Статті в журналах: "Fuzzy logic theory"

1

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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2

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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3

Ching, Hugh. "The Fuzzy Completeness Theory." Journal of Research in Philosophy and History 4, no. 1 (February 24, 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 constraint of the laws of nature, which would be discovered in the Age of Science. However, the Scientific Method of reasoning by empirical verification depends so much on faith that it is logically and empirically dismissed by mathematicians and logicians, especially, after the exposure by Thomas Kuhn and Paul Feyerabend that a scientific advancement is akin to a religious conversion. On the other hand, mathematicians and logicians have been working steadily to find the limit of reliable knowledge. In the current state of knowledge, Kurt Gödel has the last word with his Two Incompleteness Theorems, which conclude that the most reliable of human knowledge, logic, is incomplete, casting doubt whether knowledge is completely reliable. Gödel’s view is further supported by the Impossibility Theorem of Kenneth Arrow. However, Zadeh and the author of this paper extend Zadeh’s concept of Range of Value in Fuzzy Logic to that of Range of Tolerance. Accordingly, Fuzzy Logic deals with the sacrifice of precision in the process of expanding the Range of Tolerance of a creation in order for the creation to survive and flourish for all the possibility of an uncertain future. In knowledge, incompleteness in logic can be resolved by the Range of Tolerance covering the incomplete part or ignoring the infrequent impossibilities, and, thus, making logic valid, again. Knowledge is derived generally from reason. Technically, the Fuzzy Completeness Theory classifies 16 Methods of Reason. The 16 Methods are the combination of the 4 basic Methods of Reason: 1) Logic, 2) Mathematics, 3) Empirical Verification, and 4) Others, each of which has 2 forms: 1) Fuzzy and 2) Exact and two types: 1) Complete and 2) Incomplete. Gödel, Arrow, and the Author agree that no matter how rigorous is the Method of Reason the reason cannot be complete, when the reason is Exact. When a solution is newly defined as an answer within the Range of Tolerance of the solution, Fuzzy Logic resolves the incompleteness in logic and becomes the new foundation of knowledge, replacing Exact Logic. With this definition of a solution, Fuzzy Logic covers the incomplete or the impossible parts of the solution by expanding sufficiently the Range of Tolerance to make reason complete and knowledge reliable, but only within the Range of Tolerance. To summarize, even though the world’s leading intellectuals have proven, directly, that logic is incomplete and, indirectly, that knowledge is invalid, reality is still operating smoothly, and science has even demonstrated the power of knowledge. The conflict between the most reliable knowledge, namely, logic and the real world is resolved by Fuzzy Logic, which introduces the new concept of Range of Tolerance, within which reality can still operate in accordance with the laws discovered by knowledge. In sum, reality is fuzzy, not exact. The breakthrough impact of this paper centers around completeness theory and Fuzzy Logic. In the early 21st century, the mainstream knowledge is still not aware that the supply and demand model is incomplete, and that the DNA-protein system resembles computer science based on logic more than science based on experimentation. The current computer is based on exact logic and is designed for temporary existence, while the living system is design for permanent existence and must depend on the Range of Tolerance based on Fuzzy Logic to survive permanently in an uncertain future. Financial crises will be caused by the unstable investment return, which is the incomplete part in the supply demand model. Complexity crises will be caused by the lack of the requirement of permanence or complete automation, which is the ultimate solution to unlimited complexity. The 16 Methods of Reason correspond roughly to Culture Level Quotient (CLQ), which is a non-technical measure of a person, a people or a nation.

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4

Maseleno, Andino, Md Mahmud Hasan, and Norjaidi Tuah. "Combining Fuzzy Logic and Dempster-Shafer Theory." TELKOMNIKA Indonesian Journal of Electrical Engineering 16, no. 3 (December 1, 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 dealing with some of the basic problems arising in combination of evidence and data fusion. Dempster-Shafer theory provides the ability to deal with ignorance and missing information. The foundation of Fuzzy logic is natural language which can help to make full use of expert information.

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5

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

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6

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

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7

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

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8

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

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9

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

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10

Lano, K. "Intuitionistic modal logic and set theory." Journal of Symbolic Logic 56, no. 2 (June 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 intuitionistic, but there is a subset of formulae that are ‘crisp’, classical and two-valued, which represent the certain information. Quantum logic or logics weaker than intuitionistic can also be adopted as the basis, as described in [L]. The relationship of this theory to the intensional set theory MZF of [Gd] and the global intuitionistic set theory GIZF of Takeuti and Titani [TT] is also treated.

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11

PUNČOCHÁŘ, VÍT. "SUBSTRUCTURAL INQUISITIVE LOGICS." Review of Symbolic Logic 12, no. 2 (February 1, 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, it is shown how to axiomatize ${\lambda ^?}$, given the axiomatization of λ. Furthermore, the general theory is applied to some prominent logical systems in the class: classical logic Cl, intuitionistic logic Int, and t-norm based fuzzy logics, including for example Łukasiewicz fuzzy logic Ł. For the inquisitive extensions of these logics, axiomatization is provided and a suitable semantics found.

