Journal articles: 'Fuzzy logic set'

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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 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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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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BOBILLO, FERNANDO, MIGUEL DELGADO, JUAN GÓMEZ-ROMERO, and UMBERTO STRACCIA. "JOINING GÖDEL AND ZADEH FUZZY LOGICS IN FUZZY DESCRIPTION LOGICS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 20, no. 04 (2012): 475–508. http://dx.doi.org/10.1142/s0218488512500249.

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Ontologies have succeeded as a knowledge representation formalism in many domains of application. Nevertheless, they are not suitable to represent vague or imprecise information. To overcome this limitation, several extensions to classical ontologies based on fuzzy logic have been proposed. Even though different fuzzy logics lead to fuzzy ontologies with very different logical properties, the combined use of different fuzzy logics has received little attention to date. This paper proposes a fuzzy extension of the Description Logic [Formula: see text] — the logic behind the ontology language OWL 2 — that joins Gödel and Zadeh fuzzy logics. We analyze the properties of the new fuzzy Description Logic in order to provide guidelines to ontology developers to exploit the best features of each fuzzy logic. The proposal also considers degrees of truth belonging to a finite set of linguistic terms rather than numerical values, thus being closer to real experts' reasonings. We prove the decidability of the combined logic by presenting a reasoning preserving procedure to obtain a crisp representation for it. This result is generalized to offer a similar reduction that can be applied when any other finite t -norms, t -conorms, negations or implications are considered in the logic.

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buche, antje, jonas buche, and markus b. siewert. "fuzzy logic or fuzzy application? a response to Stockemer’s ‘fuzzy set or fuzzy logic?" European Political Science 15, no. 3 (2016): 359–78. http://dx.doi.org/10.1057/eps.2015.97.

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C, Swathi, Jenifer Ebienazer, Swathi M, and Suruthipriya S. "Fuzzy Logic." International Journal of Innovative Research in Information Security 09, no. 03 (2023): 147–52. http://dx.doi.org/10.26562/ijiris.2023.v0903.19.

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Fuzzy logic is a mathematical framework for reasoning about ambiguous or inaccurate information. It is founded on the idea that truth can be stated as a degree of membership in a fuzzy set rather than as a binary value of true or untrue. Fuzzy logic is used in control systems, artificial intelligence, and decision-making. This paper defines fuzzy logic and discusses its key concepts, mathematical underpinnings, and applications. We look at the benefits and drawbacks.

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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 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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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, as well as the operations of a fuzzy set and fuzzy classification systems. Fuzzy logic has been utilized to solve numerous textile-related difficulties, one of which was determining the proper clothing size. In this study, we examined fuzzy logic applications in textiles, such as the construction of fuzzy expert systems and fuzzy logic for predicting clothing size. This research demonstrates that when determining the correct size of clothing, the outcome is heavily reliant on fuzzy logic.

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Gehrke, Mai, Carol Walker, and Elbert Walker. "A Mathematical Setting for Fuzzy Logics." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05, no. 03 (1997): 223–38. http://dx.doi.org/10.1142/s021848859700021x.

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The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and -x=1-x for conjunction, disjunction and negation, respectively, is the standard propositional fuzzy logic. This is shown to be the same as three-valued logic. The propositional logic obtained when the algebra of truth values is the set {(a, b)|a≤ b and a,b∈[0,1]} of subintervals of the unit interval with component-wise operations, is propositional interval-valued fuzzy logic. This is shown to be the same as the logic given by a certain four element lattice of truth values. Since both of these logics are equivalent to ones given by finite algebras, it follows that there are finite algorithms for determining when two statements are logically equivalent within either of these logics. On this topic, normal forms are discussed for both of these logics.

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Zhang, Jinjin, Xiaoxia Zhou, Yan Zhang, and Lixing Tan. "Fuzzy Epistemic Logic: Fuzzy Logic of Doxastic Attitudes." Mathematics 13, no. 7 (2025): 1105. https://doi.org/10.3390/math13071105.

