This paper deals with the problem of searching basic properties for robust implication operators in fuzzy control. We use the word “robust” in the sense of good average behavior in different applications and in combination with different defuzzification methods. We study the behavior of the two main families of implication operators in the fuzzy control inference process. These two families are...

In this paper, three new operations have been introduced on intuitionistic fuzzy soft sets. They are based on Second Zadeh‟s implication, conjunction and disjunction operations on intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied. Index Terms — Second Zadeh‟s implication, Second Zadeh‟s conjunction, Second Zadeh‟s disjunctio...

In this paper we present some Boolean algebras in the form of lattice by using the fuzzy implication. We show that these methods lead to various and much richer algebraic structures on the set of all fuzzy implications than obtained in the literature. KeywordsFuzzy logic connectives, Fuzzy implication, Algebras, Lattice.

The Mamdani model [1] of Fuzzy Systems is the earliest and the most widely studied type of Fuzzy Systems. In this work, Residuated Implication (R-implication) operators have been explored for rule reduction in Mamdani-Type Fuzzy Systems with lossless inferencing.

In this paper, we point out that the definition of fuzzy attribute implication actually implies a minimal degree and thus may be impractical in some applications. To solve this, we introduce probability information to fuzzy inclusion degree, and discuss some properties of this definition. Illustrations verifies the correctness of probability fuzzy attribute implication.

Contrapositive symmetry (CPS) is a tautology in classical logic. In fuzzy logic, not all fuzzy implications have CPS with respect to a given strong negation. Given a fuzzy implication J , towards imparting contrapositive symmetry to J with respect to a strong negation N two techniques, viz., upper and lower contrapositivisation, have been proposed by Bandler and Kohout [Semantics of implication...

Recently, two new families of fuzzy implication functions called probabilistic implications and probabilistic S-implications were introduced by Grzegorzewski [6, 7, 9]. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In this paper we generalize these two classes and propose a new kind of construction methods for fuzzy implications which are ba...

in this paper, we firstly show that the $n$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $n$-dual operation. as a dual result, the $n$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...

The concept of quasi-coincidence of an interval-valued fuzzy set is considered. By using this new idea, the notion of interval-valued (α, β)−fuzzy k−ideals of semirings is introduced, which is a generalization of a fuzzy k−ideal. Also some related properties are studied and in particular, the interval-valued (∈,∈ ∨q)−fuzzy k−ideals in a semiring will be investigated. Finally, the concept of imp...

Many diierent fuzzy implication operators have been proposed; most of them t into one of the two classes: implication operations that are based on an explicit representation of implication A ! B in terms of &, _, and : (e.g., S-implications that are based on the formula B _ :A), and R-implications that are based on an implicit representation of implication A ! B as the weakest C for which C&B i...