Research On Multiple Attribute Decision Making Method And Its Application Based On Pythagorean Fuzzy Set Theory And TOPSIS Method

In this paper,the Pythagoras fuzzy set theory is extended to the interval Pythagorean fuzzy set and the Pythagorean trapezoidal fuzzy set,and combines the improved TOPSIS method to establish a decision model to solve the multi-attribute problem.It is applied to the examples of logistics service provider selection,school selection excellent class teacher,and beautiful city selection,which shows the effectiveness of the proposed method.The specific work is as follows:(1)The current situation analysis of the Pythagorean fuzzy set theory and the Pythagorean fuzzy multi-attribute decision-making method is carried out.The theoretical basis of multi-attribute decision-making is sorted out,and the main research contents,purpose and significance of this paper are introduced.(2)Based on the improved approximation ideal point ordering method(TOPSIS),a TOPSIS method based on the Pythagorean fuzzy set is proposed.The method constructs the information entropy and calculates the weight by using the ranking function characterized by4 parameters of Pythagorean fuzzy number,and two selection methods are proposed to avoid the inversion problem when the positive and negative ideal points are determined.And then by using the Euclidean distance of the Pythagorean fuzzy set to solve the closeness degree between each scheme and positive and negative ideal solution so as to judge the pros and cons of the scheme.Finally,the example proves that the method is effective and practical,and broaden the application scope of Pythagorean fuzzy sets in multiple attribute decision making.(3)For the problem of interval-valued Pythagorean fuzzy multi-attribute decision with unknown attribute weight,a TOPSIS multi-attribute decision-making method based on interval Pythagorean fuzzy entropy is proposed.Firstly,the algorithm of interval Pythagorean fuzzy number is broadened to subtraction and division.The strength of commitment and the direction of the strength of the interval Pythagorean fuzzy set is proposed.Defines the Euclidean distance between interval Pythagorean fuzzy numbers.Then,two kinds of interval-based Pythagorean fuzzy entropy based on hesitation are constructed,and the attribute weights are obtained.Finally,the improved TOPSIS multi-attribute decision making method is used to sort the alternatives,and the effectiveness of the method is verified by an example.(4)In this paper,a multi-attribute decision making method(MADM)based on double-base point method(TOPSIS)of trapezoidal Pythagorean fuzzy numbers is proposed.First,defined the trapezoidal Pythagorean fuzzy number,The algorithm for the trapezoidal Pythagorean fuzzy number is discussed.A scoring function,an exact function,and a trapezoidal Pythagorean fuzzy weighted average operator are also proposed.Then,theHammming distance formula between the trapezoidal Pythagorean fuzzy numbers is proposed.Finally,combined with the improved TOPSIS method,a multi-attribute decision making method based on trapezoidal Pythagorean fuzzy numbers under the condition of known attribute weights is presented.And an example analysis shows the effectiveness of the method.