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In traditional epistemic logic—particularly modal logic—agents are often assumed to have complete and certain knowledge, which is unrealistic in real-world scenarios where uncertainty, imprecision, and the incompleteness of information are common. This study proposes an extension of the logic of doxastic attitudes to a fuzzy setting, representing beliefs or knowledge as continuous values in the interval [0, 1] rather than binary Boolean values. This approach offers a more nuanced and realistic modeling of belief states, capturing the inherent uncertainty and vagueness in human reasoning. We introduce a set of axioms for the fuzzy logic of doxastic attitudes, formalizing how agents reason with regard to uncertain beliefs. The theoretical foundations of this logic are established through proofs of soundness and completeness. To demonstrate practical utility, we present a concrete example, illustrating how the fuzzy logic of doxastic attitudes can model uncertain preferences and beliefs.

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Whalen, Thomas, and Brian Schott. "Usuality, regularity, and fuzzy set logic." International Journal of Approximate Reasoning 6, no. 4 (1992): 481–504. http://dx.doi.org/10.1016/0888-613x(92)90001-g.

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Azar, Ahmad Taher. "Overview of Type-2 Fuzzy Logic Systems." International Journal of Fuzzy System Applications 2, no. 4 (2012): 1–28. http://dx.doi.org/10.4018/ijfsa.2012100101.

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Fuzzy set theory has been proposed as a means for modeling the vagueness in complex systems. Fuzzy systems usually employ type-1 fuzzy sets, representing uncertainty by numbers in the range [0, 1]. Despite commercial success of fuzzy logic, a type-1 fuzzy set (T1FS) does not capture uncertainty in its manifestations when it arises from vagueness in the shape of the membership function. Such uncertainties need to be depicted by fuzzy sets that have blur boundaries. The imprecise boundaries of a type-2 fuzzy set (T2FS) give rise to truth/membership values that are fuzzy sets in [0], [1], instead of a crisp number. Type-2 fuzzy logic systems (T2FLSs) offer opportunity to model levels of uncertainty which traditional fuzzy logic type1 struggles. This extra dimension gives more degrees of freedom for better representation of uncertainty compared to type-1 fuzzy sets. A type-1 fuzzy logic system (T1FLSs) inference produces a T1FS and the result of defuzzification of the T1FS, a crisp number, whereas a T2FLS inference produces a type-2 fuzzy set, its type-reduced fuzzy set which is a T1FS and the defuzzification of the type-1 fuzzy set. The type-reduced fuzzy set output gives decision-making flexibilities. Thus, FLSs using T2FS provide the capability of handling a higher level of uncertainty and provide a number of missing components that have held back successful deployment of fuzzy systems in decision making.

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Cornejo, M. Eugenia, David Lobo, and Jesús Medina. "Relating Multi-Adjoint Normal Logic Programs to Core Fuzzy Answer Set Programs from a Semantical Approach." Mathematics 8, no. 6 (2020): 881. http://dx.doi.org/10.3390/math8060881.

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This paper relates two interesting paradigms in fuzzy logic programming from a semantical approach: core fuzzy answer set programming and multi-adjoint normal logic programming. Specifically, it is shown how core fuzzy answer set programs can be translated into multi-adjoint normal logic programs and vice versa, preserving the semantics of the starting program. This translation allows us to combine the expressiveness of multi-adjoint normal logic programming with the compactness and simplicity of the core fuzzy answer set programming language. As a consequence, theoretical properties and results which relate the answer sets to the stable models of the respective logic programming frameworks are obtained. Among others, this study enables the application of the existence theorem of stable models developed for multi-adjoint normal logic programs to ensure the existence of answer sets in core fuzzy answer set programs.

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Zhong, Qiao. "On fuzzy measure and fuzzy integral on fuzzy set." Fuzzy Sets and Systems 37, no. 1 (1990): 77–92. http://dx.doi.org/10.1016/0165-0114(90)90065-e.

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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, as well as the operations of a fuzzy set and fuzzy classification systems. Fuzzy logic has been utilized to solve numerous textile-related difficulties, one of which was determining the proper clothing size. In this study, we examined fuzzy logic applications in textiles, such as the construction of fuzzy expert systems and fuzzy logic for predicting clothing size. This research demonstrates that when determining the correct size of clothing, the outcome is heavily reliant on fuzzy logic.

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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 existing research. An analysis revealed an increasing trend of investigations highlighting the interplay of fuzzy logic with artificial intelligence, statistical modeling, and heuristic optimization methods. The developments in methodologies of fuzzy decision-making frameworks are again examined from the perspective of applicability in real-life problem situations involving imprecise and uncertain data. Findings that fuzzy logic, therefore, contributed considerably to the enhancement of problem-solving in economics and administrative sciences through more flexible and adaptive models. Therefore, this literature review will be an excellent guide for researchers in fuzzy set theory applications to grasp existing gaps and suggest future directions for improving fuzzy methodologies across industries.

