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Homomorphisms between fuzzy information systems. (English) Zbl 1179.94090

Summary: The information system is one of the most important mathematical models in the field of artificial intelligence, and the concept of mapping is a useful tool for studying the communication between two information systems. In this work, the concepts of fuzzy relation mapping and inverse fuzzy relation mapping are first introduced and their properties are studied. Then, the notions of homomorphisms of information systems based on fuzzy relations are proposed, and it is proved that attribute reductions in the original system and image system are equivalent to each other under the condition of homomorphism.

MSC:

94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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