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A New Aggregation Method-Based Error Analysis for Decision-Theoretic Rough Sets and Its Application in Hesitant Fuzzy Information Systems

Decision-theoretic rough sets (DTRSs) capture the decision semantics and can deduce three-way decisions with respect to the minimum expected risk. Considering the new evaluation format of hesitant fuzzy sets, we extend the range of applications of DTRSs to hesitant fuzzy information systems. In this case, the integrated approach by considering the interaction between information systems and loss functions becomes one of challenges. Different from the results reported in most of the existing papers, we combine the hesitant fuzzy information system and loss functions together via error analysis. In the hesitant fuzzy information system, a new binary relation is first defined by utilizing the normalization of hesitant fuzzy elements and the distance function. Then, the calculations of the similarity class and the conditional probability are discussed. With the aid of the error analysis method, we effectively aggregate the loss functions presented in the similarity class and determine the expected losses in the format of the intervals. Based on the possibility degree, we further explore the decision rules by comparing the expected losses. With the above analysis, we design a decision-making procedure of three-way decisions in a hesitant fuzzy information system. Finally, we elaborate the application of three-way decisions in hesitant fuzzy information systems by an example of the security evaluation of peer-to-peer lending platforms and validate our methods.