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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 enhancement for supporting the others waiting search activities in this field.

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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 enhancement for supporting the others waiting search activities in this field.

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JANSSEN, JEROEN, DIRK VERMEIR, STEVEN SCHOCKAERT, and MARTINE DE COCK. "Reducing fuzzy answer set programming to model finding in fuzzy logics." Theory and Practice of Logic Programming 12, no. 6 (2011): 811–42. http://dx.doi.org/10.1017/s1471068411000093.

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AbstractIn recent years, answer set programming (ASP) has been extended to deal with multivalued predicates. The resulting formalismsallow for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining thestable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where manyefficient solvers have been constructed, to date there is no efficient fuzzy ASP solver. A well-knowntechnique for classical ASP consists of translating an ASP program P to a propositional theory whose models exactlycorrespond to the answer sets of P. In this paper, we show how this idea can be extended to fuzzy ASP, paving the wayto implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners.

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Fuentes-Penna, Alejandro, Ocotlán Díaz-Parra, Juan de D. González-Ibarra, et al. "Complexity on Fuzzy set and Fuzzy Logic for Air Quality." International Journal of Combinatorial Optimization Problems and Informatics 14, no. 2 (2023): 43–48. https://doi.org/10.61467/2007.1558.2023.v14i2.367.

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The Air quality measurement is reported as micrograms per cubic meter or parts per million. In this article, we proposed a survey of the complexity on Fuzzy Logic for air quality. The traditional air quality assessment is estimated using air quality indices as mean values of selected air pollutants, where the ambient environment has given limits without considering specific local conditions and synergic relations between air pollutants and other meteorological factors. Different models analyze the structure of data to find the characteristics of air quality similarities and to interpret the classification results by means of fuzzy logic.

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Cuong, Bui Cong. "Pythagorean Picture Fuzzy Sets, Part 1- basic notions." Journal of Computer Science and Cybernetics 35, no. 4 (2019): 293–304. http://dx.doi.org/10.15625/1813-9663/35/4/13898.

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Picture fuzzy set (2013) is a generalization of the Zadeh‟ fuzzy set (1965) and the Antanassov‟intuitionistic fuzzy set. The new concept could be useful for many computational intelligentproblems. Basic operators of the picture fuzzy logic were studied by Cuong, Ngan [10,11 ].Newconcept –Pythagorean picture fuzzy set ( PPFS) is a combination of Picture fuzzy set with theYager‟s Pythagorean fuzzy set [12-14].First, in the Part 1 of this paper, we consider basic notionson PPFS as set operators of PPFS‟s , Pythagorean picture relation, Pythagorean picture fuzzy softset. Next, the Part 2 of the paper is devoted to main operators in fuzzy logic on PPFS: picturenegation operator, picture t-norm, picture t-conorm, picture implication operators on PPFS.As aresult we will have a new branch of the picture fuzzy set theory.

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Rajagiri, Anil Kumar, Sandhya Rani MN, Syed Sarfaraz Nawaz, and Suresh Kumar T. "Speed Control of DC Motor using Fuzzy Logic Controller by PCI 6221 with MATLAB." E3S Web of Conferences 87 (2019): 01004. http://dx.doi.org/10.1051/e3sconf/20198701004.

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This thesis demonstrates the importance of Fuzzy Logic Controller. The operation of a DC motor is performed using Fuzzy Logic Controller (FLC) in MATLAB environment. Fuzzy Logic is one of the most successful applications of fuzzy set in which the variables are linguistic rather than numeric. A Fuzzy Logic Controller (FLC) is based on a set of control rules (fuzzy rules) among linguistic variables. The proposed fuzzy controller results in a better response compared to the normal response of DC motor. This thesis consists of two parts; software and hardware implementation. The software part aims to design and develop a Fuzzy Logic Controller in MATLAB Simulink. The hardware Part Consist of DC motor Driver and PCI 6221. The DC drive is used to convert AC voltage into variable DC voltage PCI 6221 is used as the hardware interface between Hardware and Software.

