Affiliations: [a] Department of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan, P.R. China | [b] Department of Mathematics and Statistics, Central South University, Changsha, Hunan, P.R. China
Correspondence:
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Corresponding author. Donghai Liu, Department of Mathematics, Hunan University of Science and Technology,
Xiangtan, Hunan 411201, P.R. China. E-mail: dhliu@hnust.edu.cn.
Abstract: An important feature of hesitant interval-valued fuzzy set(HIVFS) is that it can describe the hesitant situations flexibly. In this paper, we first introduce the hesitance degree of HIVFS, then some distance measures between hesitant interval-valued fuzzy sets(HIVFSs) based on the hesitancy degree and least common multiple principle are proposed, which can not only describe the degree of the decision makers’ hesitance in decision making process but also measure the relationship between HIVFS more objectively. Furthermore, we develop the TOPSIS method to the proposed distance measures with different preferences for the hesitancy degree and membership values. Finally, a numerical example is given to illustrate the feasibility of the proposed method, and the effectiveness of the method is verified by some comparative analysis. In order to understand the effect of the preference parameter α and the distance parameter τ in decision making process, we make the sensitivity analysis of parameters by evaluating the example about commercialization of possible emerging technology enterprises.
Keywords: Hesitance degree, hesitant interval-valued fuzzy set, the least common multiple principle, TOPSIS
