In this paper, we introduce the concept of best proximal contraction theorems in non-Archimedean fuzzy metric space for two mappings and prove some proximal theorems. As a consequence, it provides the existence of an optimal approximate solution to some equations which contains no solution. The obtained results extend further the recently development proximal contractions in non-Archimedean fuz...

The notion of intuitionistic fuzzy metric space was introduced by Park (2004) and the concept of intuitionistic fuzzy normed space by Saadati and Park (2006). Recently Mursaleen and Lohani introduced the concept of intuitionistic fuzzy 2-metric space (2009) and intuitionistic fuzzy 2-norm space. This paper studies precompactness and metrizability in this new setup of intuitionistic fuzzy 2-metr...

In this paper we embed the space of upper semicontinuous convex fuzzy sets on a Banach space into a space of continuous functions on a compact space. The following structures are preserved by the embedding: convex cone, metric, sup-semilattice. The indicator function of the unit ball is mapped to the constant function 1. Two applications are presented: strong laws of large numbers for fuzzy ran...

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

this study is an investigation of fuzzy linear regression model for crisp/fuzzy input and fuzzy output data. a least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of fuzzy numbers. the proposed approach, which can deal with both symmetric and non-symmetric fuzzy observations, is compared with several existing models by...

As a generalization of fuzzy sets , Atanassov [14] introduced and studied the concept of intuitionistic fuzzy sets park[11] using the idea of intuitionistic fuzzy sets defined the notion of intuionistic fuzzy metric spaces with the help of continuous t-norm and continuous t co-norm as a generalization of fuzzy metric space due to George & veeramani [6] had showed that every metric induces an in...

In this paper, following the ideas of (continuous) t-norm and interval numbers, a concept of (continuous) interval-valued t-norm is proposed. Based on the interval-valued fuzzy set and the continuous interval-valued t-norm, we propose a notion of interval-valued fuzzy metric space, which is a generalization of fuzzy metric space in the sense of George and Veeramani [Fuzzy Sets and Systems 64 (1...

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 ...