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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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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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Anita Sindar. "IDENTIFIKASI BERITA HOAX MENGGUNAKAN FUZZY LOGIC." Jurnal Teknoif Teknik Informatika Institut Teknologi Padang 9, no. 1 (2021): 42–46. http://dx.doi.org/10.21063/jtif.2021.v9.1.42-46.

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Berita palsu dikenal dengan hoax, berasal dari sumber berita yang kebenarannya diragukan. Media sosial menjadi salah satu keberagaman informasi yang ditawarkan dan keleluasaan dalam membentuk koneksi pertemanan. Setiap orang memiliki kebebasan dalam beropini dalam lingkup sedunia. Banyaknya keuntungan yang diperoleh sipembuat berita hoax.Logika Fuzzy memiliki beberapa kelebihan dibanding logika lain. Penggunaan konsep matematis yang mendasari penalaran Logika ini dinilai sangat sederhana, sehingga mudah dimengerti. Selain itu, data-data yang belum tepat tidak akan langsung dinilai, namun dianalisa lebih mendalam dengan batas toleransi tertentu, sehingga dinilai lebih fleksibel. Fuzzy logic menginterpretasikan statemen yang samar menjadi sebuah pengertian yang logis. Penegasan (Defuzzyfikasi), metode penegasan yang digunakan adalah metode centroid. Himpunan fuzzy adalah pengelompokkan sesuatu berdasarkan variabel bahasa (linguistik variabel), yang dinyatakan dengan fungsi keanggotaan dalam semesta U. Keanggotaan suatu nilai pada himpunan dinyatakan dengan derajat keanggotaan yang nilainya antara 0.0 sampai 1.0. penentuan tingkat penentuan berita hoax terhadap masyarakat ditentukan variabel input dan output.  Fake news is known as hoax, originating from news sources whose truth is questionable. Social media is one of the diversity of information offered and the flexibility to form friendship connections. Everyone has freedom of opinion on a worldwide basis. There are many advantages to hoax news makers. Fuzzy logic has several advantages over other logics. The use of mathematical concepts that underlie logical reasoning is considered very simple, so it is easy to understand. In addition, inaccurate data will not be immediately assessed, but will be analyzed more deeply with a certain tolerance limit, so that it is considered more flexible. Fuzzy logic interprets vague statements into a logical sense. Affirmation (defuzzyfication), the affirmation method used is the centroid method. A fuzzy set is a grouping of something based on language variables (linguistic variables), which is represented by a membership function in the universe U. Membership of a value in a set is expressed by the degree of membership whose value is between 0.0 to 1.0. determining the level of determining hoax news to the public is determined by the input and output variables.

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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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Sampa ChauPattnaik, Mitrabinda Ray, and Mitalimadhusmita Nayak. "Fuzzy Set-Based Reliability Estimation." International Journal of Software Innovation 11, no. 1 (2023): 1–14. http://dx.doi.org/10.4018/ijsi.315733.

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The rapid advancement of computer technology motivates software developers to use commercial off-the-shelf software components for system growth. For particular architectural elements (for instance, components), the reliability criteria associated with testing-based conventional procedures are unknown. In the traditional reliability estimation, the probabilistic method is applied. The source data problem, which depends on a number of factors that may or may not correspond to the real working conditions of the system, is this technique's major shortcoming. The component-based software reliability estimation is based on a number of parameters, including the individual component reliability, transition probability, failure rate, etc. Fuzzy logic converts fuzzy data into useful information, making it easier to develop creative solutions for vague and uncertain concepts based on various factors that influence reliability. To assess the reliability of component-based systems, the authors provide a fuzzy logic technique, which has the ability to improve the question of uncertainty.

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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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Guang-Quan, Zhang. "Fuzzy number-valued fuzzy measure and fuzzy number-valued fuzzy integral on the fuzzy set." Fuzzy Sets and Systems 49, no. 3 (1992): 357–76. http://dx.doi.org/10.1016/0165-0114(92)90287-e.

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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 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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Rushdi, Ali Muhammad, Mohamed Zarouan, Taleb Mansour Alshehri, and Muhammad Ali Rushdi. "A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology." Scientific World Journal 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/327390.

