[Retracted] New Types of μ‐Proximity Spaces and Their Applications

Abstract

Near set theory supplies a major basis for the perception, differentiation, and classification of elements in classes that depend on their closeness, either spatially or descriptively. This study aims to introduce a lot of concepts; one of them is μ -clusters as the useful notion in the study of μ -proximity (or μ -nearness) spaces which recognize some of its features. Also, other types of μ -proximity, termed R μ -proximity and O μ -proximity, on X are defined. In a μ -proximity space X , δ μ , for any subset K of X , one can find out nonempty collections δ μ K = G ⊆ X ∣ K δ ¯ μ G , which are hereditary classes on X . Currently, descriptive near sets were presented as a tool of solving classification and pattern recognition problems emerging from disjoint sets; hence, a new approach to basic μ -proximity structures, which depend on the realization of the structures in the theory of hereditary classes, is introduced. Also, regarding to specific options of hereditary class operators, various kinds of μ -proximities can be distinguished.

Retracted: New Types of μ-Proximity Spaces and Their Applications

“…Tis article has been retracted by Hindawi following an investigation undertaken by the publisher [1]. Tis investigation has uncovered evidence of one or more of the following indicators of systematic manipulation of the publication process:…”