Ma, Jian-Min; Yao, Yiyu Rough set approximations in multi-granulation fuzzy approximation spaces. (English) Zbl 1346.68201 Fundam. Inform. 142, No. 1-4, 145-160 (2015). Summary: Pawlak’s rough set model considers the rough approximations based on an equivalence relation. Multi-granulation rough set models concern rough approximations based on multiple equivalence relations. In this paper, we examine six types of rough set approximations in multi-granulation fuzzy approximation spaces (MGFASs). We construct a partition of the given universe based on a fuzzy binary relation in a fuzzy approximation space. Based on the partition, we introduce a pair of rough set approximations. In a multi-granulation fuzzy approximation space, by a family of fuzzy binary relations, we introduce two kinds of rough set approximations in terms of the union and intersection of fuzzy relations, respectively. A pair of rough set approximations based on the family of fuzzy binary relations is also discussed. Furthermore, the optimistic and pessimistic multi-granulation rough set approximations are investigated due to the fuzzy binary relations in a MGFAS. Properties of these rough set approximations are demonstrated. Finally, we examine relationships of them. It is proved that the lower and upper approximations generated by a family of fuzzy binary relations are the pair nearest to the undefinable set, and the pessimistic multi-granulation lower and upper approximations are the pair farthest to the undefinable set. Cited in 3 Documents MSC: 68T37 Reasoning under uncertainty in the context of artificial intelligence Keywords:multi-granulation; multi-granulation fuzzy approximation space; optimistic multi-granulation approximation; pessimistic multi-granulation approximation PDFBibTeX XMLCite \textit{J.-M. Ma} and \textit{Y. Yao}, Fundam. Inform. 142, No. 1--4, 145--160 (2015; Zbl 1346.68201) Full Text: DOI