Paper:

# Bilattice Logic for Rough Sets

## Yotaro Nakayama^{*}, Seiki Akama^{**}, and Tetsuya Murai^{***}

^{*}Nihon Unisys, Ltd.

1-1-1 Toyosu, Koto-ku, Tokyo 135-8560, Japan

^{**}C-Republic, Inc.

1-20-1 Higashi-Yurigaoka, Asao-ku, Kawasaki-shi, Kanagawa 215-0012, Japan

^{***}Chitose Institute of Science and Technology

758-65 Bibi, Chitose, Hokkaido 066-8655, Japan

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.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.24, No.6, pp. 774-784, 2020.

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