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Journal articles on the topic 'Theory of fuzzy logic'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

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 (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 t

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2

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

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3

Ching, Hugh. "The Fuzzy Completeness Theory." Journal of Research in Philosophy and History 4, no. 1 (2021): p52. http://dx.doi.org/10.22158/jrph.v4n1p52.

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The Two Incompleteness Theorems of Kurt Friedrich Gödel and the Impossibility Theorem of Kenneth Arrow claim that logic, the most reliable of human knowledge, is incomplete or can be inconsistent. The Fuzzy Completeness Theory states that the Fuzzy Logic of Lotfi A. Zadeh has resolved the incompleteness and impossibility in logic and made logic complete and knowledge reliable with the new concept of Range of Tolerance, within which logic is still complete and knowledge, valid. In the Age of Reason about 300 years ago just prior to the Age of Science, reasoning is free for all, without the cons

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Maseleno, Andino, Md Mahmud Hasan, and Norjaidi Tuah. "Combining Fuzzy Logic and Dempster-Shafer Theory." TELKOMNIKA Indonesian Journal of Electrical Engineering 16, no. 3 (2015): 583. http://dx.doi.org/10.11591/tijee.v16i3.1651.

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This research aims to combine the mathematical theory of evidence with the rule based logics to refine the predictable output. Integrating Fuzzy Logic and Dempster-Shafer theory by calculating the similarity between Fuzzy membership function. The novelty aspect of this work is that basic probability assignment is proposed based on the similarity measure between membership function. The similarity between Fuzzy membership function is calculated to get a basic probability assignment. The Dempster-Shafer mathematical theory of evidence has attracted considerable attention as a promising method of

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PUNČOCHÁŘ, VÍT. "SUBSTRUCTURAL INQUISITIVE LOGICS." Review of Symbolic Logic 12, no. 2 (2019): 296–330. http://dx.doi.org/10.1017/s1755020319000017.

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AbstractThis paper shows that any propositional logic that extends a basic substructural logic BSL (a weak, nondistributive, nonassociative, and noncommutative version of Full Lambek logic with a paraconsistent negation) can be enriched with questions in the style of inquisitive semantics and logic. We introduce a relational semantic framework for substructural logics that enables us to define the notion of an inquisitive extension of λ, denoted as ${\lambda ^?}$, for any logic λ that is at least as strong as BSL. A general theory of these “inquisitive extensions” is worked out. In particular,

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Arfi, Badredine. "Linguistic Fuzzy-Logic Game Theory." Journal of Conflict Resolution 50, no. 1 (2006): 28–57. http://dx.doi.org/10.1177/0022002705284708.

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Heubo-Kwegna, Olivier A. "Fuzzy Logic versus Classical Logic: An Example in Multiplicative Ideal Theory." Advances in Fuzzy Systems 2016 (2016): 1–4. http://dx.doi.org/10.1155/2016/3839265.

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We discuss a fuzzy result by displaying an example that shows how a classical argument fails to work when one passes from classical logic to fuzzy logic. Precisely, we present an example to show that, in the fuzzy context, the fact that the supremum is naturally used in lieu of the union can alter an argument that may work in the classical context.

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Lano, K. "Intuitionistic modal logic and set theory." Journal of Symbolic Logic 56, no. 2 (1991): 497–516. http://dx.doi.org/10.2307/2274696.

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The mathematical treatment of the concepts of vagueness and approximation is of increasing importance in artificial intelligence and related research. The theory of fuzzy sets was created by Zadeh [Z] to allow representation and mathematical manipulation of situations of partial truth, and proceeding from this a large amount of theoretical and applied development of this concept has occurred. The aim of this paper is to develop a natural logic and set theory that is a candidate for the formalisation of the theory of fuzzy sets. In these theories the underlying logic of properties and sets is i

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Wedding, Donald K. "Fuzzy sets and fuzzy logic: Theory and applications." Neurocomputing 14, no. 3 (1997): 302–3. http://dx.doi.org/10.1016/s0925-2312(97)88327-0.

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10

Rouvray, Dennis H. "Fuzzy sets and fuzzy logic: Theory and applications." Endeavour 20, no. 1 (1996): 44. http://dx.doi.org/10.1016/s0160-9327(96)90083-6.

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11

Lakov, Dimiter. "Fuzzy sets and fuzzy logic, theory and applications." Fuzzy Sets and Systems 84, no. 1 (1996): 114. http://dx.doi.org/10.1016/0165-0114(96)82406-7.

