay. Experimental investigation shows that with the increase of the fault diameter, the optimal fuzzy similarity coefficient decreases nonlinearly
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25

Mordeson, John N. "Rough set theory applied to (fuzzy) ideal theory." Fuzzy Sets and Systems 121, no. 2 (July 2001): 315–24. http://dx.doi.org/10.1016/s0165-0114(00)00023-3.

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26

Bordley, Robert F. "Fuzzy set theory, observer bias and probability theory." Fuzzy Sets and Systems 33, no. 3 (December 1989): 347–54. http://dx.doi.org/10.1016/0165-0114(89)90123-1.

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27

Luo, Dong Ling, Chen Yin Wang, Yang Yi, Dong Ling Zhang, and Xiao Cong Zhou. "Fuzzy Maximum Independent Set Problem." Applied Mechanics and Materials 687-691 (November 2014): 1161–65. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.1161.

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Edge covering problem, dominating set problem, and independent set problem are classic problems in graph theory except for vertex covering problem. In this paper, we study the maximum independent set problem under fuzzy uncertainty environments, which aims to search for the independent set with maximum value in a graph. First, credibility theory is introduced to describe the fuzzy variable. Three decision models are performed based on the credibility theory. A hybrid intelligence algorithm which integrates genetic algorithm and fuzzy simulation is proposed due to the unavailability of traditional algorithm. Finally, numerical experiments are performed to prove the efficiency of the fuzzy decision modes and the hybrid intelligence algorithm.
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28

Zwick, Rami, and Hans-Jurgen Zimmermann. "Fuzzy Set Theory and Its Applications." American Journal of Psychology 106, no. 2 (1993): 304. http://dx.doi.org/10.2307/1423177.

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29

HONDA, Nakaji, and Ario OHSATO. "FUZZY SET THEORY AND ITS APPLICATIONS." Kodo Keiryogaku (The Japanese Journal of Behaviormetrics) 13, no. 2 (1986): 64–89. http://dx.doi.org/10.2333/jbhmk.13.2_64.

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30

Adlassnig, Klaus-Peter. "Fuzzy Set Theory in Medical Diagnosis." IEEE Transactions on Systems, Man, and Cybernetics 16, no. 2 (1986): 260–65. http://dx.doi.org/10.1109/tsmc.1986.4308946.

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31

Sabri Abd Al Razzaq, Audia, and Luay Abd Al Hani Al Swidi. "On Classification of Fuzzy Set Theory." Journal of Engineering and Applied Sciences 14, no. 14 (December 20, 2019): 4786–94. http://dx.doi.org/10.36478/jeasci.2019.4786.4794.

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32

S. Thangavadivelu and T. S. Colvin. "TRAHFICABILITY DETERMINATION USING FUZZY SET THEORY." Transactions of the ASAE 34, no. 5 (1991): 2272–78. http://dx.doi.org/10.13031/2013.31867.

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33

Chaira, Tamalika, and A. K. Ray. "Threshold selection using fuzzy set theory." Pattern Recognition Letters 25, no. 8 (June 2004): 865–74. http://dx.doi.org/10.1016/j.patrec.2004.01.018.

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34

Moore, Ramon, and Weldon Lodwick. "Interval analysis and fuzzy set theory." Fuzzy Sets and Systems 135, no. 1 (April 2003): 5–9. http://dx.doi.org/10.1016/s0165-0114(02)00246-4.

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35

Fugui, Shi. "Pointwise uniformities in fuzzy set theory." Fuzzy Sets and Systems 98, no. 1 (August 1998): 141–46. http://dx.doi.org/10.1016/s0165-0114(96)00364-8.

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36

Zirillit, A., A. Tiano, G. N. Robert, and R. Sutton. "Autopilot Designed with Fuzzy Set Theory." IFAC Proceedings Volumes 34, no. 7 (July 2001): 71–76. http://dx.doi.org/10.1016/s1474-6670(17)35061-9.

