期刊
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
卷 120, 期 -, 页码 151-183出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ijar.2020.02.005
关键词
Three-way decision; Rough set; Incomplete information; Similarity; Satisfiability; Fuzzy logic
资金
- National Natural Science Foundation of China [61473239, 61976130]
- China Scholarship Council [201707000052]
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 brief 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. (C) 2020 Elsevier Inc. All rights reserved.
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