Multi-attribute decision making with hesitant fuzzy information based on least common multiple principle and reference ideal method

The TOPSIS method is a technique for establishing order preference by similarity to the ideal solution, however, the traditional TOPSIS method cannot deal with the situation where the ideal solution vary between the minimum value and the maximum value. Considering the reference ideal can be any set or a point between the minimum value and maximum value, we introduce a reference ideal-TOPSIS method under the hesitant fuzzy decision environment in this paper. Firstly, we propose some new distance measures between hesitant fuzzy sets (HFSs), which take the hesitance degree of hesitant fuzzy element and the least common multiple expansion (LCME) principle into consideration. Then the reference ideal-TOPSIS method is developed by combing the proposed distance measures and reference ideal theory. Furthermore, we apply the proposed reference ideal-TOPSIS method to illustrate its practical use and make sensitivity analysis of distance measure parameters to observe the stability of the decision making results. A comparison analysis with the existing methods is also given to verify its rationality and effectiveness.