A Novel Three-Way Investment Decisions Based on Decision-Theoretic Rough Sets with Hesitant Fuzzy Information

As a classic model of three-way decisions, the decision-theoretic rough sets (DTRSs) have been adopted to help make profit-based investment decisions. However, there is epistemic uncertainty in the assessment of investment projects, hence the hesitant fuzzy sets (HFSs) are appropriate tool for characterizing the revenue functions and cost functions. To get a more reasonable result in the three-way investment decisions, we introduce HFSs to DTRSs and explore a new three-way investment decision model. Firstly, we take into account the revenue and cost of DTRSs with hesitant fuzzy elements and propose a hesitant fuzzy decision-theoretic rough sets (HFDTRSs) model. Then, we calculate the revenue functions and cost functions by aggregating hesitant fuzzy elements with the Bayesian decision procedure. Considering the differences in the personalities and attitudes of decision-makers, we propose optimistic strategy and pessimistic strategy to aggregate revenue functions and cost functions. Finally, based on the score of profit maximization, we make three-way investment decisions. A case study of coal investment was used to demonstrate the proposed methods.