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12

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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13

PERLOVSKY, LEONID I. "FUZZY DYNAMIC LOGIC." New Mathematics and Natural Computation 02, no. 01 (March 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 of the mind.

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14

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 (September 1, 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 with only one fuzzy component. 2) The definition is based on grade of membership and is lacking the rigor of axiomatic formulation. A new interpretation of complex fuzzy membership enables polar and Cartesian representation of the membership function where the two function components carry uncertain information. Moreover, the new interpretation is used to define complex fuzzy classes and develop an axiomatic based theory of complex propositional fuzzy logic. Additionally, the generalization of the theory to multidimensional fuzzy grades of membership has been demonstrated. In this paper we propose an axiomatic framework for first order predicate complex fuzzy logic and use this framework for axiomatic definition of complex fuzzy classes. We use these rigorous definitions to exemplify inference in complex economic systems. The new framework overcomes the main limitations of current theory and provides several advantages. First, the derivation of the new theory is based on axiomatic approach and does not assume the existence of complex fuzzy sets or complex fuzzy classes. Second, the new form significantly improves the expressive power and inference capability of complex fuzzy logic and class theory. The paper surveys the current state of complex fuzzy sets, complex fuzzy classes, and complex fuzzy logic; and provides an axiomatic basis for first order predicate complex fuzzy logic and complex class theory.

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15

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

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16

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

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17

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

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18

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

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19

LIAU, CHURN JUNG, and BERTRAND I.-PENG LIN. "FUZZY LOGIC WITH EQUALITY." International Journal of Pattern Recognition and Artificial Intelligence 02, no. 02 (June 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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20

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

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21

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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22

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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23

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

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24

Ardin, Cemal. "Applying fuzzy logic theory to performance management." Pressacademia 5, no. 1 (June 30, 2017): 153–62. http://dx.doi.org/10.17261/pressacademia.2017.584.

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25

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 (August 2020): 1353–61. http://dx.doi.org/10.1109/tla.2020.9111670.

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26

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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27

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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28

Journal, Baghdad Science. "Study and Analysis the Mathematical Operations of Fuzzy Logic." Baghdad Science Journal 6, no. 3 (September 6, 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 enhancement for supporting the others waiting search activities in this field.

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29

Ramot, D., M. Friedman, G. Langholz, and A. Kandel. "Complex fuzzy logic." IEEE Transactions on Fuzzy Systems 11, no. 4 (August 2003): 450–61. http://dx.doi.org/10.1109/tfuzz.2003.814832.

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30

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 (October 4, 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. Finally, the fuzzy logic controller has been completely innovated by Particle Swarm Optimization algorithm. The study results will be represented under digital simulation form, as well as comparison between traditional fuzzy logic controller with fuzzy logic control–particle swarm optimization speed controller being obtained.

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31

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 (June 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 that this new model satisfies the required axioms. As an example, we present an application to decision-making, comparing the results against the ones based on the original model.

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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 (October 31, 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, because DLs are the logical foundation of the Semantic Web. Currently, there have been lots of fuzzy extensions of DLs with Zadeh's fuzzy logic theory papers published, to investigate fuzzy DLs and more importantly serve as identifying the direction of fuzzy DLs study. In this paper, we aim at providing a comprehensive literature overview of fuzzy DLs, and we focus our attention on fuzzy extensions of DLs based on fuzzy set theory. Other relevant formalisms that are based on approaches like probabilistic theory or non-monotonic logics are covered elsewhere. In detail, we first introduce the existing fuzzy DLs (including the syntax, semantics, knowledge base, and reasoning algorithm) from the origin, development (from weaker to stronger in expressive power), some special techniques, and so on. Then, the other important issues on fuzzy DLs, such as reasoning, querying, applications, and directions for future research, are also discussed in detail. Also, we make a comparison and analysis.

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33

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 results illustrate that this controller has more superiority than the conventional controller.

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34

Perfilieva, Irina. "Fuzzy transforms: Theory and applications." Fuzzy Sets and Systems 157, no. 8 (April 2006): 993–1023. http://dx.doi.org/10.1016/j.fss.2005.11.012.

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35

Běhounek, Libor, Ulrich Bodenhofer, and Petr Cintula. "Relations in Fuzzy Class Theory:." Fuzzy Sets and Systems 159, no. 14 (July 2008): 1729–72. http://dx.doi.org/10.1016/j.fss.2007.10.012.

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36

Kroupa, Tomáš. "Filters in fuzzy class theory." Fuzzy Sets and Systems 159, no. 14 (July 2008): 1773–87. http://dx.doi.org/10.1016/j.fss.2008.01.002.

