Study On Some Problems Of The Multi-attribute Group-Decision Making Using The Interval-valued Intuitionistic Fuzzy Sets

Group-decision making is an important field in the decision-making theory research. There are many fuzziness and uncertainty decision-making problems in reality, so it is an important train of thoughts that applying the fuzzy sets theory to the groupdecision making.However,the fuzzy sets theory is in the development and perfects itself: since the fuzzy sets was proposed,the intuitionistic fuzzy sets,the interval-valued intuitionistic fuzzy sets are one after the other proposed and are attracted experts' more attention.We study the literature about the theories and methods on group-decision making,then found that:the interval-valued intuitionistic fuzzy sets(IVIFSs) theory is seldom applied to study group-decision making problems.The author tries to apply this theory to study the fuzzy multi-attribute group-decision making problems,the main contents is as follows:1,Giving out the geometric meaning of the one dimensional interval-valued intuitionistic fuzzy sets;Considering the intuitionistic fuzzy distance definition,we give out the two unified definitions of the interval-valued intuitionistic fuzzy distance:Hamming distance,Euclidean distance and their normalized distances.These distances not only illustrate the three parameters(the degree interval of belongingess,the degree interval of nonbelongingness and the intuitionistic fuzzy interval) not only develop from the three parameters(the degree of belongingess,the degree of nonbelongingness and the intuitionistic fuzzy degree) of the intuitionistic fuzzy distance,but also reflect the existence of intuitionistic fuzzy interval in decision makers' evaluation.2,First,the model of multi-attribute group-decision making based on the IVIFSs is put forward;Then,an interval-valued intuitionistic fuzzy multi-attribute groupdecision making method based on the Set Pair Analysis(SPA) is proposed,while the weights of criteria and experts is the classical data,the data of the decision matrices belongs to the IVIFSs.By this method,we can make order of the alternatives by the shi(μ(A_i));Finally,a numerical example is given to apply this method,its experiment shows that the p,q which is in the operator H_p,qaffect the ordering of the alternatives, which help the decision maker make decision flexibly.3,By the Hamming distance which is based on the Hausdorff metric,a new method for solving the consensus degree aggregation problem of the experts' opinions is proposed.First,the Hamming distance based on the Hausdorff metric is defined, which is get from the interval-valued intuitionistic fuzzy sets' Hamming distance and the Hausdorff distance;Then,the relative consensus degree of each expert to the other experts' is aggregated for every alternative;Furthermore,we aggregate all the experts consensus degree into an aggregated consensus degree as the experts group's;Finally, a numerical example is given to apply this method.