When a class of fuzzy value functions constitute a metric space, the completeness and separability is an important problem that must be considered to discuss the approximation of fuzzy systems. In this paper, Firstly, a new tK-integral norm is defined by introducing two induced operators, and prove that the class of tK-integrable fuzzy value functions is a metric space. And then, the integral t...

In this paper, we introduce the notions of fuzzy $alpha$-Geraghty contraction type mapping and fuzzy $beta$-$varphi$-contractive mapping and establish some interesting results on the existence and uniqueness of fixed points for these two types of mappings in the setting of fuzzy metric spaces and non-Archimedean fuzzy metric spaces. The main results of our work generalize and extend some known ...

The study of theory of fuzzy sets was initiated by Zadeh in 1965. Since then many authors have extended and developed the theory of fuzzy sets in the fields of topology and analysis. The notion of fuzzy metric spaces has very important applications in quantum particle physics. As a result many authors have extended the Banach's Contraction Principle to fuzzy metric spaces and proved fixed ...

Decision makers sometimes tend to express their preferences in intuitionistic fuzzy form. Based on evidence theory and grey relational analysis (GRA) technique, this paper aims at investigating multiple attribute decision making problems, in which both attribute values and weight values take the form of intuitionistic fuzzy numbers (IFNs). To this end, each intuitionistic fuzzy evaluation ratin...

In this paper we prove a common fixed point theorem for two fuzzy mappings defined on metric spaces. These mappings are assumed to satisfy certain contractive inequality involving functions which are generalizations of altering distance functions. We also note that this fuzzy fixed point result is derivable from a multi-valued fixed point result.

In this paper, we obtain some common fixed point theorems for four fuzzy mappings in complete ordered metric linear spaces. These mappings are assumed to satisfy certain contractive inequality involving functions which are generalizations of altering distance functions. We also note that this fuzzy fixed point result is derivable from a multi-valued fixed point result.

Considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. This paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology.We study interrelationships between this theory and other fuzzy theories suchas intuitionis...

We consider the concept of fuzzy quasi-contractions initiated by '{C}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{H}$-contractive mappings on M-complete fuzzy metric spaces in the sense of George and Veeramani.The results are illustrated by a representative example.

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...