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37

McLean, R. G., and M. W. Warner. "Locale theory and fuzzy topology." Fuzzy Sets and Systems 54, no. 1 (February 1993): 91–97. http://dx.doi.org/10.1016/0165-0114(93)90364-n.

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38

Onisawa, Takehisa. "Fuzzy theory in reliability analysis." Fuzzy Sets and Systems 30, no. 3 (May 1989): 361–63. http://dx.doi.org/10.1016/0165-0114(89)90031-6.

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39

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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40

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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41

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 (August 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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42

Yang, Eunsuk. "Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics." Axioms 10, no. 4 (October 25, 2021): 273. http://dx.doi.org/10.3390/axioms10040273.

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Анотація:

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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43

Frič, Roman. "Łukasiewicz Logic and the Divisible Extension of Probability Theory." Tatra Mountains Mathematical Publications 78, no. 1 (October 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 the “classical core” of divisible probability theory. They send crisp random events to crisp random events and Dirac probability measures to Dirac probability measures. The nonconservative observables send some crisp random events to genuine fuzzy events and some Dirac probability measures to nondegenerated probability measures. They constitute the added value of transition from classical to divisible probability theory.

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44

Chai, Xiao Long, Gui Wu Hu, and Ai Xiang Chen. "Semantics Integral Operator Fuzzy Logic." Applied Mechanics and Materials 263-266 (December 2012): 3382–86. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.3382.

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A new Operator Fuzzy logic in the theory of semantics integral has been defined. In the way of combining syntax and semantics of the formulas, this logic which named SIOFL can give an index to the truth degree of a proposition formula. It can give the quantum measure of default information with the obtained knowledge. With the character of non-monotonic, the logic system is suitable for approximate reasoning when some information is lacked.

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45

KLIR, GEORGE J. "FOUNDATIONS OF FUZZY SET THEORY AND FUZZY LOGIC: A HISTORICAL OVERVIEW." International Journal of General Systems 30, no. 2 (January 2001): 91–132. http://dx.doi.org/10.1080/03081070108960701.

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46

Zhang, Xiaohong, Xiangyu Ma, and Xuejiao Wang. "Filters in Strong BI-Algebras and Residuated Pseudo-SBI-Algebras." Mathematics 8, no. 9 (September 4, 2020): 1513. http://dx.doi.org/10.3390/math8091513.

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Анотація:

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 the non-commutative fuzzy logics, we extend strong BI-algebra to the non-commutative case, and propose the concept of pseudo-strong BI (SBI)-algebra, which is the common extension of quantum B-algebras, pseudo-BCK/BCI-algebras and other algebraic structures. We establish the filter theory and quotient structure of pseudo-SBI- algebras. Moreover, based on prequantales, semi-uninorms, t-norms and their residual implications, we introduce the concept of residual pseudo-SBI-algebra, which is a common extension of (non-commutative) residual lattices, non-associative residual lattices, and also a special kind of residual partially-ordered groupoids. Finally, we investigate the filters and quotient algebraic structures of residuated pseudo-SBI-algebras, and obtain a unity frame of filter theory for various algebraic systems.

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47

Buhusi, Catalin V. "The across-fiber pattern theory and fuzzy logic." Physiology & Behavior 69, no. 1-2 (April 2000): 97–106. http://dx.doi.org/10.1016/s0031-9384(00)00192-x.

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48

Arfi, Badredine. "Causality in social theory via linguistic fuzzy logic." Quality & Quantity 47, no. 2 (September 1, 2011): 853–80. http://dx.doi.org/10.1007/s11135-011-9570-6.

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49

Belluce, L. P. "Semisimple Algebras of Infinite Valued Logic and Bold Fuzzy Set Theory." Canadian Journal of Mathematics 38, no. 6 (December 1, 1986): 1356–79. http://dx.doi.org/10.4153/cjm-1986-069-0.

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Анотація:

In classical two-valued logic there is a three way relationship among formal systems, Boolean algebras and set theory. In the case of infinite-valued logic we have a similar relationship among formal systems, MV-algebras and what is called Bold fuzzy set theory. The relationship, in the latter case, between formal systems and MV-algebras has been known for many years while the relationship between MV-algebras and fuzzy set theory has hardly been studied. This is not surprising. MV-algebras were invented by C. C. Chang [1] in order to provide an algebraic proof of the completeness theorem of the infinitevalued logic of Lukasiewicz and Tarski. Having served this purpose (see [2]), the study of these algebras has been minimal, see for example [6], [7]. Fuzzy set theory was also being born around the same time and only in recent years has its connection with infinite-valued logic been made, see e.g. [3], [4], [5]. It seems appropriate then, to take a further look at the structure of MV-algebras and their relation to fuzzy set theory.

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50

Im, Eun-Ok, and Wonshik Chee. "Fuzzy logic and nursing." Nursing Philosophy 4, no. 1 (April 2003): 53–60. http://dx.doi.org/10.1046/j.1466-769x.2003.00116.x.

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