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Journal articles on the topic 'Fuzzy sets'

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Published: 4 June 2021
Last updated: 29 July 2024

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1

Thakur, S. S., and Annamma Philip. "Pairwise fuzzy connectedness between fuzzy sets." Mathematica Bohemica 122, no. 4 (1997): 375–80. http://dx.doi.org/10.21136/mb.1997.126217.

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2

Wang, Guo-jun, and Ying-Yu He. "Intuitionistic fuzzy sets and -fuzzy sets." Fuzzy Sets and Systems 110, no. 2 (March 2000): 271–74. http://dx.doi.org/10.1016/s0165-0114(98)00011-6.

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3

Lee, Seok Jong, and Eun Pyo Lee. "Fuzzyr-continuous and fuzzyr-semicontinuous maps." International Journal of Mathematics and Mathematical Sciences 27, no. 1 (2001): 53–63. http://dx.doi.org/10.1155/s0161171201010882.

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We introduce a new notion of fuzzyr-interior which is an extension of Chang's fuzzy interior. Using fuzzyr-interior, we define fuzzyr-semiopen sets and fuzzyr-semicontinuous maps which are generalizations of fuzzy semiopen sets and fuzzy semicontinuous maps in Chang's fuzzy topology, respectively. Some basic properties of fuzzyr-semiopen sets and fuzzyr-semicontinuous maps are investigated.
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4

Tuan, Han-Wen, and Henry Chung-Jen Chao. "Non–fuzzy sets for intuitionistic fuzzy sets." Journal of Discrete Mathematical Sciences and Cryptography 21, no. 7-8 (November 17, 2018): 1509–14. http://dx.doi.org/10.1080/09720529.2017.1367467.

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5

Shi, Fu-Gui, and Chao-Zan Fan. "Fuzzy soft sets as L-fuzzy sets." Journal of Intelligent & Fuzzy Systems 37, no. 4 (October 25, 2019): 5061–66. http://dx.doi.org/10.3233/jifs-182828.

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6

DUBOIS, DIDIER, and HENRI PRADE. "ROUGH FUZZY SETS AND FUZZY ROUGH SETS*." International Journal of General Systems 17, no. 2-3 (June 1990): 191–209. http://dx.doi.org/10.1080/03081079008935107.

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7

Mukherjee, M. N., and S. P. Sinha. "Fuzzyθ-closure operator on fuzzy topological spaces." International Journal of Mathematics and Mathematical Sciences 14, no. 2 (1991): 309–14. http://dx.doi.org/10.1155/s0161171291000364.

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The paper contains a study of fuzzyθ-closure operator,θ-closures of fuzzy sets in a fuzzy topological space are characterized and some of their properties along with their relation with fuzzyδ-closures are investigated. As applications of these concepts, certain functions as well as some spaces satisfying certain fuzzy separation axioms are characterized in terms of fuzzyθ-closures andδ-closures.
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8

DEMİRCİ, MUSTAFA. "GENUINE SETS, VARIOUS KINDS OF FUZZY SETS AND FUZZY ROUGH SETS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11, no. 04 (August 2003): 467–94. http://dx.doi.org/10.1142/s0218488503002193.

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In this paper, deriving the type-m fuzzy sets, intuitionistic fuzzy sets, Φ-fuzzy sets, rough sets, fuzzy rough sets and rough fuzzy sets as particular genuine sets, and establishing their connections with genuine sets, it is demonstrated that the theory of genuine sets provides a powerful tool to model various different kinds of uncertainty in a mathematical way. Furthermore, it is also shown that the genuine set theoretic descriptions of type-m fuzzy sets, intuitionistic fuzzy sets and fuzzy rough sets point out new features of these set notations, originated from the peculiar characteristics of genuine sets.
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9

Mohite, Trupti. "On Convexity of Fuzzy Sets and Fuzzy Relations." International Journal of Science and Research (IJSR) 12, no. 7 (July 5, 2023): 758–61. http://dx.doi.org/10.21275/sr23710111006.

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10

Mu, Beining. "Fuzzy Julia Sets and Fuzzy Superior Julia Sets." Highlights in Science, Engineering and Technology 72 (December 15, 2023): 375–80. http://dx.doi.org/10.54097/5c5hp748.

