Distance and Similarity Measures for Soft Sets

TL;DR

This paper critiques existing soft set similarity measures, corrects previous errors, introduces new set operation-based measures, and demonstrates their effectiveness in financial diagnosis applications.

Contribution

It identifies flaws in prior similarity measures, proposes improved set operation-based measures, and validates their application in financial diagnosis.

Findings

Previous similarity measures contained errors.

New measures outperform existing ones in accuracy.

Application to financial diagnosis shows practical effectiveness.

Abstract

In [P. Majumdar, S. K. Samanta, Similarity measure of soft sets, New Mathematics and Natural Computation 4(1)(2008) 1-12], the authors use matrix representation based distances of soft sets to introduce matching function and distance based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corllary of our result. The fundamental assumption of Majumdar et al has been shown to be flawed. This motivates us to introduce set operations based measures. We present a case (Example 28) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed herein decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.