We introduce the notion of N-topo nilpotent fuzzy set in a fuzzy neighborhood ring and develop some fundamental results. Here we show that a fuzzy neighborhood ring is locally inversely bounded if and only if for all 0 < α < 1, the α-level topological rings are locally inversely bounded. This leads us to prove a characterization theorem which says that if a fuzzy neighborhood ring on a division...

In many data mining processes, neighborhood operators play an important role as they are generalizations of equivalence classes which were used in the original rough set model of Pawlak. In this article, we introduce the notion of fuzzy neighborhood system of an object based on a given fuzzy covering, as well as the notion of the fuzzy minimal and maximal descriptions of an object. Moreover, we...

In many data mining processes, neighborhood operators play an important role as they are generalizations of equivalence classes which were used in the original rough set model of Pawlak. In this article, we introduce the notion of fuzzy neighborhood system of an object based on a given fuzzy covering, as well as the notion of the fuzzy minimal and maximal descriptions of an object. Moreover, we...

in this paper, we present gauss-sidel and successive over relaxation (sor) iterative methods for finding the approximate solution system of fuzzy sylvester equations (sfse), ax + xb = c, where a and b are two m*m crisp matrices, c is an m*m fuzzy matrix and x is an m*m unknown matrix. finally, the proposed iterative methods are illustrated by solving one example.

In the last decades, many efforts have been made to solve multimodal optimization problems using Particle Swarm Optimization (PSO). To produce good results, these PSO algorithms need to specify some niching parameters to define the local neighborhood. In this paper, our motivation is to propose the novel neighborhood structures that remove undesirable niching parameters without sacrificing perf...

In this paper, we introduce the concepts of L-fuzzy generalized neighborhood system(f-gns for short) and L-fuzzy generalized topology (fgt, for short)(where L is a fuzzy lattice) which are generalizations of generalized topology and neighborhood systems defined by Csaszar[5]. We also introduce and investigate with the help of these new concepts the concepts of L-(ψ1, ψ2) continuity and L-fuzzy ...

in this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where a~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisti...

In this paper, we present Gauss-Sidel and successive over relaxation (SOR) iterative methods for finding the approximate solution system of fuzzy Sylvester equations (SFSE), AX + XB = C, where A and B are two m*m crisp matrices, C is an m*m fuzzy matrix and X is an m*m unknown matrix. Finally, the proposed iterative methods are illustrated by solving one example.

The theory of neighborhood systems is abstracted from the geometric notion of "near" or "negligible distances." It is a "new" theory of the classical concept of neighborhood systems within the context of advanced computing. By definition neighborhood systems include both rough sets and topological spaces as special cases. The deeper and more interesting part is in its interactions with fuzzy se...