In this paper, we study in-depth certain properties of interval-valued fuzzy sets and Atanassov’s intuitionistic fuzzy sets (A-IFSs). In particular, we study the manner in which to construct different interval-valued fuzzy connectives (or Atanassov’s intuitionistic fuzzy connectives) starting from an operator. We further study the law of contradiction and the law of excluded middle for these se...

The Intuitionistic Fuzzy Sets (IFSs), proposed in 1983, are extensions of fuzzy sets. Some years after their introduction, sequentially, intuitionistic fuzzy propositional logic, intuitionistic fuzzy predicate logic, intuitionistic fuzzy modal logic and intuitionistic fuzzy temporal logic have been introduced, presented here shortly. During the last 25 years, different intuitionistic fuzzy tool...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy subsemimodule of a semimodule with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on...

In the present paper an Open Problem proposed by K. Atanassov is completely solved. As a result a possible approach for correction of inconsistent expert estimates is provided. The solution is constructed by selecting a specific p-intuitionistic fuzzy set and then mapping it to the traditional interpretation triangle of the intuitionistic fuzzy sets.

We introduce the concept of the intuitionistic fuzzy proximity as a generalization of fuzzy proximity, and investigate its properties. Also we investigate the relationship among intu-itionistic fuzzy proximity and fuzzy proximity, and intuitionistic fuzzy topology. 1. Introduction. As a generalization of fuzzy sets, the concept of intuitionistic fuzzy sets was introduced by Atanassov [1]. Recen...

Intuitionistic fuzzy sets (IFSs) have attracted more and more scholars’ attention due to their powerfulness in expressing vagueness and uncertainty. In the course of decision making with IFSs, aggregation operators play a very important role since they can be used to synthesize multidimensional evaluation values represented as intuitionistic fuzzy values into collective values. This paper propo...

Similarity of intuitionistic fuzzy sets (IFSs) is an important measure to indicate the similarity degree between IFSs. Recently, Ye (2011) proposed a similarity measure between IFSs based on the cosine concept. Although this cosine similarity measure has good concept and merit, the measure is not satisfied the definition of a similarity between IFSs and not presented well for analyzing IFS data...

This paper extends the technique for order preference by similarity to ideal solution (TOPSIS) for solving multi-attribute group decision making (MAGDM) problems under Atanassov intuitionistic fuzzy set (IFS) environments. In this methodology, weights of attributes and ratings of alternatives on attributes are extracted from fuzziness inherent in decision data and making process and described u...

We propose a new approach for medical diagnosis by employing intuitionistic fuzzy sets [cf. Atanassov [1, 2]]. Solution is obtained by looking for the smallest distance [cf. Szmidt and Kacprzyk [7, 8]] between symptoms

Intuitionistic fuzzy sets introduced by Atanassov are generalization of fuzzy sets as they also handle the nondeterminacy which is caused by degree of hesitation of decision maker. The present study proposes a computational method of forecasting for fuzzy time series. In the proposed method the notion of intuitionistic fuzzy set is used in fuzzy time series forecasting with simplified computati...