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37

Gerla, G., and L. Scarpati. "Extension principles for fuzzy set theory." Information Sciences 106, no. 1-2 (April 1998): 49–69. http://dx.doi.org/10.1016/s0020-0255(97)10003-2.

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38

Deschrijver, Glad, and Etienne E. Kerre. "Uninorms in L∗-fuzzy set theory." Fuzzy Sets and Systems 148, no. 2 (December 2004): 243–62. http://dx.doi.org/10.1016/j.fss.2003.12.006.

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39

Gupta, Madan M. "Fuzzy set theory and its applications." Fuzzy Sets and Systems 47, no. 3 (May 1992): 396–97. http://dx.doi.org/10.1016/0165-0114(92)90310-z.

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40

Hisdal, E. "Interpretative versus prescriptive fuzzy set theory." IEEE Transactions on Fuzzy Systems 2, no. 1 (1994): 22–26. http://dx.doi.org/10.1109/91.273118.

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41

Virgil Negoita, Constantin. "Postmodernism, cybernetics and fuzzy set theory." Kybernetes 31, no. 7/8 (October 2002): 1043–49. http://dx.doi.org/10.1108/03684920210436327.

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42

Garg, Harish, R. Sujatha, D. Nagarajan, J. Kavikumar, and Jeonghwan Gwak. "Evidence Theory in Picture Fuzzy Set Environment." Journal of Mathematics 2021 (May 18, 2021): 1–8. http://dx.doi.org/10.1155/2021/9996281.

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Picture fuzzy set is the most widely used tool to handle the uncertainty with the account of three membership degrees, namely, positive, negative, and neutral such that their sum is bound up to 1. It is the generalization of the existing intuitionistic fuzzy and fuzzy sets. This paper studies the interval probability problems of the picture fuzzy sets and their belief structure. The belief function is a vital tool to represent the uncertain information in a more effective manner. On the other hand, the Dempster–Shafer theory (DST) is used to combine the independent sources of evidence with the low conflict. Keeping the advantages of these, in the present paper, we present the concept of the evidence theory for the picture fuzzy set environment using DST. Under this, we define the concept of interval probability distribution and discuss its properties. Finally, an illustrative example related to the decision-making process is employed to illustrate the application of the presented work.
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Oriza, Sri Delvia, and Nova Noliza Bakar. "HIMPUNAN LEMBUT KABUR HESITANT DAN APLIKASINYA DALAM PENGAMBILAN KEPUTUSAN." Jurnal Matematika UNAND 6, no. 3 (November 3, 2017): 23. http://dx.doi.org/10.25077/jmu.6.3.23-31.2017.

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Abstract. Molodstov's soft set theory is a newly emerging mathematical tool to handleuncertainty. The soft set theory can be combined with other mathematical theory like asfuzzy set theory. This paper aims to extend hesitant fuzzy set to hesitant fuzzy soft sets.Then, the complement, "AND", "OR", union, intersection operations and De Morgan'slaw are dened on hesitant fuzzy soft sets. Finally, with the help of level soft set, thehesitant fuzzy soft sets are applied to a decision making problem.Kata Kunci: Soft set, Fuzzy set, Hesitant fuzzy set, Hesitant fuzzy soft set, Level softset
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Jin, Lizhong, Junjie Chen, and Xiaobo Zhang. "An Outlier Fuzzy Detection Method Using Fuzzy Set Theory." IEEE Access 7 (2019): 59321–32. http://dx.doi.org/10.1109/access.2019.2914605.

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45

K.Balasubramaniyan. "Beals Fuzzy Set and its Application in Group Theory." Advances in Nonlinear Variational Inequalities 28, no. 6s (March 4, 2025): 762–73. https://doi.org/10.52783/anvi.v28.4424.