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The Modern Syllogistic Method (MSM) of propositional logic ferrets out from a set of premisesallthat can be concluded from it in the most compact form. The MSM combines the premises into a single function equated to 1 and then produces the complete product of this function. Two fuzzy versions of MSM are developed in Ordinary Fuzzy Logic (OFL) and in Intuitionistic Fuzzy Logic (IFL) with these logics augmented by the concept of Realistic Fuzzy Tautology (RFT) which is a variable whose truth exceeds 0.5. The paper formally proves each of the steps needed in the conversion of the ordinary MSM into a fuzzy one. The proofs rely mainly on the successful replacement of logic 1 (or ordinary tautology) by an RFT. An improved version of Blake-Tison algorithm for generating the complete product of a logical function is also presented and shown to be applicable to both crisp and fuzzy versions of the MSM. The fuzzy MSM methodology is illustrated by three specific examples, which delineate differences with the crisp MSM, address the question of validity values of consequences, tackle the problem of inconsistency when it arises, and demonstrate the utility of the concept of Realistic Fuzzy Tautology.

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Han, Seunghan, and Walter Stechele. "Default Reasoning for Forensic Visual Surveillance based on Subjective Logic and Its Comparison with L-Fuzzy Set Based Approaches." International Journal of Multimedia Data Engineering and Management 2, no. 1 (2011): 38–86. http://dx.doi.org/10.4018/jmdem.2011010103.

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Default reasoning can provide a means of deriving plausible semantic conclusion under imprecise and contradictory information in forensic visual surveillance. In such reasoning under uncertainty, proper uncertainty handling formalism is required. A discrete species of Bilattice for multivalued default logic demonstrated default reasoning in visual surveillance. In this article, the authors present an approach to default reasoning using subjective logic that acts in a continuous space. As an uncertainty representation and handling formalism, subjective logic bridges Dempster Shafer belief theory and second order Bayesian, thereby making it attractive tool for artificial reasoning. For the verification of the proposed approach, the authors extend the inference scheme on the bilattice for multivalued default logic to L-fuzzy set based logics that can be modeled with continuous species of bilattice structures. The authors present some illustrative case studies in visual surveillance scenarios to contrast the proposed approach with L-fuzzy set based approaches.

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Dubois, Didier, Jérôme Lang, and Henri Prade. "Timed Possibilistic Logic." Fundamenta Informaticae 15, no. 3-4 (1991): 211–34. http://dx.doi.org/10.3233/fi-1991-153-403.

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This paper is an attempt to cast both uncertainty and time in a logical framework. It generalizes possibilistic logic, previously developed by the authors, where each classical formula is associated with a weight which obeys the laws of possibility theory. In the possibilistic temporal logic we present here, each formula is associated with a time set (a fuzzy set in the more general case) which represents the set of instants where the formula is certainly true (more or less certainly true in the general case). When a particular instant is fixed we recover possibilistic logic. Timed possibilistic logic generalizes possibilistic logic also in the sense that we substitute the lattice structure of the set of the (fuzzy) subsets of the temporal scale to the lattice structure underlying the certainty weights in possibilistic logic. Thus many results from possibilistic logic can be straightforwardly generalized to timed possibilistic logic. Illustrative examples are given.

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Devita, Retno, and Sarjon Defit. "Accurately Determining Labor Test Results Using the Rough Set Method." Jurnal Penelitian Pendidikan IPA 10, no. 4 (2024): 1723–30. http://dx.doi.org/10.29303/jppipa.v10i4.7069.

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An exam is something that must be done to test a person's ability or intelligence. The laboratory exam in the Computer Systems study program at Putra Indonesia University "YPTK" Padang consists of a digital systems exam, a fuzzy logic control exam, and a tool presentation. The Labor Exam must be passed by students who will take the comprehensive exam. In this study, laboratory exam data was taken for 20 students. So far, processing of student laboratory exam results has been done manually so it takes a long time to make decisions. To overcome this problem, a Rough Set method is used to determine laboratory test results. The Rough Set method is part of machine learning. This research produces 29 rules as knowledge, namely {Digital System} Or {A} = 3 rules, {Fuzzy Logic} Or {B} = 3 rules, {Tool Presentation} Or {C} = 3 rules, {Fuzzy Logic, Tool Percentage} Or {BC} = 6 rules, {Digital System, Fuzzy Logic} Or {AB} = 6 rules and {Digital System, Tool Percentage} Or {AC} = 8 rules. The Rough Set method can determine student laboratory exam results (pass or fail) accurately.

