Research On Multi-attribute Decision Making Methods With Hesitant 2-Tuple Linguistic Information

In the real decision making,there is a wide range of multi-attribute decision making problems using linguistic evaluation information to express preferences.As a model for expressing linguistic evaluation information,2-tuple linguistic representation model can effectively avoid the information loss in the fusion process of linguistic information.However,since the realistic decision-making environment affected by many factors is complex and the theoretical knowledge and practical experience of decision-makers are not comprehensive enough,people often hesitate when they evaluate the decision making problems.As one of the extended forms of 2-tuple linguistic representation model,the hesitant 2-tuple linguistic information model has a strong ability to describe the linguistic decision making information in this kind of indecisive situation.In this paper,the multi-attribute decision making methods based on the hesitant 2-tuple linguistic information are studied,and the main research work is as follows:(1)A hesitant 2-tuple linguistic grey relational group decision making approach based on prospect theory is proposedFor the hesitant 2-tuple linguistic multi-attribute group decision making problems in which both the attribute weights and the decision maker weights are completely unknown,a comparison method between two hesitant 2-tuple linguistic elements is given,a method for determining the decision maker weights is proposed by means of the matrix vec operator and the grey relational analysis,and the maximizing deviation method is introduced to calculate the weights of attributes.The hesitant 2-tuple linguistic prospect value function is acquired on the basis of the prospect theory and the grey relational coefficient.And then the alternatives are ranked according to the ratio of gains to losses of the alternatives.The proposed method is applied to a numerical example of investment decision to show the decision making process.Based on the degree of discrimination,the proposed method is compared with other methods,which shows that the proposed decision making method is reasonable and effective.(2)A hesitant 2-tuple linguistic multi-attribute group decision making method based on ELECTRE is proposedThe ELECTRE method takes into account the partial compensability among attributes,and the decision results are more consistent with the real decision making situation.Therefore,the ELECTRE method is extended to the multi-attribute group decision making problems in which the decision information is the hesitant 2-tuple linguistic element,and a decision making method based on ELECTRE is proposed.The possibility degree formula for comparing two hesitant 2-tuple linguistic elements is defined,and the distance measure is introduced.The hesitant 2-tuple linguistic concordance set,discordance set,and the indifference set are determined by the possibility degree formula in the method.The hesitant 2-tuple linguistic concordance index and discordance index are respectively determined based on the weighted possibility degree and the distance measure,and their corresponding matrices can be constructed.The comprehensive dominance matrix is determined via the Hadamard product between the concordance matrix and the complementary matrix of the discordance matrix,and then the net dominant value is determined,and the alternatives are ranked by that.Finally,the feasibility and effectiveness of the proposed method are demonstrated by the application of numerical example and comparison with other methods.(3)A hesitant fuzzy 2-tuple linguistic multi-attribute decision method based on TOPSIS and grey relational degree is proposedCombining the advantages of the hesitant fuzzy linguistic term set and 2-tuple linguistic representation model,the hesitant fuzzy 2-tuple linguistic set can express the linguistic evaluation information more flexibly and accurately.A decision making method based on TOPSIS method and grey relational degree is proposed to solve the multi-attribute decision making problems in which the decision information is hesitant fuzzy 2-tuple linguistic set.The hesitancy index of the hesitant fuzzy 2-tuple linguistic set is defined,which is combined with the mean function to compare the magnitudes of two hesitant fuzzy 2-tuple linguistic sets.The distance measure of hesitant fuzzy 2-tuple linguistic set is defined,and the grey relational coefficient can be determined based on that.A deviation-based method is proposed to determine the attribute weights.In order to achieve the aim that the optimal solution is nearest to the positive ideal solution and farthest from the negative ideal solution at the same time,the revised closeness index based on the distance measure is introduced,and the revised closeness index based on grey relational degree is defined.The comprehensive revised closeness index of each alternative is obtained by combining the above mentioned two revised closeness indices,and the ranking of alternatives is realized accordingly.Finally,the proposed method is applied to a decision example and compared with other methods.The results show that the proposed method is feasible.