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

2025-12-24

AI Summary

Classical three-way decision theory under incomplete information is constrained by its reliance on equivalence relations and binary satisfiability, limiting its applicability to real-world uncertain and incomplete data. Method: This paper proposes a unified three-way decision framework integrating similarity and satisfiability. It introduces novel concepts—including object approximation measure, formula α-meaning set, and semantic confidence—by synergizing rough set theory, fuzzy similarity measures, logical semantic quantification, α-cuts, and approximate reasoning. The framework incorporates two similarity-driven and two satisfiability-driven three-way partitioning mechanisms. Contribution: By relaxing the traditional assumptions of equivalence and bivalence, the approach enables robust classification and decision-making under missing data. It significantly enhances uncertainty modeling capability and establishes a new paradigm for three-way decision-making in incomplete information environments.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Preferences

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Extends three-way decision to incomplete information scenarios
• Proposes similarity and satisfiability measures for generalization
• Introduces new approaches using approximability and confidence concepts

Innovation

• Similarity degree measure for incomplete information
• Satisfiability degree generalization for formulas
• Approximability and confidence in three-way decision