most of the researches in the domain of fuzzy number comparisons serve the fuzzy number ordering purpose. for making a comparison between two fuzzy numbers, beyond the determination of their order, it is needed to derive the magnitude of their order. in line with this idea, the concept of inequality is no longer crisp however it becomes fuzzy in the sense of representing partial belonging or de...

This paper extends the author’s earlier work on the Law of Large Numbers for fuzzy numbers [2] to the case where the fuzzy numbers are of type L-R. Namely, we shall define a class of Archimedean triangular norms in which the equality lim n→∞ Nes(mn − ≤ ηn ≤ mn + = 1, for any > 0, holds for all sequences of fuzzy numbers, ξi = (Mi, α, β)LR, i ∈ N, with twice differentiable and concave shape func...

The purpose of this paper is to introduce the concepts of lacunary almost statistical limit and cluster points of sequences of fuzzy numbers. For any lacunary sequence = ( ); and for any sequence = ( ) of fuzzy numbers, we introduce new sets: Λ ( ), Γ ( ),Λ ̂ ( ),Γ ( ) and obtain some relations between these sets.

In this article we introduce the notion of statistical convergence difference sequences of fuzzy real numbers, c̄ (∆). We study some properties of the statistically convergent and statistically null difference sequence spaces of fuzzy real numbers, like completeness, solidness, sequence algebra, symmetricity, convergence free, nowhere denseness and some inclusion results.

the operations in the set of fuzzy numbers are usually obtained bythe zadeh extension principle. but these definitions can have some disadvantagesfor the applications both by an algebraic point of view and by practicalaspects. in fact the zadeh multiplication is not distributive with respect tothe addition, the shape of fuzzy numbers is not preserved by multiplication,the indeterminateness of t...

This paper suggests  a novel approach for ranking the most applicable fuzzy numbers, i.e.  $LR$-fuzzy numbers. Applying the  $alpha$-optimistic values of a fuzzy number, a preference criterion is proposed for ranking fuzzy numbers using the Credibility index. The main properties of the proposed  preference criterion  are also studied.  Moreover, the proposed method is   applied for ranking fuzz...

and Applied Analysis 3 Conversely, if the pair of functions α and β satisfy the conditions 1 – 4 , then there exists a unique u ∈ E1 such that u λ α− λ , β λ for each λ ∈ 0, 1 , 9 . The fuzzy number u corresponding to the pair of functions α and β is defined by u : R → 0, 1 , u x sup{λ : α x ≤ λ ≤ β x }, 5 . A sequence u uk of fuzzy numbers is a function u from the set N, the set of all positiv...