A generalized cost-sensitive model for decision-theoretic three-way approximation of fuzzy sets

Decision-theoretic three-way approximation of a fuzzy set F exploits a three-element set {0, 0.5, 1} in order to approximate F. By relying on an optimum pair of thresholds (alpha , beta) , it changes elements' membership grade mu F(x) to 0, 0.5 and 1 if lF(x) < alpha , alpha 5 mu F(x) 5 b and mu F(x) > beta respectively. A general three-element system, {n , m , p} , 0 <= n < m <= p <= 1, has been proposed in the literature. However, the main issue is to determine appropriate n not equal 0, m not equal 0.5 and p not equal 1. A recent advancement has determined m(0 < m < 1). However, n = 0 and p =1 are still imposed by the model. This restriction on the values of n and p lacks general adaptation for different types of membership distribution. In this paper, a novel way of determining appropriate values of n , m , and p is given without the aforesaid restriction. We consider an alternative {n , m , p} formula for computing the optimum pair (a , b) in cost-sensitive three-way approximation context. We use synthetic fuzzy sets and some datasets from UCI Machine Learning repository to demonstrate the suitability of the {n , m , p} system in minimizing approximation error and producing well-guided approximation regions. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The decision-theoretic three-way approximation of a fuzzy set F utilizes a three-element set {0, 0.5, 1} to approximate F, using optimum pair of thresholds (alpha, beta). The paper introduces a novel way of determining appropriate values of n, m, and p without the restriction of n = 0 and p = 1, showing the suitability of the {n, m, p} system in minimizing approximation error.