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12

Simon, Dan. "Fuzzy sets and fuzzy logic: Theory and applications." Control Engineering Practice 4, no. 9 (1996): 1332–33. http://dx.doi.org/10.1016/0967-0661(96)81492-4.

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13

Tamir, Dan E., and Abraham Kandel. "Axiomatic Theory of Complex Fuzzy Logic and Complex Fuzzy Classes." International Journal of Computers Communications & Control 6, no. 3 (2011): 562. http://dx.doi.org/10.15837/ijccc.2011.3.2135.

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Complex fuzzy sets, classes, and logic have an important role in applications, such as prediction of periodic events and advanced control systems, where several fuzzy variables interact with each other in a multifaceted way that cannot be represented effectively via simple fuzzy operations such as union, intersection, complement, negation, conjunction and disjunction. The initial formulation of these terms stems from the definition of complex fuzzy grade of membership. The problem, however, with these definitions are twofold: 1) the complex fuzzy membership is limited to polar representation w

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14

M., Bhuvaneswari, Daniel Samson P., and Anish V. "Fuzzy Logic." International Journal of Trend in Scientific Research and Development 4, no. 2 (2020): 884–87. https://doi.org/10.5281/zenodo.3843157.

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This paper proposes a detailed switching model for the medium voltage cascaded H bridge multi level inverter drive and induction motor system using fuzzy logic controller which is suitable for power system dynamic studies. The model includes the We describe in this book recent advances in the fuzzy logic based augmentation of neural networks and in optimization algorithms and their application in areas fuzzy logic can help design robust individual behaviours units. Fuzzy logic controllers incorporate heuristic control knowledge. It is convenient choice when a precise linear model of the system

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15

PERLOVSKY, LEONID I. "FUZZY DYNAMIC LOGIC." New Mathematics and Natural Computation 02, no. 01 (2006): 43–55. http://dx.doi.org/10.1142/s1793005706000300.

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Fuzzy logic is extended toward dynamic adaptation of the degree of fuzziness. The motivation is to explain the process of learning as a joint model improvement and fuzziness reduction. A learning system with fuzzy models is introduced. Initially, the system is in a highly fuzzy state of uncertain knowledge, and it dynamically evolves into a low-fuzzy state of certain knowledge. We present an image recognition example of patterns below clutter. The paper discusses relationships to formal logic, fuzzy logic, complexity and draws tentative connections to Aristotelian theory of forms and working o

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Imran, Hassan, and Kar Suman. "The application of fuzzy logic techniques to improve decision making in apparel size." World Journal of Advanced Research and Reviews 19, no. 2 (2023): 607–15. https://doi.org/10.5281/zenodo.10842475.

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Traditional set theory, or crisp set theory, is built on the concept of crisp sets. These are sets for which the membership of an element within a set is defined as either true or false; in or out; 1 or 0. This construction is extremely useful, as mathematics has shown, but it struggles to model concepts of our world that possess vagueness or uncertainty. Therefore, we explore an expansion of set theory to allow an element to be partially within a set, thus constituting what is known as a fuzzy set. This paper introduces the basic concept of fuzzy sets, which includes fuzzy sets and crisp sets

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17

Vitez, Terry Stephen, Russell Wada, and Alex Macario. "Fuzzy logic: Theory and medical applications." Journal of Cardiothoracic and Vascular Anesthesia 10, no. 6 (1996): 800–808. http://dx.doi.org/10.1016/s1053-0770(96)80210-2.

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18

Kaufmann, A. "Theory of expertons and fuzzy logic." Fuzzy Sets and Systems 28, no. 3 (1988): 295–304. http://dx.doi.org/10.1016/0165-0114(88)90036-x.

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19

Běhounek, Libor, and Petr Cintula. "Fuzzy class theory." Fuzzy Sets and Systems 154, no. 1 (2005): 34–55. http://dx.doi.org/10.1016/j.fss.2004.12.010.

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20

Journal, Baghdad Science. "Study and Analysis the Mathematical Operations of Fuzzy Logic." Baghdad Science Journal 6, no. 3 (2009): 526–32. http://dx.doi.org/10.21123/bsj.6.3.526-532.