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Dominik, Ireneusz. "Implementation of the Type-2 Fuzzy Controller in PLC." Solid State Phenomena 164 (June 2010): 95–98. http://dx.doi.org/10.4028/www.scientific.net/ssp.164.95.

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The main aim of the presented research work was to develop type-2 fuzzy logic controller, which by its own design should be “more intelligent” than type-1. Along with the intelligence it should provide better results in solving a particular problem. Type-2 fuzzy logic controller is not well-known and it is rarely used at present. The idea of type-2 fuzzy logic set was presented by Zadeh in 1975, shortly after the presentation of type-1 fuzzy set. At the beginning scientists and researchers worked on type-1. Only after developing type-1 the attention was directed towards the type-2. The first applications of type-2 fuzzy logic in control appeared in 2003. The fuzzy logic controller type-2 was tested experimentally by controlling a non-linear object: a shape memory alloy (SMA) actuator DM-01PL, made by Miga Motor company, which despite small size distinguishes itself by its 9 N strength. Comparison of experimental data of the fuzzy logic controller type-2 and type-1 clearly indicates the superiority of the former, particularly in reducing signal overshoots.

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

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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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Wen-Xiu, Zhang, L. I. Teng, M. A. Ji-Feng, and L. I. Ai-Jie. "Set-valued measure and fuzzy set-valued measure." Fuzzy Sets and Systems 36, no. 1 (1990): 181–88. http://dx.doi.org/10.1016/0165-0114(90)90091-j.

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Dai, Jianhua, and Haowei Tian. "Fuzzy rough set model for set-valued data." Fuzzy Sets and Systems 229 (October 2013): 54–68. http://dx.doi.org/10.1016/j.fss.2013.03.005.

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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 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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Zhang, Deli, and Zixiao Wang. "On set-valued fuzzy integrals." Fuzzy Sets and Systems 56, no. 2 (1993): 237–41. http://dx.doi.org/10.1016/0165-0114(93)90149-c.

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

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Fan, Tuan-Fang, Churn-Jung Liau, and Yiyu Yao. "On Modal and Fuzzy Decision Logics Based on Rough Set Theory." Fundamenta Informaticae 52, no. 4 (2002): 323–44. https://doi.org/10.3233/fun-2002-52403.

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Some modal decision logic languages are proposed for knowledge representation in data mining through the notions of models and satisfiability. The models are collections of data tables consisting of a finite set of objects described by a finite set of attributes. Some relationships may exist between data tables in a collection and the modalities of our languages are interpreted with respect to these relations in Kripkean style semantics. The notion of fuzzy decision logic is also reviewed and combined with the modal decision logic. The combined logic is shown to be useful in the representation of fuzzy sequential patterns.

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Bandaru, Ravi Kumar, Rajesh Neelamegarajan, Tahsin Oner, and Amal S. Alali. "A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras." Axioms 14, no. 5 (2025): 347. https://doi.org/10.3390/axioms14050347.

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This study introduces the concept of an intuitionistic fuzzy SBCK-subalgebra (SBCK-ideal) and explores the level set of an intuitionistic fuzzy set within the context of Sheffer stroke BCK-algebras. These newly defined concepts are crucial for understanding the interaction between intuitionistic logic and Sheffer stroke BCK-algebras. The paper establishes a connection between subalgebras and level sets in the framework of Sheffer stroke BCK-algebras, demonstrating that the level set of intuitionistic fuzzy SBCK-subalgebras corresponds precisely to their subalgebras, and conversely. Additionally, the study provides novel results regarding the structural properties of Sheffer stroke BCK-algebras under intuitionistic fuzzy logic, specifically focusing on the conditions under which fuzzy sets become SBCK-subalgebras or SBCK-ideals. This work contributes to the theoretical foundations of fuzzy logic in algebraic structures, offering a deeper understanding of the interplay between intuitionistic fuzzy sets and the algebraic operations within Sheffer stroke BCK-algebras.

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Wang, Zhong Wei, and Li Xin Lu. "Logistics Demand Forecasting with Asymmetry-Width Probabilistic Fuzzy Logic System." Advanced Materials Research 706-708 (June 2013): 2012–16. http://dx.doi.org/10.4028/www.scientific.net/amr.706-708.2012.

