We consider some modifications of the neural gas algorithm. First, fuzzy assignments as known from fuzzy c-means and neighborhood cooperativeness as known from self-organizing maps and neural gas are combined to obtain a basic Fuzzy Neural Gas. Further, a kernel variant and a simulated annealing approach are derived. Finally, we introduce a fuzzy extension of the ConnIndex to obtain an evaluati...

The notion of fuzzy is context dependent, so for each context very often there is a fuzzy theory. Present papers use the notion of neighborhood systems to unify them. A neighborhood system is an association that assigns to each datum a list of data (a neighborhood). Rough sets and topological spaces are special cases. A “real world” fuzzy set should allow small amount of perturbation, so it sho...

Recently, Particle Swarm Optimization (PSO) algorithm has exhibited good performance across a wide range of application problems. A quick review of the literature reveals that research for solving the Quadratic Assignment Problem (QAP) using PSO approach has not much been investigated. In this paper, we design a hybrid meta-heuristic fuzzy scheme, called as variable neighborhood fuzzy particle ...

Based on fuzzy gp*-closed sets and gp*-open sets, in this paper we have introduced gp*- neighborhoods, gp*-Interior gp*-Closure. Also investigated some of their elementary properties discuss important theorems

In this paper, for a complete residuated lattice L, we present the categorical properties of ?-neighborhood spaces and their relationships to neighborhood stratified L-neighborhood spaces. The main results are: (1) category is topological category; (2) can be embedded in as reflective subcategory, when L meet-continuous lattice, subcategory; (3) continuous (resp., spaces) simultaneously corefle...

In this paper we introduce various notions of continuous fuzzy proper functions by using the existing notions of fuzzy closure and fuzzy interior operators like Rτ -closure, Rτ -interior, etc., and present all possible relations among these types of continuities. Next, we introduce the concepts of α-quasi-coincidence, qα r -pre-neighborhood, qα r -pre-closure and qα r pre-continuous function in...