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This article examine the past study of fuzzy Mandelbrot set and fuzzy superior Mandelbrot set, then give the definition of fuzzy Julia sets and fuzzy superior Julia sets with the idea of utilizing membership functions to represent the escape velocity of Julia sets or superior Julia sets of each complex number in the definition of fuzzy Mandelbrot set and fuzzy superior Mandelbrot set inherited while the membership functions are selected to distinguish complex numbers with different escape velocity and same orbit. Then some examples of fuzzy Julia sets and fuzzy superior Julia sets are presented. With some observation of the examples, some analytical and topological properties of fuzzy Julia sets are demonstrated and sketches of the proofs are also presented. In the part of fuzzy superior Julia sets, some trivial conclusions as well as an example is presented where more complicated properties which involves the study into very chaotic behaviors are left open.
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11

Zimmermann, H. J. "Fuzzy sets." Fuzzy Sets and Systems 133, no. 2 (January 2003): 273–74. http://dx.doi.org/10.1016/s0165-0114(02)00360-3.

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12

Virgil Negoita, Constant. "Fuzzy Sets." Fuzzy Sets and Systems 133, no. 2 (January 2003): 275. http://dx.doi.org/10.1016/s0165-0114(02)00361-5.

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13

Mares, Milan. "Fuzzy sets." Scholarpedia 1, no. 10 (2006): 2031. http://dx.doi.org/10.4249/scholarpedia.2031.

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14

Atanassov, Krassimir. "Type-1 Fuzzy Sets and Intuitionistic Fuzzy Sets." Algorithms 10, no. 3 (September 13, 2017): 106. http://dx.doi.org/10.3390/a10030106.

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15

Çoker, Doǧan. "Fuzzy rough sets are intuitionistic L-fuzzy sets." Fuzzy Sets and Systems 96, no. 3 (June 1998): 381–83. http://dx.doi.org/10.1016/s0165-0114(97)00249-2.

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16

Sebastian, Sabu, and T. V. Ramakrishnan. "Multi-fuzzy Sets: An Extension of Fuzzy Sets." Fuzzy Information and Engineering 3, no. 1 (March 2011): 35–43. http://dx.doi.org/10.1007/s12543-011-0064-y.

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17

Lee, Keon-Myung. "Comparison of Interval-valued fuzzy sets, Intuitionistic fuzzy sets, and bipolar-valued fuzzy sets." Journal of Korean Institute of Intelligent Systems 14, no. 2 (April 1, 2004): 125–29. http://dx.doi.org/10.5391/jkiis.2004.14.2.125.

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18

Yu, Bicheng, Xuejun Zhao, Mingfa Zheng, Xiujiu Yuan, and Bei Hou. "Entropy on Intuitionistic Fuzzy Sets and Hesitant Fuzzy Sets." Journal of Mathematics 2022 (February 7, 2022): 1–10. http://dx.doi.org/10.1155/2022/1585079.

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Since the sufficient conditions for the maximum value of the intuitionistic fuzzy entropy are not unified and the hesitant fuzzy entropy cannot be compared when the lengths of the hesitation fuzzy elements are not equal, improved axiomatic definitions of intuitionistic fuzzy entropy and hesitant fuzzy entropy are proposed, and new intuitionistic fuzzy entropy and hesitant fuzzy entropy based on the improved axiomatic definitions are established. This paper defines the fuzzy entropy that satisfies the properties based on the axiomatized definition of fuzzy entropy and, based on the fuzzy entropy, defines new intuitionistic fuzzy entropy and hesitant fuzzy entropy, so that the three are unified in form. The validity and rationality of the proposed intuitionistic fuzzy entropy and hesitant fuzzy entropy are verified by analysis.
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19

Sabir, Pishtiwan O. "Generalized Semistrongly Convex Fuzzy Sets." Journal of Zankoy Sulaimani - Part A 18, no. 3 (April 21, 2016): 241–48. http://dx.doi.org/10.17656/jzs.10553.

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20

Kungumaraj, E., and K. Nirmaladevi. "Fuzzy Strongly gs Closed sets in Fuzzy Topological spaces." International Journal of Trend in Scientific Research and Development Volume-2, Issue-2 (February 28, 2018): 857–59. http://dx.doi.org/10.31142/ijtsrd9482.

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21

M.Palanisamy and A. Vadivel. "On Fuzzy e^*-Open Sets and Fuzzy (D,S)^*-Sets." International Journal of Fuzzy Mathematical Archive 14, no. 01 (2017): 101–8. http://dx.doi.org/10.22457/ijfma.v14n1a12.

