Relations and Applications on Proximity Structures

The purpose of this work is to construct a type of proximity relations in ideally proximity spaces based on an ideal I and three types of the proximity δ. Examples are given for the constructed relation. The constructed γ -relation is a pre- basic (resp., Ef, Lo) - proximity if δ is the basic (resp., Ef, Lo)- proximity. Properties and characterization of γ - relation are obtained. Connections between types of ideal and properties of γ -relation are obtained. The suggested relation can help in the fields of uncertainty processing in the context of rough set data analysis which are related to a lot of real life applications.