In this paper, we firstly introduce the definition of fuzzy metric sets, and discuss properties induced by Hausdorff metric. Then prove limit theorems for set-valued random variables in space; convergence is about The work an extension from classical results to space.

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

General topology can be regarded as a special case of fuzzy topology where all membership functions in question take values 0 and 1 only. The usual fuzzy metric spaces, fuzzy Hausdorff topological vector spaces, and Menger probabilistic metric spaces are all the special cases of F-type fuzzy topological spaces. Therefore, one would expect weaker results in the case of fuzzy topology. Recently s...

Gregori and Romaguera introduced, in 2004, the notion of a KM-fuzzy quasi-metric space as natural asymmetric generalization concept fuzzy metric sense Kramosil Michalek. Ever since, various authors have discussed several aspects such spaces, including their topological (quasi-)metric properties well connections with domain theory relationship other structures. In particular, development fixed p...

Abstract This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, fixed point results for set-valued cone-contraction mappings. We theorem rational type cone-contractions spaces. Our extend improve given literature.

We shall prove a weak law of large numbers for the uncorrelated (see Definition 3.1) fuzzy random variable sequence with respect to uniform Hausdorff metric $d_H^{\infty}$, which is an extension independent variables.

In this paper, we shall present strong laws of large numbers (SLLN’s) for independent (not necessary identically distributed) fuzzy set-valued random variables whose base space is a separable Banach space or an Euclidean space, in the sense of the extended Hausdorff metric d∞ H .We apply the method to the sequence of independent identically distributed fuzzy set-valued random variables to give ...

After Zadeh pioneering’s paper [15], where the Theory of Fuzzy Sets was introduced, hundreds of examples have been supplied where the nature of uncertainty in the behavior of a given system possesses fuzzy rather than stochastic nature. Non-stationary fuzzy systems described by fuzzy processes look as their natural extension into the time domina. From different viewpoints they were carefully st...

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...