A Problem on Decision Making Through Soft Approximation Space

This paper aims at defining the idea of soft rough set in a modified manner for strengthening the mechanism to handle the problem of uncertainty since it is an effective mathematical tool for approaching various types of unpredictability. The connection between rough set and soft set is established during the course of derivation developing related properties pertinent to this concept. In-place of an equivalence relation, a soft set is used to break the universe in to innumerable fragments for identifying each objects which leads to an approximation space called soft approximation space. In consequence soft lower approximation operator, soft upper approximation operator is introduced. Some examples are presented giving interesting properties of soft rough approximations. A comparison between the proposed method and the previous one is accomplished. The concept of soft rough approximate inclusion relation is presented and its properties are derived. Finally, four types of soft covering based rough sets have been defined by using soft neighborhoods, soft cohesion and soft inverse neighborhood along with examining related properties. In addition, soft rough set is defined in a new way without using full soft set.