Fuzzy functions in fuzzy logic with fuzzy equality
Vilém Novák (2001)
Acta Mathematica et Informatica Universitatis Ostraviensis
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Vilém Novák (2001)
Acta Mathematica et Informatica Universitatis Ostraviensis
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Adam Grabowski (2017)
Formalized Mathematics
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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 formalization of fuzzy logic (together with t-norms and t-conorms, formalized previously).
Jeon, Joung Kon, Jun, Young Bae, Park, Jin Han (2005)
International Journal of Mathematics and Mathematical Sciences
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Lupiáñez, Francisco Gallego (2005)
International Journal of Mathematics and Mathematical Sciences
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Nedzad Dukic, Zikrija Avdagic (2004)
Mathware and Soft Computing
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In this paper we establish equivalence between a theory of fuzzy functional dependences and a fragment of fuzzy logic. We give a way to interpret fuzzy functional dependences as formulas in fuzzy logic. This goal is realized in a few steps. Truth assignment of attributes is defined in terms of closeness between two tuples in a fuzzy relation. A corresponding fuzzy formula is associated to a fuzzy functional dependence. It is proved that if a relation satisfies a fuzzy functional dependence,...
Ramadan, A.A., Abbas, S.E., Abd El-Latif, A.A. (2005)
International Journal of Mathematics and Mathematical Sciences
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Ludovic Lietard, Daniel Rocacher (2009)
Control and Cybernetics
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Milan Mareš (2011)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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The structures of the fuzzy information theory are focused on the concept of fuzzy entropy, where the individual information of symbols is considered only implicitely. This paper aims to fill this gap and to study the concepts of fuzzy information. Special attention is paid to the typical fuzzy set theoretical paradigma of monotonicity of operations.
Francisco Gallego Lupiáñez (2003)
Mathware and Soft Computing
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The basic concepts of the theory of intuitionistic fuzzy topological spaces have been defined by D. Çoker and co-workers. In this paper, we define new notions of Hausdorffness in the intuitionistic fuzzy sense, and obtain some new properties, in particular on convergence.