GDTRSET: a generalized decision-theoretic rough sets based on evidence theory

Decision-theoretic rough sets (DTRS), produced by Bayesian risk minimum principle and three-way decision theory, is a novel methodology to deal with risk decision problems. As one of the two basic concepts in DTRS, conditional probability is used for measuring the probability of objects belonging to different states. The calculation of condition probability needs a complete information system as prior information. However, we often encounter complicate scenario where prior information is lacking, it is more common that several agents may be involved in a decision process and give their opinion. To model uncertain information of experts' assessment, a Generalized Decision-Theoretic Rough Sets based on Evidence Theory (GDTRSET) is put forward in this paper. The proposed GDTRSET extends the set of states by introducing a new uncertain state. Correspondingly, instead of using conditional probability in DTRS, basic probability assignment in evidence theory is utilized for describing the belief of objects belonging to different states. The proposed GDTRSET first discusses the determination of conditional probability without prior information, which can handle uncertain information efficiently and flexibly. Besides, a unified framework for classification based on the proposed GDTRSET is presented, taking advantage of three-way and risk decision perspectives for classification. A case study of the Iris dataset is finally illustrated the efficiency of the proposed GDTRSET.