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The aim of this paper is to introduce some new classes of fuzzy sets and some new classes of fuzzy continuity namely fuzzy e ∗ -open sets, fuzzy (D, S)-sets, fuzzy (DS, ε)-sets, fuzzy (D, S)∗ -sets, fuzzy (DS, ε) ∗ -sets, fuzzy e-continuity, fuzzy (D, S)∗ - continuity and fuzzy (DS, ∈)∗ -continuity. Properties of these new concepts are investigated. Moreover, some new decompositions of fuzzy continuity are provided.
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22

Aqeel, Radhwan Mohammed, and Anhar Ahmed Nasser. "On Fuzzy Pre-Λ-Sets and Fuzzy Semi-Λ- Sets." Electronic Journal of University of Aden for Basic and Applied Sciences 4, no. 1 (March 31, 2023): 139–46. http://dx.doi.org/10.47372/ejua-ba.2023.1.229.

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This paper is devoted to study the notions of fuzzy pre-Λ-set, fuzzy semi-Λ- set, fuzzy pre- V -set and fuzzy semi- V - set in fuzzy topological space. We study some properties and discuss the relationships between fuzzy pre-Λ-set, fuzzy semi-Λ- set, fuzzy pre- V -set and fuzzy semi- V - set and relevant concepts in fuzzy topological spaces and to investigate some basic yet essential properties.
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23

Pawlak, Zdzisław. "Rough sets and fuzzy sets." Fuzzy Sets and Systems 17, no. 1 (September 1985): 99–102. http://dx.doi.org/10.1016/s0165-0114(85)80029-4.

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24

Burgin, Mark, and Vladimir Kuznetsov. "Fuzzy sets as named sets." Fuzzy Sets and Systems 46, no. 2 (March 1992): 189–92. http://dx.doi.org/10.1016/0165-0114(92)90131-m.

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25

Cong, Cuong Bui, Roan Thi Ngan, and Le Ba Long. "Some New De Morgan Picture Operator Triples in Picture Fuzzy Logic." Journal of Computer Science and Cybernetics 33, no. 2 (January 3, 2018): 143–64. http://dx.doi.org/10.15625/1813-9663/33/2/10706.

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A new concept of picture fuzzy sets (PFS) were introduced in 2013, which are directextensions of the fuzzy sets and the intuitonistic fuzzy sets. Then some operations on PFS withsome properties are considered in [ 9,10 ]. Some basic operators of fuzzy logic as negation, tnorms, t-conorms for picture fuzzy sets firstly are defined and studied in [13,14]. This paper isdevoted to some classes of representable picture fuzzy t-norms and representable picture fuzzyt-conorms on PFS and a basic algebra structure of Picture Fuzzy Logic – De Morgan triples ofpicture operators.
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26

Riyadh Kareem, Noor, and . "Fuzzy tgp-closed sets and fuzzy t^* gp-closed sets." International Journal of Engineering & Technology 7, no. 4.36 (December 9, 2018): 718. http://dx.doi.org/10.14419/ijet.v7i4.36.24229.

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In this paper, we aim to address the idea of fuzzy -set and fuzzy -set in fuzzy topological space to present new types of the fuzzy closed set named fuzzy -closed set and fuzzy -closed set. We will study several examples and explain the relations of them with other classes of fuzzy closed sets. Moreover, in a fuzzy locally indiscrete space we can see that these two sets are the same.
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27

Meng, Dan, Xiaohong Zhang, and Keyun Qin. "Soft rough fuzzy sets and soft fuzzy rough sets." Computers & Mathematics with Applications 62, no. 12 (December 2011): 4635–45. http://dx.doi.org/10.1016/j.camwa.2011.10.049.

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28

Thangaraj, G., and N. Raji. "ON FUZZY BAIRE SETS AND FUZZY PSEUDO-OPEN SETS." Advances in Fuzzy Sets and Systems 28, no. 1 (June 30, 2023): 31–64. http://dx.doi.org/10.17654/0973421x23003.

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29

Yang, Yingjie, and Chris Hinde. "A new extension of fuzzy sets using rough sets: R-fuzzy sets." Information Sciences 180, no. 3 (February 2010): 354–65. http://dx.doi.org/10.1016/j.ins.2009.10.004.

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30

Saaty, Thomas L., and Liem T. Tran. "Fuzzy Judgments and Fuzzy Sets." International Journal of Strategic Decision Sciences 1, no. 1 (January 2010): 23–40. http://dx.doi.org/10.4018/jsds.2010103002.

