in this paper, new definitions of $l$-fuzzy closure operator, $l$-fuzzy interior operator, $l$-fuzzy remote neighborhood system, $l$-fuzzy neighborhood system and $l$-fuzzy quasi-coincident neighborhood system are proposed. it is proved that the category of $l$-fuzzy closure spaces, the category of $l$-fuzzy interior spaces, the category of $l$-fuzzy remote neighborhood spaces, the category of ...

Introduction and motivation To explain the motivation of our work we give a short glimpse into the history of Fuzzy Topology called more recently Lattice-Valued Topology or Many Valued Topology. In 1968, C. L. Chang [1] introduced the notion of a fuzzy topology on a set X as a subset τ ⊆ [0, 1] satisfying the natural counterparts of the axioms of topology: (1) 0X , 1X ∈ τ ; (2) U, V ∈ τ ⇒ U ∧ V...

The aim of this paper is to introduce and study a new concept ofstrong double $(A)_ {Delta}$-convergent sequence offuzzy numbers with respect to an Orlicz function and also someproperties of the resulting sequence spaces of fuzzy   numbers areexamined. In addition, we define the double$(A,Delta)$-statistical convergence of fuzzy  numbers andestablish some connections between the spaces of stron...

Let $(u_n)$ be a sequence of fuzzy numbers.  We recover the slow oscillation of $(u_n)$ of fuzzy numbers from the Ces`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. Further, fuzzy analogues of some well known classical Tauberian theorems for Ces`{a}ro summability method are established as particular cases.

In this paper, we address the problem of predicting the location of amyloidogenic regions in proteins. The language of protein sequence can be described by using a formal system such as fuzzy context-free grammar, and the problem of amyloidogenic region recognition can be replaced by fuzzy grammar induction. The induced fuzzy grammar achieved 70.6% accuracy and 96.7% specificity on a recently p...

the idea of difference sequences of real (or complex) numbers was introducedby ki zmaz cite{kizmaz}. in this paper, using the difference operator and alacunary sequence, we introduce and examine the class of sequence $bv_{theta}left(  delta,mathcal{f}right)  .$ we study some of its properties likesolidity, symmetricity, etc.

– The purpose of this paper is to explore the following issues in depth: is Non-Classical Logic, by any means, useful to Mathematics at all? Do we see any use in any Non-Classical Logic system in the scope of Mathematics? Can one confound Mathematics with, for instance, Fuzzy Logic applications? If NCL is not useful in Mathematics, is it useful, for instance, in Theology at all? Where lies the ...

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...