We study the norm induced by the supremum metric on the space of fuzzy numbers. And then we propose a method for constructing a norm on the quotient space of fuzzy numbers. This norm is very natural and works well with the induced metric on the quotient space.

In this paper, we introduce the concept of ∈chainable intuitionistic fuzzy metric space akin to the notion of ∈chainable fuzzy metric space, introduced by Cho, and Jung [6] and prove a common fixed point theorem for weakly compatible mappings in this newly defined space.

The purpose of our paper is to obtain a common fixed point theorem for two pairs of self-mappings of compatible of type (K) in a complete intuitionistic fuzzy Metric space with example. Our result generalized and improves similar other results in literature.

We prove a related fixed point Theorem for four mappings which are not continuous in four fuzzy metric spaces, one of them is a sequentially compact fuzzy metric space. Our Theorem in the metric version generalizes Theorem 4 of [1]. Finally, We give a fuzzy version of Theorem 3 of [1].

Cho et al. [2] introduced the notion of semicompatible maps in a d-topological space. They define a pair of self-maps (S,T) to be semicompatible if conditions (i) Sy = Ty implies that STy = TSy; (ii) for sequence {xn} in X and x ∈ X , whenever {Sxn} → x,{Txn} → x, then STxn → Tx, as n→∞, hold. However, in Fuzzy metric space (ii) implies (i), taking xn = y for all n and x = Ty = Sy. So, we defin...

in this paper, we discuss the equivalent conditions of pretopological and topological $l$-fuzzy q-convergence structures and define $t_{0},~t_{1},~t_{2}$-separation axioms in $l$-fuzzy q-convergence space. {furthermore, $l$-ordered q-convergence structure is introduced and its relation with $l$-fuzzy q-convergence structure is studied in a categorical sense}.

We establish results on invariant approximation for fuzzy nonexpansive mappings defined on fuzzy metric spaces. As an application a result on the best approximation as a fixed point in a fuzzy normed space is obtained. We also define the strictly convex fuzzy normed space and obtain a necessary condition for the set of all t-best approximations to contain a fixed point of arbitrary mappings. A ...

in this paper, we introduce a function in order to measure the distancebetween two order intervals of fuzzy numbers, and show that this function isa metric. we investigate some properties of this metric, and finally presentan application. we think that this study could provide a more generalframework for researchers studying on interval analysis, fuzzy analysis andfuzzy decision making.

Using the idea of approach space due to Robert Lowen [Approach spaces. The missing link in the topology-uniformitymetric triad], we define the notion of fuzzy approach spaces as a natural generalization of fuzzy metric spaces due to Kramosil and Michalek [Kybernetika , 11, 1975, 336–344] and prove some properties of fuzzy approach spaces. Keywords— Approach spaces, Fuzzy approach spaces, Fuzzy ...