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...

In this work we present novel methods of generating fuzzy implications from the given ones. 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 so far.

It is well known that knowledge-based systems would be more robust and smarter if they can deal with the inconsistent, incomplete or imprecise knowledge, which has been referred to as common sense knowledge. In this paper, we discuss fuzzy implications in the sense of common sense reasoning. F i rs t ly , we analyse the ra t i ona l i t y of some exist ing fuzzy implications based on the discus...

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.

The purpose of this paper is to describe an adaptive fuzzy cognitive map based on the random neural network model. The adaptive fuzzy cognitive map changes its fuzzy causal web as causal patterns change and as experts update their causal knowledge. We show how the adaptive random fuzzy cognitive map can reveal implications of models composed of dynamic processes.

A new family of fuzzy implications, motivated by classic Sheffer stroke operator, is introduced. Sheffer stroke, which is a negation of a conjunction and is called NAND as well, is one of the two operators that can be used by itself, without any other logical operators, to constitute a logical formal system. Classical implication can be presented just by Sheffer stroke operator in two ways whic...

In this work we give a state-of-the-art review of two of the most established classes of fuzzy implications, viz., (S,N)and R-implications. Firstly, we discuss their properties, characterizations and representations. Many new results concerning fuzzy negations and (S,N)-implications, notably their characterizations with respect to the identity principle and ordering property, are presented, whi...