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There are a lot of approaches in logistics demand forecasting field and perform different characters. The probabilistic fuzzy set (PFS) and probabilistic fuzzy logic system is designed for handling the uncertainties in both stochastic and nonstochastic nature. In this paper, an asymmetric probabilistic fuzzy set is proposed by randomly varying the width of asymmetric Gaussian membership function. And the related PFLS is constructed to be applied to a logistics demand forecasting. The performance discloses that the asymmetry-width probabilistic fuzzy set performs better than precious symmetric one. It is because the asymmetric probabilistic fuzzy sets variability and malleability is higher than this of the symmetric probabilistic fuzzy set.

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Sheikh, Md. Rafiqul Islam, Rion Takahashi, and Junji Tamura. "Power System Stabilization by Fuzzy Set Theory Based Control of Smes." DIU Journal of Science & Technology 6, no. 2 (2024): 33–41. https://doi.org/10.5281/zenodo.13731695.

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At present fuzzy logic control is receiving increasing emphasis in process control applications. The paper describes the application of fuzzy logic control in a power system that uses a 12- pulse bridge converter associated with Superconductive Magnetic Energy Storage (SMES) unit. The fuzzy control is used in both the frequency and voltage control loops, replacing the conventional control method. The control algorithms have been developed in detail and simulation results are presented. These results clearly indicate the superior performance of fuzzy control during the dynamic period of energy transfer between the power system and SMES unit.

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Abdy, Muhammad, Awi Dassa, and Sri Julia Nensi. "Konsep Himpunan Fuzzy pada Paradoks Russel." Journal of Mathematics, Computations, and Statistics 2, no. 2 (2020): 189. http://dx.doi.org/10.35580/jmathcos.v2i2.12582.

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Himpunan fuzzy menggunakan dasar logika fuzzy untuk menyatakan suatu objek menjadi anggota dengan derajat keanggotaan ( ), tetapi Logika fuzzy melanggar hukum logika biner sehingga muncul anggapan bahwa logika fuzzy memiliki masalah yang sama dengan paradoks. Tetapi nilai kebenarana logika fuzzy tergantung dari derajat keanggotaan yang dimilikinya sehingga dapat ditarik sebuah kesimpulan dari besar darajat keanggotaan tersebut, sedangkan paradoks nilai kebenarannya tidak dapat ditarik kesimpulan apapun. Paradoks merupakan bentuk kritik landasan yang bertujuan untuk mengungkapkan dan menentukan inkonsistensi atau kontradiksi yang dihasilkan dari beberapa eksperimen mental dalam matematika, salah satu paradoks yang terkenal dalam kritik landasan teori himpunan adalah paradok Russel Pemecahan paradoks Russel dengan menggunakan konsep teori himpunan fuzzy diperoleh derajat keanggotaan adalah 0.5 merupakan pernyataan setengah benar (half true) dan adalah 0.5 jugan merupakan pernyataan setengah benar (half true). Kata kunci: Logika fuzzy, himpunan fuzzy, paradoks, paradoks Russel.Fuzzy sets use the basis of fuzzy logic to declare an object to be a member with the degree of membership ( ), but fuzzy logic violates the law of binary logic so that the assumption arises that fuzzy logic has the same problem with paradox. But the true value of fuzzy logic depends on the degree of membership it has so that a conclusion can be drawn from the large membership ranks, while the paradox of its value cannot be drawn any conclusions. The paradox is a form of ground criticism that aims to express and determine the inconsistencies or contradictions that result from several mental experiments in mathematics, one of the paradoxes that is well-known in critics of set theory is Russel's paradox . The paradoxical solution of Russell by using fuzzy set theory concepts is that the degree of membership is 0.5 and is 0.5.Keywords: Fuzzy Logic, fuzzy set, paradox, Russel paradox.

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Sherin, Naja. "Fuzzy Logic and Set Theory in Artificial Intelligence Decision-Making." International Journal for Research in Applied Science and Engineering Technology 13, no. 5 (2025): 1656–58. https://doi.org/10.22214/ijraset.2025.70546.