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The last decade of this 20th century provides a wide spread of applications of one of the computer techniques, which is called Fuzzy Logic. This technique depends mainly on the fuzzy set theory, which is considered as a general domain with respect to the conventional set theory. This paper presents in initiative the fuzzy sets theory and fuzzy logic as a complete mathematics system. Here it was explained the concept of fuzzy set and defined the operations of fuzzy logic. It contains eleven operations beside the other operations which related to fuzzy algebra. Such search is considered as an en

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Saleh, Muna Hadi. "Study and Analysis the Mathematical Operations of Fuzzy Logic." Baghdad Science Journal 6, no. 3 (2009): 526–32. http://dx.doi.org/10.21123/bsj.2009.6.3.526-532.

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The last decade of this 20th century provides a wide spread of applications of one of the computer techniques, which is called Fuzzy Logic. This technique depends mainly on the fuzzy set theory, which is considered as a general domain with respect to the conventional set theory. This paper presents in initiative the fuzzy sets theory and fuzzy logic as a complete mathematics system. Here it was explained the concept of fuzzy set and defined the operations of fuzzy logic. It contains eleven operations beside the other operations which related to fuzzy algebra. Such search is considered as an en

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22

Sultanova, A., and Sh. Guliyeva. "GENERALIZED EXPERT OPINION BASED ON FUZZY NUMBER." Sciences of Europe, no. 113 (March 27, 2023): 78–81. https://doi.org/10.5281/zenodo.7773844.

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Fuzzy logic is a mathematical discipline that brings structure to the way we use and interpret our behavior in our daily lives. We see concepts of fuzzy logic in many places of our life. Fuzzy logic is particularly useful in highly complex systems that are difficult to understand and interpret, and in processes that rely on human thought, perception, or decision-making. Fuzzy theory, which is the basis of fuzzy logic, is a mathematical expression of fuzzy concepts. Another innovation in fuzzy theory is the nature of the information used. Fuzzy theory uses perceptual knowledge rather than measu

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23

Tran, Tien. "The Optimization of Marine Diesel Engine Rotational Speed Control Process by Fuzzy Logic Control Based on Particle Swarm Optimization Algorithm." Future Internet 10, no. 10 (2018): 99. http://dx.doi.org/10.3390/fi10100099.

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The marine main diesel engine rotational speed automatic control plays a significant role in determining the optimal main diesel engine speed under impacting on navigation environment conditions. In this article, the application of fuzzy logic control theory for main diesel engine speed control has been associated with Particle Swarm Optimization (PSO). Firstly, the controller is designed according to fuzzy logic control theory. Secondly, the fuzzy logic controller will be optimized by Particle Swarm Optimization (PSO) in order to obtain the optimal adjustment of the membership functions only.

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24

Graeme, Heald. "Issues with Reliability of Fuzzy Logic." International Journal of Trend in Scientific Research and Development 2, no. 6 (2018): 829–34. https://doi.org/10.31142/ijtsrd18573.

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Since 1973, fuzzy logic has been rejected by a majority of linguists as a theory for dealing with vagueness in natural language. However, control engineers apply fuzzy vagueness in natural language to control system problems. A real world example of automatic fan control has shown that i fuzzy logic can be applied ii probability theory can better model the control system iii Boolean algebra with decision processes can also be applied. In addition, a redundancy issue for fuzzy logic has been raised. Moreover, a number of inherent flaws of fuzzy logic from an engineering viewpoint have been iden

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25

Lasaraiya, Suriana, Mohd Azrul Abd Rajak, Che Haziqah Che Hussin, and Nurliyana Juhan. "A COMPARISON ON STUDENTS’ PERFORMANCE IN MATHEMATICS SUBJECT USING FUZZY LOGIC THEORY." Journal of Information System and Technology Management 7, no. 29 (2022): 86–96. http://dx.doi.org/10.35631/jistm.729007.

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The education system in Malaysia employs classical method in evaluation students’ progress performances during their foundation level. The result was obtained by adding all the assessments scored and was graded based on grade A, A-, B+, B, …, and F. Somehow, non-classical methods may be applied such as fuzzy logic, where it can be applied to many forms of decision making. This paper proposed evaluation on students’ performances by using fuzzy logic approach. The assessment score obtained based on their assignment, midterm examination and final term examination of 26 Agriscience students, in Pr

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26

Dukić, Nedžad. "The Semantic Distance, Fuzzy Dependency and Fuzzy Formulas." Sarajevo Journal of Mathematics 2, no. 2 (2024): 137–46. http://dx.doi.org/10.5644/sjm.02.2.01.

