An Accurate Method for Determining Hesitant Fuzzy Aggregation Operator Weights and Its Application to Project Investment

As a generalization of fuzzy sets, hesitant fuzzy set is a very useful technique to represent decision makers’ hesitancy in decision making. Various hesitant fuzzy weighted operators have been developed to aggregate hesitant fuzzy information, but it seems that there is no investigation on the weighted approach of obtaining their weights, which is decisive for the calculation and comparison of hesitant fuzzy elements (HFEs) in multicriteria group decision making. In this paper, we propose an accurate weighted method (AWM) of monotonicity and proportionality, based on nothing but the score function and the new deviation function. Because of the above properties, AWM may be an accurate and objective technique to calculate the weights of HFEs and aggregation operator. Then, based on this weighted approach, we develop two new hesitant fuzzy ordered weighted aggregation operators, that is, hesitant fuzzy ordered accurate weighted averaging and hesitant fuzzy ordered accurate weighted geometric operators, and study their relationships and properties. In the end, an illustrative project investment problem is used to demonstrate how to apply the proposed weighted approach and to observe the computational consequences resulting from new aggregation operators. This work contributes significantly to improve the hesitant fuzzy theory, and proposes two new hesitant fuzzy aggregation operators.