In this paper, the issue of the law of large numbers for fuzzy variables is considered. Since in credibility theory convergence in credibility implies convergence almost sure, the strong law of large numbers is defined via convergence in credibility, while the weak law of large numbers is defined through convergence almost sure. Based on the convergence results about the unform integrability of...

the purpose of this paper is to generalize the concepts of statisticalconvergence of sequences of fuzzy numbers defined by a modulus functionusing difference operator $delta$ and give some inclusion relations.

In this paper we introduce a new type of fuzzy metric space and obtain several properties it. Also some topological boundedness are investigated. The notion convergence sequences together with the cauchy in discussed basic results related to these notions

in this paper, we investigate the l-fuzzy proximities and the relationships betweenl-fuzzy topologies, l-fuzzy topogenous order and l-fuzzy uniformity. first, we show that the category of-fuzzy topological spaces can be embedded in the category of l-fuzzy quasi-proximity spaces as a coreective full subcategory. second, we show that the category of l -fuzzy proximity spaces is isomorphic to the ...

The concepts of (λ ,μ)−fuzzy subsemigroup and various (λ ,μ)−fuzzy ideals of a semigroup were introduced by generalizing (∈,∈∨q)−fuzzy subsemigroup and (∈,∈∨q)−fuzzy ideal. The regular semigroup was characterized by the properties of the middle parts of various (λ ,μ)−fuzzy ideals, and several equivalence conditions of regular semigroups were obtained.

Nanda 1 studied sequence of fuzzy numbers and showed that the set of all convergent sequences of fuzzy numbers form a complete metric space. Nuray 2 proved the inclusion relations between the set of statistically convergent and lacunary statistically convergent sequences of fuzzy numbers. Kwon and Shim 3 studied statistical convergence and lacunary statistical convergence of sequences of fuzzy ...

The concept of (∈,∈∨ q)-fuzzy h-ideals of hemirings is introduced and some characterizations are described. We show that a hemiring S is hhemiregular if and only if for any (∈,∈∨ q)-fuzzy right h-ideal F and (∈,∈∨ q)fuzzy left h-ideal G, F ◦0.5 G = F ∩0.5 G. Finally, the concept of implicationbased fuzzy h-ideals of hemirings is considered. 2010 Mathematics Subject Classification: 16Y60, 13E05,...

The concepts of ∈-soft sets and q-soft sets in AG-groupoids are introduced and some related properties are investigated. In particular, we describe the relationships among ordinary fuzzy interior ideals and soft interior ideals over an AG-groupoid S. Moreover, we study the relation-ships among (∈, ∈ ∨q)fuzzy interior ideals, ( ) , q ∈∈∨ -fuzzy interior ideals, (α; β)-fuzzy interior ideals and s...