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In this paper we establish a connection between one fragment fuzzy logic and the theory of fuzzy functional dependencies on the basic of the semantic distance. We give a way to interpret fuzzy functional dependencies as formulas in fuzzy logic. For a set of fuzzy dependencies $F$ and single fuzzy functional dependency $f,$ we show that $F$ implies $f$ as fuzzy functional dependencies if and only if $F$ implies $f$ under the logic interpretation. 2000 Mathematics Subject Classification. 03B52

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27

Demir Sağlam, Sevilay, and Gül Karadeniz Gözeri. "Some Properties of Boolean-like Laws in Fuzzy Logic." Symmetry 17, no. 4 (2025): 548. https://doi.org/10.3390/sym17040548.

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This article focuses on the relationships between fuzzy logic and classical logic properties using fuzzy t-norms, t-conorms, and fuzzy implications. It aims to contribute to fuzzy set theory by extending the Boolean laws in classical logic to fuzzy logic. We determine the necessary and sufficient conditions for validating the generalizations of the proposed properties from classical to fuzzy logic. Additionally, we provide examples demonstrating the practical applicability of this approach and its advantages over conventional methodologies, reinforcing its effectiveness.

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28

Saleem, Adeel, Kholiddinov Ilkhombek Khosiljonovich, Kholiddinova Mashkhurakhon Mutalibjon Qizi, Komolddinov Sokhib, Sharobiddinov MirzohidShakhobiddin Ugli, and Soliev Sokhibjon Obidovich. "Estimation of powerquality in distribution system using fuzzy logic theory." Indonesian Journal of Electrical Engineering and Computer Science 32, no. 3 (2023): 1236. http://dx.doi.org/10.11591/ijeecs.v32.i3.pp1236-1245.

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There are several methods are used to calculate the power quality indicators. These objectives are now served by the most recent soft computing theories, such as neural networks, fuzzy time series, fuzzy logic theory, and other techniques. The fuzzy logic theory is one of the methods used to calculate the power quality indicators for the distribution electric network in this paper. It resolves the issue of forecasting the voltage values on distribution electrical networks' buses and enhances the quality of electricity in the face of fluctuating consumer loads and uncertainty. This paper propos

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Mohammed, Mohammed Jasim. "Literature Review of Fuzzy Set Theory: Applications and Methodologies." Journal of Economics and Administrative Sciences 31, no. 146 (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 existin

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30

Guang-Quan, Zhang. "Fuzzy limit theory of fuzzy complex numbers." Fuzzy Sets and Systems 46, no. 2 (1992): 227–35. http://dx.doi.org/10.1016/0165-0114(92)90135-q.

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31

LIAU, CHURN JUNG, and BERTRAND I.-PENG LIN. "FUZZY LOGIC WITH EQUALITY." International Journal of Pattern Recognition and Artificial Intelligence 02, no. 02 (1988): 351–65. http://dx.doi.org/10.1142/s0218001488000212.

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The concept of fuzzy equality and its related contents to the first order predicate calculus are discussed. It is proved that, in the viewpoint of computational logic, resolution and paramodulation mechanisms are complete and sound for fuzzy logic with equality. Term rewriting system, that is the set of left to right directional equations, provides an essential computational paradigm for word problems in universal algebra. We embody the fuzzy equality to the theory of this computation system and give an algorithmic solution to the word problems in fuzzy algebra.

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32

Ma, Z. M., Fu Zhang, Hailong Wang, and Li Yan. "An overview of fuzzy Description Logics for the Semantic Web." Knowledge Engineering Review 28, no. 1 (2012): 1–34. http://dx.doi.org/10.1017/s0269888912000306.

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AbstractInformation imprecision and uncertainty exist in many real world applications, and such information would be retrieved, processed, shared, reused, and aligned in the maximum automatic way possible. As a popular family of formally well-founded and decidable knowledge representation languages, fuzzy Description Logics (fuzzy DLs), which extend DLs with fuzzy logic, are very well suited to cover for representing and reasoning with imprecision and uncertainty. Thus, a requirement naturally arises in many practical applications of knowledge-based systems, in particular the Semantic Web, bec

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33

Burstein, Gabriel, Constantin Virgil Negoita, and Menachem Kranz. "Kabbalah Logic and Semantic Foundations for a Postmodern Fuzzy Set and Fuzzy Logic Theory." Applied Mathematics 05, no. 09 (2014): 1375–85. http://dx.doi.org/10.4236/am.2014.59129.

