Three-way decision with incomplete information based on similarity and satisfiability

TL;DR

This paper extends three-way decision theory to incomplete information scenarios by introducing similarity measures and satisfiability degrees, enabling more practical decision-making in real-world applications.

Contribution

It generalizes existing formulations of three-way decision to incomplete information, proposing new similarity and satisfiability measures for enhanced decision analysis.

Findings

Introduces a similarity degree measure as a generalization of equivalence relations.

Proposes approaches using alpha-similarity classes and approximability of objects.

Develops a satisfiability degree measure for formulas and related decision methods.

Abstract

Three-way decision is widely applied with rough set theory to learn classification or decision rules. The approaches dealing with complete information are well established in the literature, including the two complementary computational and conceptual formulations. The computational formulation uses equivalence relations, and the conceptual formulation uses satisfiability of logic formulas. In this paper, based on a briefly review of these two formulations, we generalize both formulations into three-way decision with incomplete information that is more practical in real-world applications. For the computational formulation, we propose a new measure of similarity degree of objects as a generalization of equivalence relations. Based on it, we discuss two approaches to three-way decision using alpha-similarity classes and approximability of objects, respectively. For the conceptual formulation, we propose a measure of satisfiability degree of formulas as a quantitative generalization of satisfiability with complete information. Based on it, we study two approaches to three-way decision using alpha-meaning sets of formulas and confidence of formulas, respectively. While using similarity classes is a common method of analyzing incomplete information in the literature, the proposed concept of approximability and the two approaches in conceptual formulation point out new promising directions.