Hesitant fuzzy psychological distance measure

Distance is an indispensable measure in many fields such as clustering analysis, decision making and pattern recognition, etc. When calculating the distance of hesitant fuzzy information, the existing methods normally only take the values of the attributes into consideration while ignore the preferential relationship between the options, which may not meet some actual situations. Thus, it is necessary to propose a new distance measure for hesitant fuzzy information considering both the two aspects. In order to realize this in our paper, firstly, a multi-attribute space is built, in which each attribute is given a unique weight from the experts to show the subjective importance; secondly, the distance vector between the hesitant fuzzy sets (HFSs) is constructed and a balancing coefficient is proposed; thirdly, a novel distance measure for HFS, called the hesitant fuzzy psychological distance measure is developed. In view of the experts’ preferences for the options, the proposed hesitant fuzzy psychological distance between the alternatives can be enlarged relative to the traditional hesitant fuzzy distance measures, which shows a good reasonability in reflecting the experts’ subjective preferences for different alternatives. Furthermore, two numerical examples are used to illustrate the effectiveness and feasibility of the hesitant fuzzy psychological distance measure.