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Artificial Intelligence (AI) systems require the ability to make decisions under uncertainty and imprecision, which are common in real-world scenarios. Traditional methods struggle to handle such vagueness. Fuzzy Set Theory and Fuzzy Logic, introduced by Lotfi Zadeh, provide a framework for dealing with these issues. This paper explores how fuzzy systems enhance decision-making in AI, offering theoretical insights, practical applications, mathematical formulations, and the integration of fuzzy systems with other AI models. It also discusses the challenges and future directions in this research area.

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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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Lee-Kwang, Hyung, and Ju-Jang Lee. "Fuzzy Logic and Intelligence System." Journal of Advanced Computational Intelligence and Intelligent Informatics 4, no. 5 (2000): 319–20. http://dx.doi.org/10.20965/jaciii.2000.p0319.

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These papers are originally published in the proceedings of Korea fuzzy logic and intelligent systems society (KFIS) fall conference in 1999. Eight papers are selected for this special issue. Major topics of them are fuzzy theory, neural network, inference system, intelligent controller, etc. In this issue, Seihwan Park and Hyung Lee-Kwang extend the concept of fuzzy hypergraph to type-2 fuzzy hypergraph using type-2 fuzzy sets. It has not only the same properties of hypergraphs but also the extended properties of them. It is also shown that interval valued fuzzy hypergraph is a special case of type-2 fuzzy hypergraph. Jung-Heum Yon, Yong-Taek Kim, Jae-Yong Seo and Hong-Tae Jeon design an efficient neural network called dynamic multidimensional wavelet neural network. It can perform an effective dynamic mapping with less dimensions of the input signal. These features show one way to compensate the weakness of the diagonal recurrent neural network and feedforward wavelet neural network. Yigon Kim, Yang Hee Jung and Young Chel Bae propose a new method for diagnosis of insulation aging using wavelet. It measures the partial discharge on-line from data acquisition system and analyses it using wavelet to acquire 21) patterns. They design a neuro-fuzzy model that diagnoses an electrical equipment using the data. Byung-Jae Choi, Seong-Woo Kwak and Byung Kook Kim develop an adaptive fuzzy logic controller. A sole input fuzzy variable is used to simplify the design procedure and the switching hyperplane of sliding mode control is used to improve the adaptability. Myung-Geun Chun, Keun-Chang Kwak and Jeong-Woong Ryu show an efficient fuzzy rule generation scheme for adaptive network-based fuzzy inference system using the conditional fuzzy c-means and fuzzy equalization methods. They apply this method to the truck backer-upper control and Box-Jenkins modeling problem. Daijin Kim proposes a new data classification method based on the tolerant rough set that extends the existing equivalent rough set. Twostage classification method is used. All data are classified by using the lower approximation at the first stage and then the non-classified data at the first stage are classified again by using the rough membership functions obtained from the upper approximation set. Min-Soeng Kim, Sun-Gi Hong and Ju-Jang Lee incorporate the Q-learning algorithm into the fuzzy logic controller. Modified fuzzy rule is used for the incorporation. As a result, a fuzzy logic controller is obtained that can learn through experience. Dong Hwa Kim designs a new 2-DOF PID controller and applies it to the operating data based transfer function of Gun-san Gas turbine in Korea. We hope that this issue can be helpful to readers and we appreciate professor Kaoru Hirota for his interest and support for the publication.

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Chang, Te-Chuan, C. William Ibbs, and Keith C. Crandall. "A fuzzy logic system for expert systems." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 2, no. 3 (1988): 183–93. http://dx.doi.org/10.1017/s0890060400000640.

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Using the theory of fuzzy sets, this paper develops a fuzzy logic reasoning system as an augmentation to a rule-based expert system to deal with fuzzy information. First, fuzzy set theorems and fuzzy logic principles are briefly reviewed and organized to form a basis for the proposed fuzzy logic system. These theorems and principles are then extended for reasoning based on knowledge base with fuzzy production rules. When an expert system is augmented with the fuzzy logic system, the inference capability of the expert system is greatly expanded; and the establishment of a rule-based knowledge base becomes much easier and more economical. Interpretations of the system’s power and possible future research directions conclude the paper.

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Blondeel, Marjon, Steven Schockaert, Martine De Cock, and Dirk Vermeir. "Fuzzy autoepistemic logic and its relation to fuzzy answer set programming." Fuzzy Sets and Systems 239 (March 2014): 51–80. http://dx.doi.org/10.1016/j.fss.2012.09.012.

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Journal articles on the topic 'Fuzzy logic set'

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