Keyun Qin

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.

Interval neutrosophic sets (INSs), characterized by truth, indeterminacy and falsity membership degrees, handle the uncertain and inconsistent information that commonly exists in real-life systems, and constitute an extension of the interval valued fuzzy set and interval valued intuitionistic fuzzy set. The existing works on similarity measures for INSs are mostly constructed by distance measures and entropies. Meanwhile, the degree of similarity is expressed as a single number, even if the interval-valued information is considered. This may lead to a loss of interval-valued information. In order to cope with these issues, in this paper, we introduce a new approach to constructing the similarity measures for INSs using fuzzy equivalencies. First, based on fuzzy equivalencies and aggregation operators, the definition of interval-valued fuzzy equivalence is generalized to interval neutrosophic values. Then, based on the framework of INSs, we propose the definition and construction method of the similarity measure using the interval neutrosophic fuzzy equivalence. The similarity degree is expressed as an interval and could retain more information than ever before. In addition, according to practical situations, one can obtain different similarities by selecting the parameters in fuzzy equivalence. Due to the increase in edge computing, it is necessary to reasonably offload the client’s resource and assign them to the edge server to balance the resource usage. The Similarity measure is conductive to select and match the client and edge server. Finally, an illustrative example verifies that the proposed method can find a reasonable client and edge server, as well as effectiveness in the edge computing application.