The reduction and fusion of fuzzy covering systems based on the evidence theory

This paper studies reduction of a fuzzy covering and fusion of multi-fuzzy covering systems based on the evidence theory and rough set theory. A novel pair of belief and plausibility functions is defined by employing a method of non-classical probability model and the approximation operators of a fuzzy covering. Then we study the reduction of a fuzzy covering based on the functions we presented. In the case of multiple information sources, we present a method of information fusion for multi-fuzzy covering systems, by which objects can be well classified in a fuzzy covering decision system. Finally, by using the method of maximum flow, we discuss under what conditions, fuzzy covering approximation operators can be induced by a fuzzy belief structure.