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34

Imran Hassan and Suman Kar. "The application of fuzzy logic techniques to improve decision making in apparel size." World Journal of Advanced Research and Reviews 19, no. 2 (2023): 607–15. http://dx.doi.org/10.30574/wjarr.2023.19.2.1576.

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Traditional set theory, or crisp set theory, is built on the concept of crisp sets. These are sets for which the membership of an element within a set is defined as either true or false; in or out; 1 or 0. This construction is extremely useful, as mathematics has shown, but it struggles to model concepts of our world that possess vagueness or uncertainty. Therefore, we explore an expansion of set theory to allow an element to be partially within a set, thus constituting what is known as a fuzzy set. This paper introduces the basic concept of fuzzy sets, which includes fuzzy sets and crisp sets

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35

Macho Stadler, M., and M. A. de Prada Vicente. "Fuzzy t-net theory." Fuzzy Sets and Systems 37, no. 2 (1990): 225–35. http://dx.doi.org/10.1016/0165-0114(90)90045-8.

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36

Zhang, Xiaohong, Xiangyu Ma, and Xuejiao Wang. "Filters in Strong BI-Algebras and Residuated Pseudo-SBI-Algebras." Mathematics 8, no. 9 (2020): 1513. http://dx.doi.org/10.3390/math8091513.

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The concept of basic implication algebra (BI-algebra) has been proposed to describe general non-classical implicative logics (such as associative or non-associative fuzzy logic, commutative or non-commutative fuzzy logic, quantum logic). However, this algebra structure does not have enough characteristics to describe residual implications in depth, so we propose a new concept of strong BI-algebra, which is exactly the algebraic abstraction of fuzzy implication with pseudo-exchange principle (PEP). Furthermore, in order to describe the characteristics of the algebraic structure corresponding to

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37

BOUCHET, AGUSTINA, JUAN IGNACIO PASTORE, RAFAEL ESPIN ANDRADE, MARCEL BRUN, and VIRGINIA BALLARIN. "ARITHMETIC MEAN BASED COMPENSATORY FUZZY LOGIC." International Journal of Computational Intelligence and Applications 10, no. 02 (2011): 231–43. http://dx.doi.org/10.1142/s1469026811003070.

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Fuzzy Logic is a multi-valued logic model based on fuzzy set theory, which may be considered as an extension of Boolean Logic. One of the fields of this theory is the Compensatory Fuzzy Logic, based on the removal of some axioms in order to achieve a sensitive and idempotent multi-valued system. This system is based on a quadruple of continuous operators: conjunction, disjunction, order and negation. In this work we present a new model of Compensatory Fuzzy Logic based on a different set of operators, conjunction and disjunction, than the ones used in the original definition, and then prove th

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38

Weigert, Thomas J., Jing-Pha Tsai, and Xuhua Liu. "Fuzzy operator logic and fuzzy resolution." Journal of Automated Reasoning 10, no. 1 (1993): 59–78. http://dx.doi.org/10.1007/bf00881864.

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39

Guang-Yuan, Wang, and Ou Jin-Ping. "Theory of fuzzy random vibration with fuzzy parameters." Fuzzy Sets and Systems 36, no. 1 (1990): 103–12. http://dx.doi.org/10.1016/0165-0114(90)90084-j.

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40

Frič, Roman. "Łukasiewicz Logic and the Divisible Extension of Probability Theory." Tatra Mountains Mathematical Publications 78, no. 1 (2021): 119–28. http://dx.doi.org/10.2478/tmmp-2021-0008.

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Abstract We show that measurable fuzzy sets carrying the multivalued Łukasiewicz logic lead to a natural generalization of the classical Kolmogorovian probability theory. The transition from Boolean logic to Łukasiewicz logic has a categorical background and the resulting divisible probability theory possesses both fuzzy and quantum qualities. Observables of the divisible probability theory play an analogous role as classical random variables: to convey stochastic information from one system to another one. Observables preserving the Łukasiewicz logic are called conservative and characterize t

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Sharma, Anshul, C. K. Susheel, Rajeev Kumar, and V. S. Chauhan. "Active Control of Thermally Induced Vibrations in Smart Structure Instrumented with Piezoelectric Materials." Applied Mechanics and Materials 612 (August 2014): 169–74. http://dx.doi.org/10.4028/www.scientific.net/amm.612.169.

