Methods To Multi-Attribute Decision Making With Picture Fuzzy Information And Their Application

Multi-attribute decision-making problem widely exists in real life.With the increasing complexity of decision-making scenarios in modern social life and business environments,how to build powerful and flexible multi-attribute decision-making methods to provide decision makers with scientifically valid results is a major research challenge in decision-making.In the field of decision science,researchers never stop exploring excellent multi-attribute decision methods.Research on multi-attribute decision making has focused on two issues: first,how to accurately express decision evaluation information,and second,how to effectively aggregate evaluation information from multiple attributes.For the first point,a growing number of scholars are introducing fuzzy information into multi-attribute decision-making processes to more fully describe human evaluative information.For the second point,evaluation information is aggregated mainly through information aggregation operators or traditional information evaluation methods.Predecessors have introduced intuitionistic fuzzy sets into multi-attribute decision making,and have proposed some multi-attribute decision methods for intuitionistic fuzzy information environments based on various information aggregation operators and traditional information evaluation methods,respectively.These methods have subsequently been widely used to solve practical problems,but they still fall short in their consideration of hesitant information.Picture fuzzy set is expanded on the basis of intuitionistic fuzzy sets with a neutral membership degree,the information description capability of which is relatively stronger.However,the researches on multi-attribute decision-making methods based on picture fuzzy sets are few and not go far enough.In order to better apply the advantages of picutre fuzzy sets to multi-attribute decision-making,this thesis applies picture fuzzy information to multi-attribute decision problems,and proposes new multi-attribute decision-making methods based on two ways of aggregating information.In the perspective of information aggregation operators,some picture fuzzy Dombi Heronian mean operators and a multi-attribute decision-making method based on these operators are proposed.In the perspective of information aggregation based on the traditional evaluation method,the picture fuzzy hierarchy analysis process and its multi-attribute decision algorithm are explored.Based on the methodological study,this study applies the proposed method to the decision problem of ERP service provider selection to clarify the process of using the aforementioned method and verify the superiority of the method through results analysis and method comparison analysis.The new proposed multi-attribute decision-making methods based on picture fuzzy information in this paper can solve multi-attribute decision-making problems more effectively and flexibly,and enrich the existing research.The main contributions include:(1)In the environment of picture fuzzy information,a new multi-attribute decision-making method based on Dombi t-norm and t-conorm and Heronian mean operator is developed.By utilizing the flexible Dombi operations and the Heronian mean operator with powerful information aggregation capabilities,this method can effectively consider the relationship between attributes during the information aggregation process,and can flexibly adjust the degree of information aggregation and the consideration of relationship between attributes through parameters.By using a new score function of picture fuzzy set proposed in this paper,this method can more effectively and fully use picture fuzzy evaluation information in multi-attribute decision-making.In addiction,compared with other multi-attribute decision-making methods based on picture fuzzy information aggregation operators,this method is more flexible and effective.(2)The analytic hierarchy process is expanded in the context of picture fuzzy information for the first time;a multi-attribute decision-making algorithm based on picture fuzzy analytic hierarchy process is innovatively proposed.We introduce the concept of picture fuzzy preference relation,exponential score function,the picture fuzzy multiple preference relation and its associated consistent preference relation.According to this,we propose the analytic hierarchy process based on optimal transfer matrix which can be used to process picture fuzzy information and solve the problem of multi-attribute decision-making with uncertain attribute weights.Besides,experts can freely use picture fuzzy numbers to express preference information and the proposed method can automatically correct the consistency of preference relationships,which provides reliable and accurate information basis and therefore ensures the effectiveness of decision results.By using different score functions of picture fuzzy set to deal with the preference information and different aggregation operators to calculate the total priority weight vector,this method can be more flexibly applied to solve actual multi-attribute decision-making problems.