Answering a recent question posed by Gregori, Morillas and Sapena (“On a class of completable fuzzy metric spaces”, Fuzzy Sets and Systems, 161 (2010), 2193–2205) we present two examples of non strong fuzzy metrics (in the sense of George and Veeramani).

The formulation of strong and weak laws of large numbers for fuzzy random variables based on variance is given. The concept of the variance of fuzzy random variables, introduced by K1 orner (Fuzzy Sets and Systems 92 (1997) 83) and by Feng (Fuzzy Sets and Systems 120 (2001) 487) demonstrates its e2ciency. c © 2002 Elsevier Science B.V. All rights reserved.

The aim of this paper is to point out and correct some errors of two theorems for IFSs in Atanassov (Two theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 2000) and bring forward a new theorem for IFSs. In the end, some elementary, but non-standard equalities between IFSs were formulated.

We provide an extension of the notion of chain-valued frame introduced by Pultr and Rodabaugh in [Category theoretic aspects of chain-valued frames: parts I and II, Fuzzy Sets and Systems 159 (2008) 501–528 and 529–558] by relaxing the assumption that L be a complete chain. As a result of this investigation we formulate the category L-Frm of L-frames under the weaker assumption that L is a comp...

The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by Özkoç and Aslım [10] called weakly $eR$-open functions and $e$-$theta$-open functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topolo...

‎in this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. moreover, we study some more properties of this type of closed spaces.

This paper introduces the concepts of fuzzy pseudo-open sets in fuzzy topological spaces and fuzzy pseudo-continuous functions between fuzzy topological spaces. Several characterizations of fuzzy pseudo-open sets are established. A conditions under which fuzzy hyper-connected spaces become fuzzy Baire spaces, is obtained by means of fuzzy pseudo-open sets. Several examples are given to illustra...

The purpose of this paper is to define and study some new types hesitant fuzzy open sets namely, α -open, preopen, semiopen, b-open β -open in topological space. Some properties the relationships between these are investigated. Furthermore, them subspace introduced.