Operations on soft sets revisited

TL;DR

This paper redefines fundamental operations on soft sets to ensure they obey classical set-theoretic laws, enhancing their mathematical consistency and applicability.

Contribution

It introduces new definitions for intersection, complement, and difference of soft sets that preserve classical set properties.

Findings

New operations inherit all basic properties of classical set operations

Redefinitions ensure consistency with classical set theory

Supports more reliable applications in uncertainty modeling

Abstract

Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft sets from given soft sets, some operations on soft sets have been proposed. Unfortunately, such operations cannot keep all classical set-theoretic laws true for soft sets. In this paper, we redefine the intersection, complement, and difference of soft sets and investigate the algebraic properties of these operations along with a known union operation. We find that the new operation system on soft sets inherits all basic properties of operations on classical sets, which justifies our definitions.