Krassimir T. Atanassov

Interval valued intuitionistic fuzzy sets

In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets (IVIFSs) will be introduced. We will omit the majority of the proofs below, which are, in general, analogous to the proofs from Chapter 1.

More on intuitionistic fuzzy sets

Abstract New results on intuitionistic fuzzy sets are introduced. Two news operators on intuitionistic fuzzy sets are defined and their basic properties are studied.

Operators over interval valued intuitionistic fuzzy sets

Abstract Different operators are defined over the interval valued intuitionistic fuzzy sets and their basic properties are studied.

On Intuitionistic Fuzzy Sets Theory

This book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the authors previous book on Intuitionistic Fuzzy Sets, published by Springer in 1999 (Atanassov, Krassimir T., Intuitionistic Fuzzy Sets, Studies in Fuzziness and soft computing, ISBN 978-3-7908-1228-2, 1999). Since the aforementioned book has appeared, the research activity of the author within the area of intuitionistic fuzzy sets has been expanding into many directions. The results of the authors most recent work covering the past 12 years as well as the newest general ideas and open problems in this field have been therefore collected in this new book.

Two theorems for intuitionistic fuzzy sets

Two theorems related to the relations between some of the operators, defined over the intuitionistic fuzzy sets are formulated and proved.

Intuitionistic fuzzy Prolog

Abstract A logic programming system which uses a theory of intuitionistic fuzzy sets to model various forms of uncertainty is presented. To represent uncertainty of facts and rules, a pair of two different real numbers (degree of truth and degree of falsity) are associated. The problem of propagating uncertainty through logical inference and various models of interpretation are considered. The framework discussed allows knowledge representation and inference under uncertainty in the form of rules suitable for expert systems.

Discussion: Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper “Terminological difficulties in fuzzy set theory---the case of “Intuitionistic Fuzzy Sets” ”

In reply to Dubois and colleagues, here it is discussed the relationship between the notion of intuitionistic fuzzy set as proposed by the author in 1983 and the notion proposed in 1984 by Takeuti and Titani under the same name. It is demonstrated also the main direction of research, which does not (and in some cases, cannot) have analogues in fuzzy sets theory.

Remarks on the intuitionistic fuzzy sets

The pseudo-fixed points of all operators defined over the intuitionistic fuzzy sets are determined.

Elements of intuitionistic fuzzy logic. Part I

The definition of the notion of intuitionistic fuzzy set is the basis for defining intuitionistic fuzzy logics of different kinds. In this paper, we construct two versions of intuitionistic fuzzy propositional calculus (IFPC) and a version of intuitionistic fuzzy predicate logic (IFPL).

Elements of Intuitionistic Fuzzy Logics

The definition of intuitionistic fuzzy sets will serve as a basis for further definitions of the elements of the intuitionistic fuzzy logics (IFLs). Here we shall present basic elements of: Intuitionistic Fuzzy Propositional Calculus (IFPC), Intuitionistic Fuzzy Predicate Logic (IFPL), Intuitionistic Fuzzy Modal Calculus (IFMC), and Temporal Intuitionistic Fuzzy Logic (TIFL).