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In this paper, we establish the idea of Beal’s fuzzy set (BFS) and study the concept of Beal’s fuzzy abelian subgroups, Beal’s fuzzy normal subgroups, Centralizer, Normalizer and Beal’s fuzzy cyclic subgroups. we obtain those concepts instead of various product of Beal’s fuzzy set. Finally, homomorphic images and pre-images of Beal’s fuzzy sets are established
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46

Novák, Vilém. "Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory." Mathematics 8, no. 3 (March 16, 2020): 432. http://dx.doi.org/10.3390/math8030432.

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In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notions of rough set theory have already been included in AST. Using fuzzy type theory, we generalize basic concepts of rough set theory and the topological concepts of AST to become the concepts of the fuzzy set theory. We will give mostly syntactic proofs of the main properties and relations among all the considered concepts, thus showing that they are universally valid.
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47

Mohammed, Mohammed Jasim. "Literature Review of Fuzzy Set Theory: Applications and Methodologies." Journal of Economics and Administrative Sciences 31, no. 146 (April 1, 2025): 197–216. https://doi.org/10.33095/9p0kjy98.

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This paper represents a comprehensive literature survey of the research published in the Journal of Economics and Administrative Sciences (JEAS) on applications and methodologies of fuzzy set theory. The review traced how fuzzy logic has been evolving in decision-making, optimization, and modeling uncertainties in published articles such as economics, management, and engineering. The categorization of fuzzy methodologies into various domains such as fuzzy linear programming, fuzzy regression, fuzzy control systems, and fuzzy multi-criteria decision-making relies heavily on the study of existing research. An analysis revealed an increasing trend of investigations highlighting the interplay of fuzzy logic with artificial intelligence, statistical modeling, and heuristic optimization methods. The developments in methodologies of fuzzy decision-making frameworks are again examined from the perspective of applicability in real-life problem situations involving imprecise and uncertain data. Findings that fuzzy logic, therefore, contributed considerably to the enhancement of problem-solving in economics and administrative sciences through more flexible and adaptive models. Therefore, this literature review will be an excellent guide for researchers in fuzzy set theory applications to grasp existing gaps and suggest future directions for improving fuzzy methodologies across industries.
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48

Alkhazaleh, Shawkat, and Abdul Razak Salleh. "Fuzzy Soft Multiset Theory." Abstract and Applied Analysis 2012 (2012): 1–20. http://dx.doi.org/10.1155/2012/350603.

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In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh et al. in 2011 introduced the definition of a soft multiset as a generalization of Molodtsov's soft set. In this paper we give the definition of fuzzy soft multiset as a combination of soft multiset and fuzzy set and study its properties and operations. We give examples for these concepts. Basic properties of the operations are also given. An application of this theory in decision-making problems is shown.
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Zhou, Yong, and Ling Tian. "Applying Fuzzy Set Theory to Analysis Driving Maneuver." Applied Mechanics and Materials 361-363 (August 2013): 2244–48. http://dx.doi.org/10.4028/www.scientific.net/amm.361-363.2244.

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Abstract:
The conventional statistical models have their limitations in modeling the natural human driving behavior. This may be overcome by applying fuzzy set based approach to describe drivers decisions. This paper proposes a fuzzy set based car-following model to simulate the driving maneuver. Emphasis is placed on the research undertaken to establish fuzzy sets and systems and model validation. Research results have shown that the fuzzy set application is very encouraging.
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50

Saleem, Kholoud W., Suzan A. A. Abu-harbid, and Abrahim A. A. Tentush. "A study on some relations on multi-fuzzy (left-right)ideals of rings." Journal of Pure & Applied Sciences 20, no. 4 (December 30, 2021): 177–81. http://dx.doi.org/10.51984/jopas.v20i4.1763.

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Abstract:
multi fuzzy set theory is an extension of fuzzy set theory, which deals with the multi dimensional fuzziness. In this paper, we introduce the concepts of multi-fuzzy rings, multi fuzzy ideal, image of multi- fuzzy ideal of a ring under homomorphism, Cartesian product of multi-fuzzy set, and some related properties and theorems are investigated. The purpose of this study is to implement the fuzzy set theory and rings theory in multi-fuzzy rings.
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