This paper presents a fuzzy optimization method based on the inclusion degrees of intuitionistic fuzzy sets to solve multi-criteria decision making problems under fuzzy environments. First, the inclusion degree of intuitionistic fuzzy sets is defined and a series of specific formulas of inclusion degree are presented by means of the normal implication operators. Some formulas of inclusion degre...

Abstract The well-known Karush-Kuhn-Tucker theorem can be used, as in the fuzzy case, to find the trapezoidal approximation of a given intuitionistic fuzzy number. The method is quite technical such that obtaining the trapezoidal approximation of an intuitionistic fuzzy numbers from the trapezoidal approximation of a fuzzy number is proposed in the present paper. Among the advantages of this me...

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. Using the notion of intuitionistic fuzzy sets, Çoker [5] introduced the notion of intuitionistic fuzzy topological spaces. In this paper, we define the notion of intuitionistic fuzzy semiopen (r...

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to Hv-modules. The notion of an intuitionistic fuzzy Hv-submodule of an Hv-module is introduced, and some related properties ar...

In 1965, Zadeh introduced the concept of fuzzy subsets. Latter many authors defined different directions of fuzzy subsets. Turksen (1986) generalized the concept of fuzzy set in terms of interval-valued fuzzy set (IVFS). Several researchers present a number of results using IVFSs. Using these concept of (IVFS) Pal and Shyamal (2006) introduced interval-valued fuzzy matrices and shown several pr...

In this paper I will introduce the trapezoidal intuitionistic fuzzy numbers (IF numbers) and will prove some operations for them. Also I am going to propose a new ordering method for IF numbers in which I will consider two characteristic values of membership and non-membership functions for an IF number. These values are defined by the integral of the inverse fuzzy membership and non-membership...

The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results re...

In some multi-attribute decision making (MADM) problems, various relationships among the decision attributes should be considered. This paper investigates the prioritization relationship of attributes in MADM with trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFNs are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. Fir...

in this note, by considering the notions of the intuitionistic general l-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{l}$, there exists a minimal intuitionistic general l-fuzzy automaton recognizing $mathcal{l}$.we prove that the minimal intuitionistic general l-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, be...

in this paper, the concept of intuitionistic fuzzy mapping as a generalization of fuzzy mapping is presented, and its' relationship with intuitionistic fuzzy relations is derived. moreover, some basicoperations of intuitionistic fuzzy mappings are defined, hence we can conclude that all of intuitionistic fuzzy mappings constitute a soft algebrawith respect to these operations. afterwards, the a...