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Rough set theory is studied to manage uncertain and inconsistent information. Because Pawlak's decision logic for rough sets is based on the classical two-valued logic, it is inconvenient for handling inconsistent information. We propose a bilattice logic as the deduction basis for the decision logic of rough sets to address inconsistent and ambiguous information. To enhance the decision logic to bilattice semantics, we introduce Variable Precision Rough Set (VPRS). As a deductive basis for bilattice decision logic, we define a consequence relation for Belnap's four-valued semantics and provide a bilattice semantic tableau TB4 for a deduction system. We demonstrate the soundness and completeness of TB4 and enhance it with weak negation. [ABSTRACT FROM AUTHOR]

Rough sets theory is used to handle uncertain and inconsistent information. While, Pawlak’s decision logic of rough sets is based on classical bivalence logic, this may cause a limitation for the various reasoning. In this study, we propose four-valued logics, as the deduction basis for the decision logic. To provide four-valued semantics to decision logic of rough set, we introduce a Ziarko’s variable precision rough set. As a deductive system, we adopt tableau calculi and define a consequence relation to construct deductive system based on four-valued semantics. Furthermore, weak-negation is introduced to compensate the deduction property of four-value logics. Finally, we discuss Henkin-type proof of the completeness theorem for the system. [ABSTRACT FROM AUTHOR]

In multiple-attribute decision making (MADM) problems, one often needs to deal with decision information with uncertainty. During the last decade, Yang and Singh (1994) have proposed and developed an evidential reasoning (ER) approach to deal with such MADM problems. Essentially, this approach is based on an evaluation analysis model and Dempster's rule of combination in the Dempster-Shafer (D-S) theory of evidence. This paper reanalyzes the ER approach explicitly in terms of D-S theory and then proposes a general scheme of attribute aggregation in MADM under uncertainty. In the spirit of such a reanalysis, previous ER algorithms are reviewed and two other aggregation schemes are discussed. Theoretically, it is shown that new aggregation schemes also satisfy the synthesis axioms, which have been recently proposed by Yang and Xu (2002) for which any rational aggregation process should grant. A numerical example traditionally examined in published sources on the ER approach is used to illustrate the discussed techniques. [ABSTRACT FROM AUTHOR]