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Using fuzzy set theory has become attractive to many people. However, the many references cited here and in other works, little thought is given to why numbers should be made fuzzy before plunging into the necessary simulations to crank out numbers without giving reason or proof that it works to one’s advantage. In fact it does not often do that, certainly not in decision making. Regrettably, many published papers that use fuzzy set theory presumably to get better answers were not judged thoroughly by reviewers knowledgeable in both fuzzy theory and decision making. Buede and Maxwell (1995), who had done experiments on different ways of making decisions, found that fuzzy does the poorest job of obtaining the right decision as compared with other ways. “These experiments demonstrated that the MAVT (Multiattribute Value Theory) and AHP (Analytic Hierarchy Process) techniques, when provided with the same decision outcome data, very often identify the same alternatives as ‘best’. The other techniques are noticeably less consistent with the Fuzzy algorithm being the least consistent.”
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31

García, Josefa M., and Pascual Jara. "Gradual Sets: An Approach to Fuzzy Sets." Advances in Fuzzy Systems 2023 (February 27, 2023): 1–18. http://dx.doi.org/10.1155/2023/6163672.

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In the fuzzy theory of sets and groups, the use of α-levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong α-levels, it is possible to establish a one to one correspondence which makes possible doubly, a gradual and a functorial treatment of the fuzzy theory. The main result of this paper is to identify the class of fuzzy sets, respectively, fuzzy groups, with subcategories of the functorial categories Set (0, 1], resp., Gr (0, 1]. In this line, the algebraic potential of this theory will be reached, in forthcoming papers.
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32

Shang, You-guang, Xue-hai Yuan, and E. Stanley Lee. "The n-dimensional fuzzy sets and Zadeh fuzzy sets based on the finite valued fuzzy sets." Computers & Mathematics with Applications 60, no. 3 (August 2010): 442–63. http://dx.doi.org/10.1016/j.camwa.2010.04.044.

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33

Močkoř, Jiří, and David Hýnar. "On Unification of Methods in Theories of Fuzzy Sets, Hesitant Fuzzy Set, Fuzzy Soft Sets and Intuitionistic Fuzzy Sets." Mathematics 9, no. 4 (February 23, 2021): 447. http://dx.doi.org/10.3390/math9040447.

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The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories. It is proven that ad hoc defined basic concepts in individual theories, such as concepts of power set structures in these theories, relations or approximation operators defined by these relations are only special examples of applications of the monad theory in categories. This makes it possible, on the one hand, to unify basic constructions in all these theories and, on the other hand, to verify the legitimacy of ad hoc definitions of these constructions in individual theories. This common background also makes it possible to transform these basic concepts from one theory to another.
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34

WEI, LI-LI, and WEN-XIU ZHANG. "PROBABILISTIC ROUGH SETS CHARACTERIZED BY FUZZY SETS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, no. 01 (February 2004): 47–60. http://dx.doi.org/10.1142/s0218488504002643.

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Theories of fuzzy sets and rough sets have emerged as two major mathematical approaches for managing uncertainty that arises from inexact, noisy, or incomplete information. They are generalizations of classical set theory for modelling vagueness and uncertainty. Some integrations of them are expected to develop a model of uncertainty stronger than either. The present work may be considered as an attempt in this line, where we would like to study fuzziness in probabilistic rough set model, to portray probabilistic rough sets by fuzzy sets. First, we show how the concept of variable precision lower and upper approximation of a probabilistic rough set can be generalized from the vantage point of the cuts and strong cuts of a fuzzy set which is determined by the rough membership function. As a result, the characters of the (strong) cut of fuzzy set can be used conveniently to describe the feature of variable precision rough set. Moreover we give a measure of fuzziness, fuzzy entropy, induced by roughness in a probabilistic rough set and make some characterizations of this measure. For three well-known entropy functions, including the Shannon function, we show that the finer the information granulation is, the less the fuzziness (fuzzy entropy) in a rough set is. The superiority of fuzzy entropy to Pawlak's accuracy measure is illustrated with examples. Finally, the fuzzy entropy of a rough classification is defined by the fuzzy entropy of corresponding rough sets. and it is shown that one possible application of it is lies in measuring the inconsistency in a decision table.
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35

Chen, Juanjuan, Shenggang Li, Shengquan Ma, and Xueping Wang. "m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/416530.

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Recently, bipolar fuzzy sets have been studied and applied a bit enthusiastically and a bit increasingly. In this paper we prove that bipolar fuzzy sets and0,12-sets (which have been deeply studied) are actually cryptomorphic mathematical notions. Since researches or modelings on real world problems often involve multi-agent, multi-attribute, multi-object, multi-index, multi-polar information, uncertainty, or/and limit process, we put forward (or highlight) the notion ofm-polar fuzzy set (actually,0,1m-set which can be seen as a generalization of bipolar fuzzy set, wheremis an arbitrary ordinal number) and illustrate how many concepts have been defined based on bipolar fuzzy sets and many results which are related to these concepts can be generalized to the case ofm-polar fuzzy sets. We also give examples to show how to applym-polar fuzzy sets in real world problems.
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36

Wu, Hsien-Chung. "Duality in Fuzzy Sets and Dual Arithmetics of Fuzzy Sets." Mathematics 7, no. 1 (December 22, 2018): 11. http://dx.doi.org/10.3390/math7010011.

