Interval-valued Intuitionistic Hesitant Fuzzy Multiple Attribute TOPSIS Decision-making Method And Its Application

There are many decision problems in every aspect of our life. There are some decision problems in real life,which are difficult to process objectively and comprehensively by use the real number, the fuzzy number or the intuitionistic fuzzy numbers. In many practical situations, due to the decision makers’limited knowledge and the uncertainty of evaluation objects, decision makers often can not provide an accurate assessment of value, but shilly-shally at several evaluation values. In order to solve these problems, Torra proposed Hesitant fuzzy sets (HFSs) in 2009. Until now some experts have studied the decision methods which based on hesitant fuzzy sets, but the evaluation value of these research were accurate. In most cases we are very difficult to give an accurate data to evaluations, in order to make the given evaluation value express the meaning of decision makers more comprehensively, the interval-valued hesitate fuzzy sets appear. In the decision method of general fuzzy sets, although there are some studies on interval-valued intuitionistic fuzzy numbers, these does not apply to hesitate fuzzy sets. In order to express the decision information more fully in real life, this article make a study on the TOPSIS decision method, which is based on the interval-valued intuitionistic hesitant fuzzy sets.This paper has done the following work:Firstly, this paper gives the definition and the properties of the distance measures for interval-valued intuitionistic hesitant fuzzy sets, which based on the distance measures for interval-valued intuitionistic fuzzy sets and hesitant fuzzy sets. And the properties were proved by the interval-valued intuitionistic hesitant fuzzy Hamming distance measure. Then definite the interval-valued intuitionistic hesitate fuzzy standard Euclidean distance measure; generalized mixed interval-valued intuitionistic hesitate fuzzy distance measure; generalized interval-valued intuitionistic hesitant fuzzy standard Hausdorff distance measure; generalized mixed interval-valued intuitionistic hesitant fuzzv standard Hausdorff distance measure: generalized interval-valued intuitionistic hesitant tuzzy standard weighted distance measure and generalized continuous interval-valued intuitionistic hesitant fuzzy weighted distance measure. And the validity and practicability of the defined distance measures are validated by an analysis of example.Secondly, according to the positive and negative ideal point’determination method of other forms of fuzzy sets, and combining with the characteristics of interval-valued intuitionistic hesitant fuzzy sets, the paper gives the determination method of positive and negative ideal point of interval-valued intuitionistic hesitant fuzzy sets. And an example verify the method is effective and feasible. Considering that in many decision problems attribute weight value is unknown, the paper gives the model to determine the weights of attributes by the maximum deviation method of interval-valued intuitionistic hesitant fuzzy sets; clearly structure interval-valued intuitionistic hesitant fuzzy form of nonlinear programming model, and gives the specific steps to solve model.Finally, in this paper based on interval-valued intuitionistic hesitant fuzzy sets, we established a multiple attribute decision-making TOPSIS model, which combine the interval-valued intuitionistic hesitant fuzzy sets with the traditional TOPSIS method. The analysis model solved the problems in some practical decision-making process, which include decision maker cannot provide a precise number, a margin of error, several possible value distribution, several possible numerical or interval-valued numbers, but the number of several possible interval-valued intuitionistic fuzzy numbers for evaluation object, due to the time pressure; lack of knowledge or data; limited attention and lack of ability to process information of policy makers. And through the example of project risk investment, model has been successfully applied to multiple attribute decision making of project risk investment.