RETRACTED: New Types of μ-Proximity Spaces and Their Applications (Retracted Article)

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 mu-clusters as the useful notion in the study of mu-proximity (or mu-nearness) spaces which recognize some of its features. Also, other types of mu-proximity, termed R mu-proximity and O mu-proximity, on X are defined. In a mu-proximity space, for any subset K of X, one can find out nonempty collections delta mu, 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 mu-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 mu-proximities can be distinguished.