An Extension of Soft Operations on Generalized Soft Subsets

Abstract

Existing Literature, Problem and Limitation: To address problems of fuzzy data in various fields, Molodtsov presented soft set theory, a broad mathematical technique for ambiguity. This theory has been used in a variety of pure and practical mathematical fields. It is
evident in this theory that soft subsets and soft equal relations significantly contributed to soft topology, lattices, soft groups, etc. Existing research is limited in that various features, such as associative, distributive, etc., are not confirmed by some current soft subsets for soft product operations. Purpose: While studying soft subsets, we observe that several algebraic properties have not yet been investigated on various generalized soft subsets to enhance algebraic structures in soft set theory. So, this article investigates some of these algebraic properties on different generalized soft subsets on different soft operations. Contribution: This study demonstrates a few counterexamples that some algebraic properties are unsatisfied by generalized soft subsets. Based on this approach, we present some crucial theorems and results that show these significant features on all soft subsets by employing additional conditions. A universal complement property in soft set theory in relation to soft complements (negation complement (c) and relative complement (r )) is propounded. Limitation: The sole restriction of these results is that two generalised soft subsets (soft J-subset and soft L-subset) do not satisfy the union and intersection condition of classical mathematics as described in section 4