Affiliations: [a] School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, P.R. China | [b] Key Laboratory of Complex System Optimization andBig Data Processing in Department of Guangxi Education, Yulin NormalUniversity, Yulin, Guangxi, P.R. China | [c] School of Artificial Intelligence, GuangxiUniversity for Nationalities, Nanning, Guangxi, P.R. China
Correspondence:
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Corresponding author. Zhaowen Li, Key Laboratory of Complex System Optimization and Big Data Processing in Department of Guangxi Education, Yulin Normal University, Yulin, Guangxi 537000, P.R. China. E-mail: [email protected].
Abstract: An information system (IS) is an important mathematical tool for artificial intelligence. A fuzzy probabilistic information system (FPIS), the combination of some fuzzy relations in the same universe which satisfies the probability distribution, can be seen as an IS with fuzzy relations. A FPIS overcomes the shortcoming that rough set theory assumes elements in the universe with equal probability and leads to lose some useful information. This paper integrates the probability distribution into the fuzzy relations in a FPIS and studies its reduction. Firstly, the concept of a FPIS is introduced and its reduction is proposed. Then, the fuzzy relations in a FPIS are divided into three categories (P-necessary, P-relatively necessary and P-unnecessary fuzzy relations) according to their importance. Next, entropy measurement for a FPIS is investigated. Moreover, some reduction algorithms are constructed. Finally, an example is given to verify the effectiveness of these proposed algorithms.
