In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of...

Taking intuitionistic fuzzy sets as the structures of truth values, we propose the notions of intuitionistic fuzzy context-free grammars (IFCFGs, for short) and pushdown automata with final states (IFPDAs). Then we investigate algebraic characterization of intuitionistic fuzzy recognizable languages including decomposition form and representation theorem. By introducing the generalized subset c...

In this paper, we investigate an assignment problem in which cost coefficients are triangular intuitionistic fuzzy numbers. In conventional assignment problem, cost is always certain. This paper develops an approach to solve an intuitionistic fuzzy assignment problem where cost is not deterministic numbers but imprecise ones. Here, the elements of the costs (profits) matrix of the assignment pr...

In this paper, we introduce a new class of implicit functions and also common property (E.A) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. We are not aware of any paper dealing with such implicit functions in modified intuit...

In this paper, the Multiple Attribute Group Decision Making (MAGDM) problems is based on the attribute weights calculated from completely unknown information using the Maximal Entropy OWA weights. The interval-valued intuitionistic fuzzy ordered weighted averaging (IIFOWA) operator is utilized to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the dec...

in this paper, we introduce intuitionistic fuzzy contraction mappingand prove a fixed point theorem in intuitionistic fuzzy metric spaces.

The concept of intuitionistic fuzzy sets is the generalization of the concept of fuzzy sets. The theory of intuitionistic fuzzy sets is well suited to dealing with vagueness. Recently, intuitionistic fuzzy sets have been used to build soft decision making models that can accommodate imprecise information, and two solution concepts about the intuitionistic fuzzy core and the consensus winner for...

The aim of this study is to introduce the concept of intuitionistic fuzzy (left, right) hyperideal in intuitionistic fuzzy semihypergroup based on the concept of intuitionistic fuzzy space as a direct generalization of the concept of fuzzy ideals in fuzzy semigroups, through the new approach of fuzzy space introduced by Dib and fuzzy hypergroup introduced by Fathi. A relationship between the in...

On the basis of the concept of grades of a fuzzy point to belongingness (∈) or quasi-coincident (q) or belongingness and quasi-coincident (∈ ∧q) or belongingness or quasi-coincident (∈ ∨q) in an intuitionistic fuzzy set of a ring, the notion of a (α,β )intuitionistic fuzzy subring and ideal is introduced by applying the Lukasiewicz 3-valued implication operator. Using the notion of fuzzy cut se...

After the introduction of fuzzy sets by Zadeh [20] in 1965, several researchers have been working on the generalization of the fuzzification. In 1986, Atanassov [2] introduced the notion of intuitionistic fuzzy sets. For more details on the intuitionistic fuzzy sets, we refer to [2-4]. Fuzzy sets are intuitionistic fuzzy sets but the converse is not necessarily true [18]. Kim and Jun [7, 8] int...