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...

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

A Fuzzy Extractor (Dodis et al., Eurocrypt 2004) is a two-step protocol that turns a noisy secret into a uniformly distributed key R. To eliminate noise, the generation procedure takes as input an enrollment value ω and outputsR and a helper string P that enables further reproduction ofR from some close reading ω′. Boyen highlighted the need for reusable fuzzy extractors (CCS 2004) that remain ...

Given a compact and connected metric space (continuum) X, we study topological and dynamical properties of the hyperspace of normal fuzzy sets F1(X) equipped with the Hausdorff, endograph or sendograph metric. Among the many results we show that it is contractible, path connected, locally contractible, locally path connected, locally simply connected and locally connected. For the endograph met...

Some asymptotic properties of point estimation with n-dimensional fuzzy data with respect to a special L2-metric ρ are investigated in this paper. It is shown that the collection of all n-dimensional fuzzy data endowed with the ρ-metric is a complete and separable space. Some criterions for point estimation in such fuzzy environments are proposed and the sample mean and variance and covariance ...

In this paper we study the relationships existing between total measurability in variation and Gould type fuzzy integrability (introduced and studied in [21]), giving a special interest on their behaviour on atoms and on finite unions of disjoint atoms. We also establish that any continuous real valued function defined on a compact metric space is totally measurable in the variation of a regula...

Let X be a compact metric space, let φ be a continuous self-map on X , and let F(X) denote the space of fuzzy sets on X equipped with the levelwise topology. In this paper we study relations between various dynamical properties of a given (crisp) dynamical system (X,φ) and its Zadeh’s extension Φ on F(X). Among other things we study various (weak, strong, mild etc.) mixing properties and also s...

In this paper we establish some fixed point theorems for Generalized Contraction mappings in complete fuzzy 2-metric space which are the extension of some known result of many authors. 1 Introduction In 1965, the concept of fuzzy set was introduced initially by Zadeh [11] since then many authors have expansively developed the theory of fuzzy sets and applications. Especially Deng [1], Ereeg [2]...

This manuscript contains several new notions including intuitionistic fuzzy Nb metric space, quasi-Sb-metric pseudo-Sb-metric quasi-N-metric space and pseudo space. We prove decomposition theorem fixed-point results in the setting of Further, we provide non-trivial examples to show validity introduced results. At end, solve an integral equation, system linear equations nonlinear fractional diff...

1. Branciari. A. A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29 (2002), no. 9, 531-536. 2. Cho Y.J., Fixed points in fuzzy metric spaces, J. Fuzzy Math. 5 (4) (1997) 949-962. 3. Grabiec M. , Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27 (1988) 385-389. http://dx.doi.org/10.1016/0165-0114(88)90064-4. 4....