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A uninorm based semantic analysis of multigranulation rough set models. (Chinese. English summary) Zbl 1413.68140
Summary: A uninorm is a new type of aggregation operator whose identity element lies anywhere in $$[0, 1]$$. It is the natural generalization of both t-norms and t-conorms. This paper seeks to investigate the existing multigranulation rough set models from the viewpoint of uninorms. Precisely, we propose a new type of approach to information fusion in multigranulation space. To this end, we firstly review some basic notions about uninorms and rough set models in multigranulation spaces. Then we give a new definition of rough membership degree in multigranulation space with two equivalence relations imposed upon the universe. Based on the membership degree, we also classify the universe into three disjoint regions according to the essential idea of three-way decision. We also examine the properties of rough membership degree in detail. The obtained results show that if the rough membership degree in each Pawlak space is larger than or equal to the identity element of the concerted uninorm, then its rough membership degree in multigranulation space is larger than or equal to those in each Pawlak space, this is a type of optimistic information fusion. Contrarily, if the rough membership degree in each Pawlak space is less than or equal to the identity element of a uninorm, then the combined rough membership degree in multigranulation space is less than or equal to those in each Pawlak space, this is a type of pessimistic information fusion. Since both t-norms and t-conorms are treated as special cases of uninorms, we analyze the feature of information fusion by using these two types of uninorms. We also give the representation of the existing multigranulation rough set models by using uninorms. The obtained results show that the optimistic multigranulation rough set model can be expressed in terms of uninorms, on the contrast, the pessmistic multigranulation rough set model cannot be expressed by using uninorms. Noting that in the expression of optimistic multigranulation rough set models, the elements of boundary region are treated equally, concretely, the membership degrees of elements in boundary regions are $$\frac{1}{2}$$. We further extend this result by considering the rough membership degree proposed by Pawlak. Moreover, by using a more general notion of compromise operators, we give the new definition of rough membership degree in multigranulation space and present its semantic feature.
##### MSC:
 68T37 Reasoning under uncertainty in the context of artificial intelligence
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