Covering Based Soft Rough Fuzzy Set and its Application in Soil Chemical Analysis for Soybean Crop

Abstract

In the agricultural field several studies were done using mathematical and statistical tools. But these methods are incapable of dealing with the incompleteness and vagueness of data. Hence to deal with such data nowadays non-classical set theories are proving their worth. The study incorporates concepts of covering based rough set with soft set and fuzzy set. Various literature is available in which soft, rough, and fuzzy sets are applied but none of them are based on covering features. To analyze soil chemical treatments for the soybean crop an attempt is made through Covering based Soft Rough Fuzzy set (CSRFS). Initially, soft rough subspaces are defined. Then these subspaces are mapped with membership and non-membership functions along with appropriate regions generated through the boundary of soft rough subspaces to define soft rough fuzzy set. Lastly, the ranking of treatments is defined with set-valued mapping, and a comparison of the proposed method is done with the other existing methods. The proposed study namely CSRFS is an extension of the covering based rough set, soft set, and fuzzy set to generate a decision system for soil chemical analysis of Soybean crop.