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Multigranulation decision-theoretic rough sets (MDTRS) is a model for real-world decision making. In various existing optimistic MDTRS models, the lower and upper approximations are defined based on the strategy seeking commonality while preserving differences, while pessimistic MDTRS models based on the strategy Seeking commonality while eliminating differences in the definitions of approximations. In real-world problems, one may need different strategies in defining lower approximations and upper approximations. This paper proposes two new MDTRS approaches in the frameworks of multi-covering approximation spaces by using different strategy in defining lower and upper approximations, namely, covering-based optimistic-pessimistic multigranulation decision-theoretic rough sets and covering-based pessimistic-optimistic multigranulation decision-theoretic rough sets, respectively. We explore a number of basic properties of the proposed models. Then, we elaborate on the relationship between the proposed models and the existing ones in the literature. And we also disclose the interrelationships of the proposed models. Finally, we provide a case study to demonstrate the effectiveness of the proposed models. [ABSTRACT FROM AUTHOR]

Three way decision model, as a new and meaningful decision making method, has attracted much attention and various results and applications have been reported. This paper investigates decision-theoretic rough set (DTRS) approach in the framework of multi-covering approximation spaces. By integrating fuzzy probability measure into Bayesian decision procedure, we define the notions of covering-based mean multigranulation decision-theoretic rough sets, covering-based optimistic multigranulation decision-theoretic rough sets, and covering-based pessimistic multigranulation decision-theoretic rough sets. We first investigate the basic properties of the three proposed models. Second, we elaborate on the relationship between the proposed models and those existing in literature, and discuss the interrelationships of the models. Finally, an illustrative example is employed to show the application of the proposed models. [ABSTRACT FROM AUTHOR]

Fuzzy rough sets and multi-granularity rough sets are essential extensions of Pawlak rough sets, which have become artificial intelligence research hotspots. Previous studies of the rough sets based on the fuzzy T-equivalence relation did not take the multi-granularity into account. The multi-granularity data is typically the multi-view cognition obtained by different granularity of the data, and its distinctive feature is that the data can be presented in different granularity spaces. In this paper, we integrate the idea of multi-granularity and propose four new models of "optimistic," "pessimistic," "optimistic-pessimistic," and "pessimistic-optimistic" decision-theoretic rough sets based on the fuzzy T-equivalence relation for the first time, followed by a preliminary analysis of the intrinsic relations and properties of these new decision-theoretic rough set models by a concrete example. At last, we use experiments to show the effectiveness of suggested models, proving that they are both rational and practical. [ABSTRACT FROM AUTHOR]