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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]

Abstract: In recent years, much attention has been given to the rough set models based on two universes of discourse and different kinds of rough set models on two universes have been developed from different points of view. In this paper, a novel model, i.e., the graded rough set model on two distinct but related universes (GRSTU) is proposed from the absolute quantitative point of view. We study the basic properties of approximation operators in GRSTU, and introduce a relation matrix based algorithm to compute the lower and upper approximations of a set of objects in GRSTU. Furthermore, the relationships between classical rough set model and GRSTU are discussed and some conclusions related to the GRSTU are given. Finally, several examples are employed to demonstrate the conceptual arguments of GRSTU, and an application of GRSTU is also illuminated in details. [Copyright &y& Elsevier]

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]

Four kinds of constructive methods of rough approximation operators from existing rough sets are established, and the important conclusion is obtained: some rough sets are essentially direct applications of these constructive methods. Moreover, the new notions of non-dual multigranulation rough sets and hybrid multigranulation rough sets are introduced, and some properties are investigated. [ABSTRACT FROM AUTHOR]

This paper develops a supervised discriminant technique, called graph embedding discriminant analysis (GEDA), for dimensionality reduction of high-dimensional data in small sample size problems. GEDA can be seen as a linear approximation of a multimanifold-based learning framework in which nonlocal property is taken into account besides the marginal property and local property. GEDA seeks to find a set of perfect projections that not only can impact the samples of intraclass and maximize the margin of interclass, but also can maximize the nonlocal scatter at the same time. This characteristic makes GEDA more intuitive and more powerful than linear discriminant analysis (LDA) and marginal fisher analysis (MFA). The proposed method is applied to face recognition and is examined on the Yale, ORL and AR face image databases. The experimental results show that GEDA consistently outperforms LDA and MFA when the training sample size per class is small. [ABSTRACT FROM AUTHOR]