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Journal articles on the topic 'Fuzzy set theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 March 2023

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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

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

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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16

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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17

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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18

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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19

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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20

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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21

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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22

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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23

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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24

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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25

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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26

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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27

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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28

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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29

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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30

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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31

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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32

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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33

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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34

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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35

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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36

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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37

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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38

Sordo, J. A. "Using fuzzy set theory to assess basis set quality." Chemical Physics Letters 302, no. 3-4 (March 1999): 273–80. http://dx.doi.org/10.1016/s0009-2614(99)00102-5.

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39

DESCHRIJVER, GLAD. "ORDINAL SUMS IN INTERVAL-VALUED FUZZY SET THEORY." New Mathematics and Natural Computation 01, no. 02 (July 2005): 243–59. http://dx.doi.org/10.1142/s1793005705000172.

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Interval-valued fuzzy sets form an extension of fuzzy sets which assign to each element of the universe a closed subinterval of the unit interval. This interval approximates the "real", but unknown, membership degree. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. A method for constructing t-norms that satisfy the residuation principle is by using the ordinal sum theorem. In this paper, we construct the ordinal sum of t-norms on [Formula: see text], where [Formula: see text] is the underlying lattice of interval-valued fuzzy set theory, in such a way that if the summands satisfy the residuation principle, then the ordinal sum does too.
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40

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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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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41

T., Illakiya. "A Fuzzy Rough Set Theory based Feature Selection for Phishing Attack Classification." Journal of Advanced Research in Dynamical and Control Systems 12, SP4 (March 31, 2020): 298–306. http://dx.doi.org/10.5373/jardcs/v12sp4/20201492.

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42

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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43

Onasanya, B. O., T. S. Atamewoue, and S. Hoskova-Mayerova. "Certain fuzzy hyperstructures from a fuzzy set." Journal of Intelligent & Fuzzy Systems 39, no. 3 (October 7, 2020): 2775–82. http://dx.doi.org/10.3233/jifs-191054.

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Fuzzy set theory and also the hypergroups in the sense of Marty are both generalizations of some existing mathematical concepts which are used for modeling many real life situations. The main purpose of this paper is the study of the link between fuzzy sets and fuzzy hypergroups and fuzzy semihypergroups. As a matter of fact, some commutative fuzzy hypergroups and fuzzy semihypergroups have been constructed from fuzzy set and some of their properties were investigated.
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44

Alkhazaleh, Shawkat, Abdul Razak Salleh, and Nasruddin Hassan. "Possibility Fuzzy Soft Set." Advances in Decision Sciences 2011 (September 8, 2011): 1–18. http://dx.doi.org/10.1155/2011/479756.

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We introduce the concept of possibility fuzzy soft set and its operation and study some of its properties. We give applications of this theory in solving a decision-making problem. We also introduce a similarity measure of two possibility fuzzy soft sets and discuss their application in a medical diagnosis problem.
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45

Peric, Nebojsa. "Fuzzy logic and fuzzy set theory based edge detection algorithm." Serbian Journal of Electrical Engineering 12, no. 1 (2015): 109–16. http://dx.doi.org/10.2298/sjee1501109p.

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In this paper we will show a way how to detect edges in digital images. Edge detection is a fundamental part of many algorithms, both in image processing and in video processing. Therefore it is important that the algorithm is efficient and, if possible, fast to carry out. The fuzzy set theory based approach on edge detection is good for use when we need to make some kind of image segmentation, or when there is a need for edge classification (primary, secondary, ...). One example that motivated us is region labeling; this is a process by which the digital image is divided in units and each unit is given a unique label (sky, house, grass, ?, etc.). To accomplish that, we need to have an intelligent system that will precisely determine the edges of the region. In this paper we will describe tools from image processing and fuzzy logic that we use for edge detection as well as the proposed algorithm.
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46

Joshi, Bhagawati Prasad, Abhay Kumar, Akhilesh Singh, Pradeep Kumar Bhatt, and Bhupender Kumar Bharti. "Intuitionistic fuzzy parameterized fuzzy soft set theory and its application." Journal of Intelligent & Fuzzy Systems 35, no. 5 (November 20, 2018): 5217–23. http://dx.doi.org/10.3233/jifs-169805.

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47

Guo, Hongyue, Witold Pedrycz, and Xiaodong Liu. "Fuzzy time series forecasting based on axiomatic fuzzy set theory." Neural Computing and Applications 31, no. 8 (January 9, 2018): 3921–32. http://dx.doi.org/10.1007/s00521-017-3325-9.

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48

Muhiuddin, Ghulam, Madeline Al-Tahan, Ahsan Mahboob, Sarka Hoskova-Mayerova, and Saba Al-Kaseasbeh. "Linear Diophantine Fuzzy Set Theory Applied to BCK/BCI-Algebras." Mathematics 10, no. 12 (June 19, 2022): 2138. http://dx.doi.org/10.3390/math10122138.

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In this paper, we apply the concept of linear Diophantine fuzzy sets in BCK/BCI-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties are discussed. Additionally, characterizations of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are considered. Moreover, the associated results for linear Diophantine fuzzy subalgebras, linear Diophantine fuzzy ideals and linear Diophantine fuzzy commutative ideals are obtained.
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49

Alkhazaleh, Shawkat. "Effective Fuzzy Soft Set Theory and Its Applications." Applied Computational Intelligence and Soft Computing 2022 (April 15, 2022): 1–12. http://dx.doi.org/10.1155/2022/6469745.

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Fuzzy soft set is the most powerful and effective extension of soft sets which deals with parameterized values of the alternative. It is an extended model of soft set and a new mathematical tool that has great advantages in dealing with uncertain information and is proposed by combining soft sets and fuzzy sets. Many fuzzy decision making algorithms based on fuzzy soft sets were given. However, these do not consider the external effective on the decision it depends on the parameters without considering any external effective. In order to solve these problems, in this paper, we introduce the concept of effective fuzzy soft set and its operation and study some of its properties. We also give an application of this concept in decision making (DM) problem. Finally, we give an application of this theory to medical diagnosis (MD) and exhibit the technique with a hypothetical case study.
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50

Liu, Xiao Jing, Wei Feng Du, and Xiao Min. "Fuzzy Attribute Reduction Based on Fuzzy Similarity." Applied Mechanics and Materials 533 (February 2014): 237–41. http://dx.doi.org/10.4028/www.scientific.net/amm.533.237.

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The measure of the significance of the attribute and attribute reduction is one of the core content of rough set theory. The classical rough set model based on equivalence relation, suitable for dealing with discrete-valued attributes. Fuzzy-rough set theory, integrating fuzzy set and rough set theory together, extending equivalence relation to fuzzy relation, can deal with fuzzy-valued attributes. By analyzing three problems of FRAR which is a fuzzy decision table attribute reduction algorithm having extensive use, this paper proposes a new reduction algorithm which has better overcome the problem, can handle larger fuzzy decision table. Experimental results show that our reduction algorithm is much quicker than the FRAR algorithm.
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