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S-Implications on Complete Lattices and the Interval Constructor
Trends in Computational and Applied Mathematics, 2008 The aim of this work is to present an approach of interval fuzzy logic based on complete lattices. In particular, we study the extensions of the notions of t-conorms, fuzzy negations and S-implication, from the unit interval to arbitrary complete ...
R.H.S. Reiser +4 more
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Formal Introduction to Fuzzy Implications [PDF]
Formalized Mathematics, 2017 Summary In the article we present in the Mizar system the catalogue of nine basic fuzzy implications, used especially in the theory of fuzzy sets. This work is a continuation of the development of fuzzy sets in Mizar; it could be used to give a variety of more general operations, and also it could be a good starting point towards the ...
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Fundamental Properties of Fuzzy Implications [PDF]
Formalized Mathematics, 2018 Summary In the article we continue in the Mizar system [8], [2] the formalization of fuzzy implications according to the monograph of Baczyński and Jayaram “Fuzzy Implications” [1]. We develop a framework of Mizar attributes allowing us for a smooth proving of basic properties of these fuzzy connectives [9].
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Some Properties of the Extended Threshold Generated Implications
Fuzzy Information and EngineeringFuzzy implications play an important role in both approximating reasoning and fuzzy control, and there are many generation methods for fuzzy implications for various applications. The extended threshold generation method for fuzzy implications can induce
Zhi-Hong Yi, Li-Juan Yao, Feng Qin
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Fuzzy implications and inference processes
IEEE 3rd International Conference on Computational Cybernetics, 2005. ICCC 2005., 2006 We define fuzzy implications in general, then study their families defined from t-norms, t-conorms and strong negations. Connections between such implications and negations are established. Some basic results are presented concerning the contrapositive symmetry property. The study gives birth to a new class of t-norms.
József Tick, János Fodor
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Fuzzy inequational logic [PDF]
, 2015 We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes their semantic
Vychodil, Vilem
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INTUITIONISTIC FUZZY BI-IMPLICATOR AND PROPERTIES OF LUKASIEWICZ INTUITIONISTIC FUZZY BI-IMPLICATOR
TWMS Journal of Applied and Engineering Mathematics, 2019 This paper presents axiomatic as well as constructive definitions of intuitionistic fuzzy bi-implicators based on intuitionistic fuzzy t-norms and their intuitionistic fuzzy residual implicators. The inter-relationship among different proposed classes is presented along with a detailed study of the properties of one of these intuitionistic fuzzy bi ...
ASHRAF, S., QAYYUM, M., KERR, E. E.
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A Systematic Study on Distributivity of Threshold-Generated Implications over Uninorms
AxiomsThe distributivity of implications over fuzzy operators is a desirable property for fuzzy systems and can be employed in the elimination of the explosion of if–then rules.
Zhihong Yi
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On fuzzy reasoning schemes [PDF]
, 1999 In this work we provide a short survey of the most frequently used fuzzy reasoning schemes. The paper is organized as follows: in the first section we introduce the basic notations and definitions needed for fuzzy inference systems; in the second ...
Fullér, Róbert
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ON FUZZY IMPLICATIVE FILTERS OF LATTICE IMPLICATION ALGEBRAS
Communications of the Korean Mathematical Society, 2003 Summary: We investigate some related properties of fuzzy filters and fuzzy implicative filters in lattice implication algebras. We find a characterization of fuzzy filters and fuzzy implicative filters, and we discuss a relation between fuzzy filters and fuzzy implicative filters in lattice implication algebras.
Zhu, Yiquan, Zhang, Qun, Roh, Eun Hwan
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