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 (α , β) , it changes elements' membership grade μ F (x) to 0 , 0.5 and 1 if μ F (x) < α , α ⩽ μ F (x) ⩽ β and μ F (x) > β 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 ≠ 0 , m ≠ 0.5 and p ≠ 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 (α , β) 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. [ABSTRACT FROM AUTHOR]