During years of research, there have been defined 153 intuitionistic fuzzy implications. In the paper, it is checked which of these implications satisfy which axioms of the intuitionistic logic, whether as (classical) tautologies or as intuitionistic fuzzy tautologies. Some open problems, related to the operations of intuitionistic fuzzy propositional calculus, are formulated.

This paper deals with some dependencies between fuzzy conjunctions and fuzzy implications. More precisely, a fuzzy implication generated from a fuzzy conjunction and a fuzzy conjunction induced by a fuzzy implication is considered. In the case of a fuzzy conjunction only border conditions and monotonicity are assumed. The results are illustrated by examples of weak fuzzy connectives.

In this paper, we propose a new method for choosing implications. Our method allows to compare two fuzzy implications. If the truth value of the antecedent and the truth value of the implication are given, by means of inverse fuzzy implications we can easily optimize the truth value of the implication consequent.

A fuzzy implication, commonly defined as a two-place operation on the unit interval, is an extension of the classical binary implication. It plays important roles in both mathematical and applied sides of fuzzy set theory. Besides the basic axioms, there are many potential fuzzy implication axioms, among which eight are widely used in the literature. Different fuzzy implications satisfying diff...

In this paper we consider algebras of fuzzy truth values equipped with an implication operation. Generalizing the definition of type-1 fuzzy implications, we discuss extended fuzzy S-implications and coimplications and also extended residual implications and coimplications, in particular to the extended residual of minimum. We study the algebraic properties of these operations and their relatio...

Fuzzy attribute implications are particular if-then rules which can be extracted from data tables with fuzzy attributes. We develop fuzzy attribute logic (FAL), its syntax, semantics, and prove a classical as well as Pavelka-style completeness theorem for FAL. Also, we present relationships to completeness of sets of attribute implications w.r.t. data tables. Because of the limited scope of the...

This paper brieey reviews techniques for learning fuzzy rules. In many applications fuzzy if-then rules are not interpreted as implications , but in a procedural way that corresponds to a conjunction or Cartesian product. For this type of rules many approaches to rule learning have been proposed. However, for more complex fuzzy systems based on logical implications, there is still a need for su...