A fuzzy multigranulation decision-theoretic approach to multi-source fuzzy information systems

Decision-theoretic rough set theory (DTRS) is becoming one of the important research directions for studying set approximations using Bayesian decision procedure and probability theory in rough set community. In this paper, a novel model, fuzzy multigranulation decision-theoretic rough set model (FM-DTRS), is proposed in terms of inclusion measure of fuzzy rough sets in the viewpoint of fuzzy multigranulation. Gaussian kernel is used to compute the similarity between objects, which induces a fuzzy equivalence relation, and then we make use of Tp-norm operator with the property of Hadamart product to aggregate the multiple induced fuzzy equivalence relations. We employ the aggregated relation to fuzzily partition the universe and then obtain multiple fuzzy granulations from the multi-source information system. Moreover, some of its properties are addressed. A comparative study between the proposed fuzzy multigranulation decision-theoretic rough set model and Qian’s multigranulation decision-theoretic rough set model is made. An example is employed to illustrate the effectiveness of the proposed method which may provide an effective approach for multi-source data analysis in real applications.