In information retrieval, the uncertain implication D −→ RQ has been different logical status. In this paper, we propose another way to consider this implication in fuzzy context. We introduce a logical formulation based on logical consequence and an evaluation based on an extension of fuzzy Galois connection. The proposed matching function deals with different semantics associated with terms d...

If we know that an implication A ! B is to some extent true, and if we know that a statement A is true \to some extent", i.e., if we know that the statement m(A) is true, for some logical modiier m (\approximately", \slightly", etc.), then we can conclude that B is also true to some extent, i.e., that m 0 (B) is true for some logical modiier m 0. Thus, every fuzzy implication deenes a mapping f...

The aim of this paper is to introduce the notions of (∈,∈ ∨ q)fuzzy p-ideals, (∈,∈ ∨ q)-fuzzy q-ideals and (∈,∈ ∨ q)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterization theorems for these generalized fuzzy ideals are proved and the relationship among these generalized fuzzy ideals of BCI-algebras is discussed. It is shown that a fuzzy set of a BCI...

Intuitionistic Fuzzy Sets (IFS) are defined as pairs of mutually orthogonal fuzzy sets. We discuss this approach from an algebraic point of view. As a result we characterize two implication operators on the collection of IFS, which on a particular subset of IFS behave as a Lukasiewicz and a Gödel implication.

1. Formulation of the problem 1:1: It is necessary to represent implication in expert systems Our knowledge of complex systems is often incomplete, and therefore, we have to rely on the expert's statements, These statements are usually formulated not in mathematical terms, but in words of natural languages. Fuzzy logic is a methodology for formalizing such statements. Since a large part of expe...

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.

In this contribution we plan to characterise fuzzy implication operators based on three basic properties and the defuzzification methods suitable to be used in combination with them. We want to characterise the proper use of implication operators in Fuzzy Rule Based Systems for control problems.

In this paper, the perturbation of fuzzy connectives and the robustness of fuzzy reasoning are investigated. This perturbation of Schweizer-Sklar parameterized t-norms and its residuated implication operators are given. We show that full implication triple I algorithms based on Schweizer-sklar operators are robust for normalized Minkowski distance.

In this paper, we study some properties of intuitionistic fuzzy tautological matrix using intuitionistic fuzzy implication operator.

A new family of implication operators, called probabilistic implications, is introduced. The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic. It is shown that some well-known fuzzy implications appear as a particular probabilistic implications. Therefore, it seems that this new family of implication operators might be a useful...