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Fuzzy sets and binary-proximity-based rough sets

Authors
Journal
Information Sciences
0020-0255
Publisher
Elsevier
Publication Date
Volume
104
Identifiers
DOI: 10.1016/s0020-0255(97)00075-3

Abstract

Abstract A crisp subset is shown to be represented in a Fariñas del Cerro-Orlowska model with one equivalence relation that has two equivalence classes. A possible-worlds-restriction model is constructed by using pieces of information derived from the equivalence relation and from a piece of information about a positive instance, and crisp subset formation is demonstrated in the model. Then the formation is extended to one proximity relation case, where the relation represents the relationship between elements in a fuzzy set. A possible-worlds-restriction model is similarly constructed by using pieces of information derived from the proximity relation with implicit transitivity as well as from those pieces about both positive and negative instances. Then a well-known method of selecting maximal consistent subsets from the pieces is adopted. Because the method produces two or more equivalence relations, a fuzzy set can be represented in a Fariñas del Cerro-Orlowska model with plural equivalence relations.

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