Aims of the course: To introduce the basic notions of Mathematical Fuzzy Logic and some of the open problems in its agenda. 1. Introduction to the algebraic study of propositional logics. The cases of intuitionistic and classical logic. The general notion of algebraizable logic.

Fuzzy logic, according to Lotfi Zadeh, can be broadly considered as the union of fuzzified crisp logics. Its primary aim is to provide a formal, computationally oriented system of concepts and techniques for dealing with modes of reasoning that are approximate rather than exact. Charles Elkan’s claims are derived mainly from entangled interpretations of fuzzy logic stemming from his mathematica...

First, we introduce the concept of intuitionistic fuzzy group congruenceand we obtain the characterizations of intuitionistic fuzzy group congruenceson an inverse semigroup and a T^{*}-pure semigroup, respectively. Also,we study some properties of intuitionistic fuzzy group congruence. Next, weintroduce the notion of intuitionistic fuzzy semilattice congruence and we givethe characterization of...

In this paper we study about the higher order fuzzy sets specially about intuitionistic fuzzy sets (or vague sets).

Remarks on history, theory, and applications of intuitionistic fuzzy sets are given. Some open problems are introduced.

Based on the theory of intuitionistic fuzzy sets, the concepts of intuitionistic fuzzy subalgebras with thresholds (λ, μ) and intuitionistic fuzzy ideals with thresholds (λ, μ) of BCI-algebras are introduced and some properties of them are discussed. Keywords—BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy subalgebra with thresholds (λ, μ), intuitionistic fuzzy ideal with thresholds...

The paper focuses on the study of the contradiction between two Atanassov's intuitionistic fuzzy sets. First, taking into account some characterizations obtained in previous papers, some functions are defined in order to measure the degrees of contradiction. Besides the principal properties of these measures are pointed out. Finally, some results relating self-contradiction and contradiction be...

One of the essential formulas classical mathematical logic is (A → B) ((¬A B). In present paper, its intuitionistic fuzzy interpretation introduced, and lists all defined implications that satisfy it as a tautology an are given.

Fuzzy decision making is the collection of single or multicriteria techniques aiming at selecting the best alternative in case of imprecise, incomplete, and vague data. This chapter reviews the fuzzy decision making literature and summarizes the review results by tabular and graphical illustrations. The classification is based on the new extensions of fuzzy sets: Intuitionistic, hesitant, and t...