Soft Approximations and uni-int Decision Making

TL;DR

This paper analyzes soft set approximations and decision methods, improves Cagman's uni-int approach, and proposes a new conjecture that better solves the optimum choice problem in soft decision making.

Contribution

It introduces an improved uni-int method and a new conjecture for soft decision making, addressing shortcomings in previous approaches.

Findings

Proves equivalence of uni-int method to a less computationally intensive core-support expression.

Identifies shortcomings in existing uni-int methods.

Proposes a new conjecture that correctly solves the optimum choice problem.

Abstract

Notions of core, support and inversion of a soft set have been defined and studied. Soft approximations are soft sets developed through core and support, and are used for granulating the soft space. Membership structure of a soft set has been probed in and many interesting properties presented. The mathematical apparatus developed so far in this paper yields a detailed analysis of two works viz. [N. Cagman, S. Enginoglu, Soft set theory and uni-int decision making, European Jr. of Operational Research (article in press, available online 12 May 2010)] and [N. Cagman, S. Enginoglu, Soft matrix theory and its decision making, Computers and Mathematics with Applications 59 (2010) 3308 - 3314.]. We prove (Theorem 8.1) that uni-int method of Cagman is equivalent to a core-support expression which is computationally far less expansive than uni-int. This also highlights some shortcomings in Cagman's uni-int method and thus motivates us to improve the method. We first suggest an improvement in uni-int method and then present a new conjecture to solve the optimum choice problem given by Cagman and Enginoglu. Our Example 8.6 presents a case where the optimum choice is intuitively clear yet both uni-int methods (Cagman's and our improved one) give wrong answer but the new conjecture solves the problem correctly.