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Authors: Qin, Keyun | Luo, Junfang | Pei, Zheng

Article Type: Research Article

Abstract: Rough set approach for knowledge discovery in incomplete information systems has been extensively studied. This paper conduct a further study of valued tolerance relation based rough approximations. We make an analysis of the existing rough approximabilities and propose a new approach for lower (upper) approximability, which is a generalization of Pawlak approximation operators for complete information system. The approach has also been generalized to fuzzy cases. Some basic properties of the approximation operators are examined.

Keywords: Rough set, tolerance relation, valued tolerance relation, lower (upper) approximability

DOI: 10.3233/FI-2015-1290

Citation: Fundamenta Informaticae, vol. 142, no. 1-4, pp. 183-194, 2015

Authors: Wu, Zhengjiang | Li, Tianrui | Qin, Keyun | Ruan, Da

Article Type: Research Article

Abstract: Approximation operators play a vital role in rough set theory. Their three elements, namely, binary relation in the universe, basis algebra and properties, are fundamental in the study of approximation operators. In this paper, the interrelations among the three elements of approximation operators in L-fuzzy rough sets are discussed under the constructive approach, the axiomatic approach and the basis algebra choosing approach respectively. In the constructive approach, the properties of the approximation operators depend on the basis algebra and the binary relation. In the axiomatic approach, the induced binary relation is influenced by the axiom set and the basis algebra. …In the basis algebra choosing approach, the basis algebra is constructed by properties of approximation operators and specific binary relations. Show more

Keywords: L-fuzzy rough sets, approximation operators, basis algebra, binary relation, residuated lattice

DOI: 10.3233/FI-2011-553

Citation: Fundamenta Informaticae, vol. 111, no. 1, pp. 47-63, 2011