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 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 ...

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...

We deepen the study of two known neighborhood structures, which here will be called f · k-neighborhood structures and f · q-neighborhood structures, in the context of Šostak fuzzy topological spaces. In particular, we characterize fuzzy topologies by f · k-neighborhood structures. Moreover we introduce and discuss the notions of f · kneighborhood prestructure and f ·m-neighborhood structure in ...

Methods like DBSCAN are widely used in the analysis of spatial data. These methods are based on the neighborhood relations which use distance between points. However, these neighborhood relations consider to have at least a certain number of neighbors within a definite boundary. In this proposed work such a neighborhood analysis is done by using the benefits of fuzzy sets theory. Usage of fuzzy...

In this paper, we introduce new definitions of L-fuzzy neighborhood systems, L-fuzzy interior operators and L-fuzzy closure operators. Three characterizations of the category L-FTOP of L-fuzzy topological spaces and their L-fuzzy continuous mappings are presented by means of the category L-FNS of L-fuzzy neighborhood spaces and their continuous mappings, the category L-FIS of L-fuzzy interior s...