Interval-valued Hesitant Fuzzy Sets And Its Application To Decision Making

Decision making has wide application in engineering, social, economic and other fields. The reasonable representation of evaluation values, the determining of weight vector and the scientific processing of evaluation information have very important role in decision making. Since there are a lot of uncertainty in practical decision making problems, experts always hesitant between several possible evaluation values when they give their evaluation information. The traditional fuzzy sets introduced by Zadeh, the intuitionistic fuzzy sets, type2fuzzy sets, fuzzy multisets and other fuzzy sets are limited at this time. But the hesitant fuzzy sets (HFSs) introduced by Torra permit to present the membership degree using a set of several possible values in [0,1] instead of giving a margin of error, or some possibility distribution on the possible values, so HFSs can depict this kind of decision making problems. Despite some experts and scholars developed some methods of decision making based on HFSs, but these results were obtained on condition that the evaluation information is real numbers. Most of time it is difficult for us to use accurate data to represent our evaluation information, but the relatively reasonable interval value is often exists in decision making. There are many research on interval value based on other fuzzy decision making, but they have not been applied in HFSs. In this paper, we give further study on HFSs, introduce an interval-valued hesitant fuzzy sets, and develop the corresponding decision making method to solve practical decision making problems.The main work of this paper is:1. Considering the flexibility and practicability of the interval number in decision making, and the properties of HFSs, we give the definition of interval-valued hesitant fuzzy sets (IVHFSs), develop some basic operations and properties of elements. Based on the ideal of expectation and standard deviation, we introduce the comparison laws of IVHFEs. We also discuss the relationship of IVHFSs and other fuzzy sets.2. Base on the Hamming distance, Euclidean distance and the Hausdorff distance, we develop a series of distance measures for IVHFSs. In condition that the attribute weights are unknown, we give one method of determining the associated weighting vectors base on the ideal of stander distribution, and apply them to multiple attribute decision making.3. Considering the properties of weighted ordered weighted averaging (WOWA) operator, we develop the interval-valued hesitant fuzzy weighted ordered weighted averaging (IVHFWOWA) operator which is a new information aggregation tool, discuss its properties, give a multiple attribute group decision making model, and give the corresponding method of multiple attribute group decision making. In the end, one actual decision making problem is used to prove the effectiveness and correctness of IVHFWOWA operator.