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The conventional concept of α-level sets of fuzzy sets will be treated as the upper α-level sets. In this paper, the concept of lower α-level sets of fuzzy sets will be introduced, which can also be regarded as a dual concept of upper α-level sets of fuzzy sets. We shall also introduce the concept of dual fuzzy sets. Under these settings, we can establish the so-called dual decomposition theorem. We shall also study the dual arithmetics of fuzzy sets in R and establish some interesting results based on the upper and lower α-level sets.
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37

Dai, Songsong. "Quaternionic Fuzzy Sets." Axioms 12, no. 5 (May 18, 2023): 490. http://dx.doi.org/10.3390/axioms12050490.

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A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization of traditional fuzzy sets and complex fuzzy sets based on quaternions. The novelty of QFSs is that the range of the membership function is the set of quaternions with modulus less than or equal to one, of which the real and quaternionic imaginary parts can be used for four different features. A discussion is made on the intuitive interpretation of quaternion-valued membership grades and the possible applications of QFSs. Several operations, including quaternionic fuzzy complement, union, intersection, and aggregation of QFSs, are presented. Quaternionic fuzzy relations and their composition are also investigated. QFS is designed to maintain the advantages of traditional FS and CFS, while benefiting from the properties of quaternions. Cuts of QFSs and rotational invariance of quaternionic fuzzy operations demonstrate the particularity of quaternion-valued grades of membership.
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38

Yuan, Xue-hai, Hongxing Li, and E. Stanley Lee. "Three new cut sets of fuzzy sets and new theories of fuzzy sets." Computers & Mathematics with Applications 57, no. 5 (March 2009): 691–701. http://dx.doi.org/10.1016/j.camwa.2008.05.044.

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39

Stansfield, William D. "Fuzzy Data Sets." American Biology Teacher 69, no. 8 (October 1, 2007): 458–59. http://dx.doi.org/10.2307/4452204.

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40

Stansfield, William D. "Fuzzy Data Sets." American Biology Teacher 69, no. 8 (October 2007): 458–59. http://dx.doi.org/10.1662/0002-7685(2007)69[458:fds]2.0.co;2.

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41

Lan, Shu, and Pen Jia Yin. "Fuzzy complete sets." Fuzzy Sets and Systems 131, no. 3 (November 2002): 393–98. http://dx.doi.org/10.1016/s0165-0114(01)00168-3.

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42

Atanassov, Krassimir T. "Intuitionistic fuzzy sets." Fuzzy Sets and Systems 20, no. 1 (August 1986): 87–96. http://dx.doi.org/10.1016/s0165-0114(86)80034-3.

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43

Marsili-Libelli, Stefano. "Fuzzy sets engineering." Control Engineering Practice 4, no. 4 (April 1996): 581–83. http://dx.doi.org/10.1016/s0967-0661(96)90063-5.

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44

Cios, Krzysztof. "Fuzzy sets engineering." Neurocomputing 9, no. 3 (December 1995): 357–58. http://dx.doi.org/10.1016/0925-2312(95)90001-2.

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45

Nakajima, Nobuyuki. "Generalized fuzzy sets." Fuzzy Sets and Systems 32, no. 3 (September 1989): 307–14. http://dx.doi.org/10.1016/0165-0114(89)90262-5.

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46

Nanda, S., and S. Majumdar. "Fuzzy rough sets." Fuzzy Sets and Systems 45, no. 2 (January 1992): 157–60. http://dx.doi.org/10.1016/0165-0114(92)90114-j.

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47

Venugopalan, P. "Fuzzy ordered sets." Fuzzy Sets and Systems 46, no. 2 (March 1992): 221–26. http://dx.doi.org/10.1016/0165-0114(92)90134-p.

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48

Drossos, C. A., and G. Markakis. "Boolean fuzzy sets." Fuzzy Sets and Systems 46, no. 1 (February 1992): 81–95. http://dx.doi.org/10.1016/0165-0114(92)90269-a.

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49

Rasiowa, Helena, and Nguyen Cat Ho. "LT-fuzzy sets." Fuzzy Sets and Systems 47, no. 3 (May 1992): 323–39. http://dx.doi.org/10.1016/0165-0114(92)90298-i.

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50

Li, Q., P. Wang, and E. S. Lee. "r-fuzzy sets." Computers & Mathematics with Applications 31, no. 2 (January 1996): 49–61. http://dx.doi.org/10.1016/0898-1221(95)00192-1.

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