First of all, in this paper we propose a family of fuzzy implication operators, which the generalised Luckasiewicz ́s one, and to analyse the impacts of Smets and Magrez properties on these operators. The result of this approach will be a characterisation of a proposed family of inclusion grade operators (in Bandler and Kohout ́s manner) that satisfies the axioms of Divyendu and Dogherty. Second,...

In this paper, we introduce a new algebra called ‘EQ-algebra’, which is an alternative algebra of truth values for formal fuzzy logics. It is specified by replacing implication as the main operation with a fuzzy equality. Namely, EQ-algebra is a semilattice endowed with a binary operation of fuzzy equality and a binary operation of multiplication. Implication is derived from the fuzzy equality ...

In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...

For the last decade, fuzzy controllers have been applied with great success to a variety of domains. Nevertheless the underlying theoretical framework still remains unsatisfactory. One of the key questions still open is concerned with approximate reasoning. How should we determine the eeect of applying the fuzzy rule IF x is ~ A THEN y is ~ B] to ~ A 0 with ~ A 0 , ~ A, and ~ B being fuzzy sets...

There are several ways to extend the classical logical connectives for fuzzy truth degrees, in such a way that their behavior for the values 0 and 1 work exactly as in the classical one. For each extension of logical connectives the formulas which are always true (the tautologies) changes. In this paper we will provide a fuzzy interpretation for the usual connectives (conjunction, disjunction, ...

Using Generalized Modus Ponens reasoning, we examine the values of the inferred conclusion by using Fodor's implication in order to interpret a fuzzy if-then rule with a single input single output and the tnorm ( ) ( )( ) ( xy y x max y , x t ) λ λ − − + + = 1 1 , 1 − ≥ λ , for composition operation. This t-norm is important to use because for 1 − = λ and 0 = λ it gives the commonly used t-norm...

Modus Ponens is a key property for fuzzy implication functions that are going to be used in fuzzy inference processes. In this paper it is investigated when fuzzy implication functions derived from uninorms via residuation, usually called RU implications, satisfy the modus ponens with respect to a continuous t-norm T , or equivalently, when they are T -conditionals. For RU -implications it is p...

A class of implication functions is constructed from fuzzy negations. The interest of this new class lies in its simplicity and in the fact that when N is Idsymmetrical, the corresponding implication agrees with the residuum of a commutative semicopula.

This paper deals with ordinal sums of fuzzy implications. Some of the known constructions are recalled and new ways of generating fuzzy implications from given ones are proposed. Sufficient properties of fuzzy implications as summands for obtaining a fuzzy implication as a result are presented.

In this paper we present a method for the construction of Atanassov’s intuitionistic fuzzy S-implications that satisfy the following property: if in the intuitionistic fuzzy conditional the antecedent is equal to the consequent, then the Atanassov’s intuitionistic fuzzy implication operator has the same Atanassov’s intuitionistic fuzzy index as the antecedent and the consequent.