| With the continuous development of decision science,the multi-attribute group decision-making has begun to play an increasingly important role in modern decision-making.How to effectively express decision-making information is the primary and key issue in the study of decision-making issues.However,due to the complexity and variability of decision-making environment,the fuzziness of people’s cognition and the uncertainty of information expression,it is difficult for decision makers to give an accurate evaluation value for the evaluation of a decision.In order to preserve the integrity of information and meet people’s subjective expression,fuzzy sets came into being.With the development of fuzzy theory,intuitionistic fuzzy sets begin to be studied by a large number of experts and scholars.Among them,the range of expression of fuzzy information has also become larger and larger.From the initial intuitionistic fuzzy sets that the sum of the membership degree u expressing the degree of satisfaction and the non-membership degree v expressing the degree of dissatisfaction is less than 1,to the Pythagorean fuzzy sets which u~2+v~2≤1,to the present q-rung orthopair fuzzy sets which u~q+v~q≤1.The scope of expression of fuzzy information begins to broaden continuously,so that the expression of evaluation information is more complete and the information distortion is lower.The way of information expression is more in line with the realistic decision-making environment and people’s cognitive level.The information aggregation operator is an effective tool for processing decision information.It is simple to calculate and has some special information processing functions.For example,the power operators can eliminate the influence of extreme evaluation value on the evaluation result.The Maclaurin symmetric mean can consider the relationship between the different evaluated attributes.At the same time,the traditional information evaluation methods can also process decision information.Although their processes are complicated,they can effectively reduce the loss of information and improve the accuracy of decision-making.Therefore,in the study of multi-attribute group decision-making problem,we need to further extend these information processing tools to q-rung orthopair fuzzy environment.Therefore,this paper will study two kinds of aggregation operators based on q-rung orthopair fuzzy numbers and the corresponding multi-attribute group decision-making evaluation methods,which can adapt to the current more complex decision-making environment and play a guiding role in the practical decision-making.The main innovations of this paper are the following:(1)Based on the definition of q-rung orthopair fuzzy numbers,the operation rules,operation property,distance formula,scoring function,exact function and corresponding comparison method are proposed.They lay a theoretical foundation for the following research.(2)Combining the power operator and MSM operator with the q-rung orthopair fuzzy numbers,respectively.Then the q-rung orthopair fuzzy power aggregation operators and the q-rung orthopair fuzzy MSM aggregation operators are proposed,and combine the power operator with MSM operator to propose some power MSM aggregation operators.The properties of these operators are proved.Some multi-attribute group decision-making methods based on these operators are proposed.The effectiveness and superiority of the method are verified by some examples and the comparative analysis with other exiting methods.(3)Aiming at the problem of multi-attribute group decision making with unknown weight of experts,a new method for determining weight of experts is proposed,and the traditional TOPSIS evaluation method is extended.An improved q-rung orthopair fuzzy TOPSIS multi-attribute group decision-making method is proposed and it can effectively reduce the distortion of the information.The effectiveness and superiority of the method are verified by some examples and the comparative analysis with other exiting methods. |
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