Invariant characterizations of fuzzy information systems under some homomorphisms based on data compression and related results

摘要

A fuzzy information system is an important mathematical model in the field of artificial intelligence and the notion of homomorphisms between fuzzy information systems is a kind of tool to study data compression in fuzzy information systems. This paper investigates invariant characterizations of fuzzy information systems under some homomorphisms based on data compression. Upper-reducts, lower-reducts and reducts in a fuzzy information system are first investigated. Then, fuzzy sets in a fuzzy information system are divided into three categories according to their importance. Next, measures of uncertainty for fuzzy information systems are investigated and in order to show the performance of the proposed measures, a numerical experimental example on the Ecoli data set that comes from UCI Repository of machine learning databases is given. Finally, invariant and inverse invariant characterizations of a fuzzy information system under some homomorphisms are obtained. (C) 2018 Elsevier B.V. All rights reserved.