Pythagorean Fuzzy Multi-attribute Group Decision Making Method And Its Application

Due to the limited background and professionalism of individual decision makers,it is often difficult to give full consideration to significant decision making.The Pythagorean fuzzy set expands the concept of intuitionistic fuzzy sets,which can better express the opinions of decision makers.In addition,to select appropriate haze management supplier through the given evaluation of attributes by decision makers,and given the evaluation of haze management effect,which has great significance for achieving high haze management with low cost.Therefore,this paper summarizes the choice of haze management equipment suppliers and the evaluation of urban haze management effects as a typical Pythagorean fuzzy multi-attribute group decision problem.Pythagorean fuzzy sets have been widely used in practical decision-making problems,and research on Pythagorean fuzzy multi-attribute decision making methods has emerged in an endless stream.However,the current research on Pythagorean fuzzy multi-attribute decision making method has the following three shortcomings: First,in many studies,the weights of decision makers and the weights of attributes are given in advance,which has subjectively arbitrary,and will influence the decision result.The second is that the research on the attribute weights method with considering multiple information measurement indices of Pythagorean fuzzy numbers is relatively rare.The third is the research on Pythagorean fuzzy aggregation operators need to be study intensively.In order to make up for the above three shortcomings of the existing Pythagorean fuzzy multi-attribute decision making method,this paper proposes a multi-attribute group decision based on Pythagorean fuzzy information measurement and generalized Pythagorean fuzzy Hamacher aggregation operators based method to settle multi-attribute decision making.The method is applied to the selection of suppliers of haze management equipment and the evaluation of urban haze management effects.The main content of the article is divided into the following two aspects.1.Considering the importance of Pythagorean fuzzy information measurement for Pythagorean fuzzy multi-attribute decision making,this paper proposes a multi-attribute group decision making method based on Pythagorean fuzzy information measurement.Firstly,this paper defines the normalized projection,entropy measurement and Riemann closeness degree of Pythagorean fuzzy numbers.Based on the normalized projection of Pythagorean fuzzy numbers,this paper extends the TOPSIS(Technique for Order Preference by Similarity to an Ideal Solution)method to derive the weights of decision makers.Secondly,based on the proposed entropy measure,the paper defines the score entropy and the accuracy entropy respectively,and establishes a multi-objective parameter comprehensive deviation model to obtain the attribute weights.Then,by calculating the Riemann closeness degree of each alternative,the ranking value and ranking order of the alternatives are obtained.Finally,this paper introduces the implementation process of multi-attribute group decision making method based on Pythagoras fuzzy information measurement in detail,and the application analysis of the haze management supplier selection problem,which verifies the applicability and stability of the proposed method.2.For further studying the Pythagorean fuzzy aggregation operators,this paper proposes generalized Pythagorean fuzzy Hamacher aggregation operators based method for multi-attribute group decision making.Firstly,this paper defines the generalized Pythagorean fuzzy Hamacher weighted average and ordered weighted average aggregation operator,and discusses the theorems and properties of the proposed operators.Then,through studying Pythagorean fuzzy information measurement,this paper proposes the concept of knowledge measure and introduces the method of normalized knowledge measure to obtain attribute weight.Finally,the paper elaborates the steps of the multi-attribute group decision making method based on the generalized Pythagorean fuzzy Hamacher aggregation operator,and applies it to the evaluation of haze management effect to illustrate the applicability and effectiveness of the proposed decision method.