The distance measures between q-rung orthopair hesitant fuzzy sets and their application in multiple criteria decision making

In this paper, we first introduce the concept of q-rung orthopair hesitant fuzzy set (q-ROHFS) and discuss the operational laws between any two q-ROHFSs. Then the distance measures between q-ROHFSs are proposed based on the concept of "multiple fuzzy sets", and we develop the TOPSIS method to the proposed distance measures. The proposed distance measures not only retain the preference information expressed by q-ROHFSs, but also deal with the q-rung orthopair hesitant fuzzy decision information more objectively, In fact, the method can avoid the loss and distortion of the information in actual decision-making process. Furthermore, we give an illustrative example about the selection of energy projects to illustrate the reasonableness and effectiveness of the proposed method, which is also compared with other existing methods. Finally, we make the sensitivity analysis of the parameters in proposed distance measures about the selection of energy projects.