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In this paper, a finite element model of piezolaminated composite shell structure is developed using nine-noded degenerated shell element. The stiffness, mass and thermo-electro-mechanical coupling effect is incorporated in finite element modeling using first order shear deformation theory and linear piezoelectric theory. The sensor voltage is calculated using the same formulation and fuzzy logic controller is used to calculate the actuator voltage. The fuzzy logic controller is designed as double input-single output (DISO) system using 49 If-Then rules. The performance of fuzzy logic controll

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42

Ardin, Cemal. "Applying fuzzy logic theory to performance management." Pressacademia 5, no. 1 (2017): 153–62. http://dx.doi.org/10.17261/pressacademia.2017.584.

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43

Abreu, T., C. Minussi, M. Lopes, U. Alves, and A. Lotufo. "Electrical Customer Profile Using Fuzzy Logic Theory." IEEE Latin America Transactions 18, no. 08 (2020): 1353–61. http://dx.doi.org/10.1109/tla.2020.9111670.

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Mouzouris, G. C., and J. M. Mendel. "Nonsingleton fuzzy logic systems: theory and application." IEEE Transactions on Fuzzy Systems 5, no. 1 (1997): 56–71. http://dx.doi.org/10.1109/91.554447.

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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 uni

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Sayed, Osama R., Ayman A. Aly, and Shaoyu Zhang. "Intuitionistic Fuzzy Topology Based on Intuitionistic Fuzzy Logic." Symmetry 14, no. 8 (2022): 1613. http://dx.doi.org/10.3390/sym14081613.

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There are many symmetries in intuitionistic fuzzifying topology. In the present paper, the notion of intuitionistic fuzzifying topology as an extension of fuzzifying topology and a preliminary of the research on bi-intuitionistic fuzzy topology is introduced. A theory of intuitionistic fuzzy topology with the semantic method of intuitionistic fuzzy logic is established.

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PAPADOPOULOS, BASIL K., and APOSTOLOS SYROPOULOS. "FUZZY SETS AND FUZZY RELATIONAL STRUCTURES AS CHU SPACES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 08, no. 04 (2000): 471–79. http://dx.doi.org/10.1142/s0218488500000319.

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Chu spaces, which derive from the Chu construct of *-autonomous categories, can be used to represent most mathematical structures. Moreover, the logic of Chu spaces is linear logic. Most efforts to incorporate fuzzy set theory into the realm of linear logic are based on the assumption that fuzzy and linear negation are identical operations. We propose an incorporation based on the opposite assumption and we provide an interpretation of some linear connectives. Furthermore, we show that it is possible to represent any fuzzy relational structure as a Chu space by means of the functor G.

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Abobala, Mohammad. "On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations." Galoitica: Journal of Mathematical Structures and Applications 10, no. 1 (2023): 17–25. http://dx.doi.org/10.54216/gjmsa.0100102.

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Despite the great and rapid progress in the study of Fuzzy Logic and its applications in various scientific fields, it has not yet been used to build a consistent number theory like classical number theory. This research provides for the first time a conception of the concepts of number theory based on fuzzy logic and fuzzy membership functions, where it defines the division process, the fuzzy congruence, the greatest common divisor between integers with a fuzzy membership function. On the other hand, it presents many famous Diophantine equations formulated using fuzzy sets, in addition to man

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Sharma, Anshul, C. K. Susheel, Rajeev Kumar, and V. S. Chauhan. "Fuzzy Logic Based Active Vibration Controller." Applied Mechanics and Materials 367 (August 2013): 357–62. http://dx.doi.org/10.4028/www.scientific.net/amm.367.357.

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This paper presents fuzzy logic approach for active vibration control of composite shell structure using collocated piezoelectric sensor/actuator. The vibratory response of piezolaminated composite shell is modeled using degenerated finite shell element. Modeling is based upon first order shear deformation theory and linear piezoelectric theory. The fuzzy IF-THEN rules are established on analysis of the motion traits of laminated composite shell. The fuzzy logic controller (FLC) is designed using the sensor voltage and its derivative as inputs and actuator voltage as output. The simulation res

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Yang, Eunsuk. "Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics." Axioms 10, no. 4 (2021): 273. http://dx.doi.org/10.3390/axioms10040273.

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Recently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic MIAL (Mianorm logic) and its axiomatic extensions, together with their algebraic semantics. Next, we introduce two kinds of ternary relational semantics, called here linear Urquhart-style and Fine-style Routley–Meyer semantics, for them as algebraic Routley–Meyer-style semantics.

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