Multi-attribute Group Decision Making Methods With Uncertain Linguistic And Intuitionistic Fuzzy Information

Due to the complexity of objective things,uncertainty and fuzziness of human thinking,attribute assessment information are more given by different forms of fuzzy decision information,the fuzzy multi-attribute decision making problems are presented.In order to fully reflect the scientific and democratic of decision-making,involve decision-making groups full participation,the research of fuzzy multi-attribute group decision making theory has become an important research area.Relevant theories and methods are becoming more and more widely applied in the aspects such as society,economy,science and technology.In order to further enrich the fuzzy multi-attribute group decision making theory and methods,this paper studies uncertain linguistic and several kinds of intuitionistic fuzzy evaluation information of fuzzy multi-attribute group decision making problems,a series of group decision making method is proposed,illustrative examples analysis show the effectiveness and feasibility of the proposed methods.The main results can be summarized as follows:(1)With respect to multi-attribute group decision making problems with multi-granularity uncertain linguistic assessment information,where attribute weights are unknown completely.The uncertain linguistic evaluation matrices with multi-granularity are transformed to two-tuple decision matrices according to the continuous ITC-OWH operator.By using projection method,a goal programming model is set up to determine the attribute weights vector of individual decision maker.Then,under every decision makers,integrative attribute dominance degree between pair-wise comparisons of arbitrary alternatives are computed,a group integrative dominance degree matrix is obtained based on integrative dominance degree matrices and expert weight vector.The rank result of alternatives is obtained by the general priority time of alternatives.(2)Based on the interval grey uncertain linguistic variables' superiority to express fuzziness and grayness,three kinds of geometric aggregation operators are given based on definition and operation rules of interval grey uncertain linguistic variables.According to IGULWGA operator,evaluation matrices which given by all decision makers are aggregated to the group evaluation matrix.All attribute values of alternatives are concentrated by IGULHWGA operator,then we get comprehensive evaluation values of alternatives,the rank results of alternatives are obtained based on the rank method of the interval grey uncertain linguistic variables.(3)Research on intuitionistic fuzzy information multi-attribute group decision making method.With respect to three kinds of assessment information decision problems,there are intuitionistic fuzzy number,interval intuitionistic fuzzy number and the interval intuitionistic trapezoidal fuzzy number.Firstly,research on group decision making based on similarity degree and intuitionistic fuzzy entropy.Similarity degree between any two decision makers of alternatives under every attributes is obtained.Then,single attribute's average similarity degree between individual and group decision maker is gained,normalization processing is carried out to average similarity,decision-makers weights are determined.Attribute weights are got by calculating intuitionistic fuzzy entropy of intuitionistic fuzzy information.The rank results of alternatives are obtained based on score function.Secondly,research on interval-valued intuitionistic fuzzy group decision making based on correlation coefficient and improved TOPSIS.Calculate the correlation coefficient between individual attribute values and its mean evaluation,decision-makers weights determined by single attribute under every alternative of all decision-makers can be obtained.A target programming model is established based on the maximization of correlation coefficient between each alternative and the positive ideal alternative.Basing on the improved TOPSIS to calculate the relative correlation coefficient between each alternative and the positive and negative ideal alternative,rank result of the alternatives can be obtained.Thirdly,research on interval-valued intuitionistic trapezoidal fuzzy multi-attribute group decision making based on grey relation-projection.Definition negative extreme decision matrix and average decision matrix,according to the distance between every decision matrix and two types decision matrix,decision makers weights are determined.Basing on the minimization of relative similarity degree between each alternative and the positive(or negative)ideal alternative to get attribute weights.Grey relation-projection of every attributes to positive ideal alternative are obtained,the rank of alternatives is determined by projected values of the alternatives.(4)The possible interactions between the membership function and the non-membership function of intuitionistic uncertain linguistic number are considered,addition,multiplication,multiplication,and power multiplication are being redefined,intuitionistic uncertain linguistic weighted interaction arithmetic averaging operator,ordered arithmetic averaging operator and hybrid arithmetic averaging operator are proposed,meanwhile,intuitionistic uncertain linguistic weighted interaction geometric averaging operator,ordered geometric averaging operator and hybrid geometric averaging operator are proposed.According to the characteristics of the proposed operators,intuitionistic uncertain linguistic multi-attribute group decision mak-ing method considered interaction is investigated,an example shows the feasibility and validity of the method.(5)Research on hybrid assessment information group decision-making method.The first decision making method is based on intuitionistic fuzzy cross entropy and grey relational,different types of subjective evaluation information are unified into intuitionistic fuzzy number,weights of decision makers are determined by the new definition of score function and based on evaluation deviation between individual decision maker and the group decision makers.Using intuitionistic fuzzy entropy to determine the attribute weights,according to the cross entropy between intuitionistic fuzzy number,the rank results of alternatives are obtained based on gray correlative analysis method,group decision making method based on intuitionistic fuzzy cross entropy and grey relational are proposed.The second group decision making method is based on distance measure and support degree.By defining the distance measure of different types evaluation information,mutual support degree between two different decision makers are obtained,which is under a variety of different types of subjective evaluation information with the same alternative suppliers.Then calculating sum support degree under individual attribute values of every alternative suppliers,the sum support degree reflects the decision group's supporting degree to single attribute evaluation information which given by every decision makers,so comprehensive evaluation values of every attributes are determined.Attribute weights are determined by mean distance and standard distance between attribute values and its average.The rank results of alternatives are obtained based on gray correlative analysis method,group decision making method with hybrid assessment information based on distance measure and support degree are proposed.