A novel approach of three-way decisions with information interaction strategy for intelligent decision making under uncertainty

Abstract

As an effective tool to deal with uncertain decision-making, three-way decisions (TWD) have gained wide attention in many applications. Decision-theoretic rough sets (DTRSs) as a classic model of TWD contain two key elements, i.e., conditional probability and loss functions. In this paper, we study the determination of these two elements in depth via the information interaction and modification strategy, and further propose a novel model of TWD. First, fuzzy c-means (FCM) is used to cluster the condition attribute information and loss function information, respectively. Considering the interaction of two types of information, we design the corresponding fusion tactic of these clustering results to get equivalent classes and develop a new calculation method of conditional probability. Then, we use probabilistic hesitant fuzzy sets (P-HFSs) to aggregate the loss functions of different members of the same equivalence class and get the probabilistic hesitant fuzzy elements (P-HFEs) loss functions. In this case, P-HFSs not only reflect the hesitant situation of decision-makers, but also depict the proportion of different opinions. Regarding P-HFEs loss functions, we also investigate the modification methods of its outliers in detail. Moreover, based on the P-HFEs loss functions, we propose TWD with probabilistic hesitant fuzzy decision-theoretic rough sets (P-HFDTRSs). Finally, in order to verify the effectiveness of our proposed method, we develop a series of comparative experiments and discuss the decision results on six UCI datasets.