In this paper we study a connection between quasicopulas and generator triples of fuzzy preference structures. We study also conditions under which fuzzy implications can be used to construct generator triples. As we show, an important property of fuzzy implications that enables us to construct a generator triple from a fuzzy implication, is the contrapositive symmetry.

Finding the compromise between computational complexity and adaptation potential of linguistic fuzzy systems is important in several fields of application of fuzzy systems including fuzzy modeling and control. This paper considers the role of popular sand t-norms in fuzzy inference function in this aspect and presents some recently acquired results. First, it is shown that with simultaneous app...

In the present paper we construct a new intuitionistic fuzzy implication, giving form to Goguen’s implication. Some of its basic properties are studied and illustrated with examples. Geometrical interpretations different forms implication given. Other discussed.

In this paper, we derive new neuro-fuzzy structures called flexible neuro-fuzzy inference systems or FLEXNFIS. Based on the input-output data, we learn not only the parameters of the membership functions but also the type of the systems (Mamdani or logical). Moreover, we introduce: 1) softness to fuzzy implication operators, to aggregation of rules and to connectives of antecedents; 2) certaint...

In this paper we present a study on inference in a Fuzzy Logic Controller (FLC). Many different implication operators have been proposed in the Fuzzy Logic literature; we take into account five of them that have already been used in fuzzy control. In order to evaluate the advantages and disadvantages of each implication in practical applications, we consider the controller's defuzzified output ...

This paper presents a new abstract framework to deal in a uniform way with the increasing variety of fuzzy logics studied in the literature. By means of notions and techniques from Abstract Algebraic Logic, we perform a study of non-classical logics based on the kind of generalized implication connectives they possess. It yields the new hierarchy of implicational logics. In this framework the n...

In fuzzy set theory, comparison of fuzzy sets plays an important role. Among the several ways to compare fuzzy sets, we address the logical theoretic approach using fuzzy implications. We propose a general framework allowing to generate many measures of comparison: inclusion, similarity and distance, and study their properties. Since the literature on the use fuzzy implications for defining suc...

In this paper, we introduce a new sort of interval valued $left(in ,in vee q_{widetilde{k}}^{widetilde{delta }}right) $-fuzzy bi-ideal in ordered semigroups which is the generalization of interval valued $left( in ,in vee q_{%widetilde{k}}right) $-fuzzy bi-ideal and interval valued $left( in ,in vee qright) $-fuzzy bi-ideal of ordered semigroups. We give examples in which we show that these str...

Here a new intuitionistic fuzzy implication is constructed. Its relations with some forms of Klir and Yuan’s axioms are studied. Some open problems, related to the operations of intuitionistic fuzzy propositional calculus, are formulated.

Ordered fuzzy numbers (OFN) invented by the second author and his two coworkers in 2002 make possible to utilize the fuzzy arithmetic and to construct the Abelian group of fuzzy numbers and then an ordered ring. The definition of OFN uses the extension of the parametric representation of convex fuzzy numbers. Fuzzy implication is proposed with the help of algebraic operations and a lattice stru...