Decision-theoretic rough set approach for fuzzy decisions based on fuzzy probability measure and decision making

Article type: Research Article

Authors: Dai, Jianhua^{a; b; *} | Zheng, Guojie^b | Hu, Qinghua^a | Liu, Maofu^c | Su, Huashi^b

Affiliations: [a] School of Computer Science and Technology, Tianjin University, Tianjin, China | [b] College of Computer Science and Technology, Zhejiang University, Hangzhou, China | [c] College of Computer Science and Technology, Hubei Province Key Laboratory of Intelligent Information Processing and Real-time Industrial System, Wuhan University of Science and Technology, Wuhan, China

Correspondence: [*] Corresponding author. Jianhua Dai. E-mail: david.joshua@qq.com.

Abstract: Most existing studies on decision-theoretic rough set approach focus on crisp decisions. However, in many cases, we need to handle fuzzy concepts. This paper investigates decision-theoretic rough set approach for fuzzy decisions. By introducing fuzzy operators, we extend the traditional decision-theoretic rough set approach with crisp decisions to fuzzy concepts. Decision-theoretic rough set approach with fuzzy concepts is investigated based on fuzzy probabilistic approximation space. Bayesian decision procedure based on fuzzy probabilistic approximation space with fuzzy concepts and fuzzy probabilistic decision systems with fuzzy or continuous decision attributes are studied. The application of the proposed approach in decision making is also illustrated by an example. This study may expand the applications of decision-theoretic rough set model.

Keywords: Decision-theoretic rough set, fuzzy concepts, fuzzy decision, decision making

DOI: 10.3233/IFS-162200

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1341-1353, 2016