Multiple Attribute Decision Making Method And Its Application Based On Trapezoidal Fuzzy Set Theory

Decision making problems can be seen everywhere in people's life.From countries and societies to companies and individuals,the interests of a country and the fate of a company and an individual are inseparable from correct decisions.With the development and improvement of decision theory,multiple attribute decision making has appeared.And the knowledge related to multiple attribute decision making has played an indispensable role in many fields such as engineering,economy and military.With the continuous development of the society and the gradual prosperity of the economy,the complexity of the problem is gradually increasing,the number of uncertain factors is increasing,and the problem of difficult decision making is becoming more and more prominent.Fuzzy theory can just solve such problems.For the fuzzy multiple attribute decision making problem,which form of fuzzy number can more reasonably reflect the uncertainty of the decision information that is the main research problem of this paper.By giving intuitionistic,Pythagorean and interval-valued Pythagorean trapezoidal fuzzy numbers,and different ranking methods are combined,this paper give multiple attribute decision making methods based on the trapezoidal fuzzy numbers.At the same time,the proposed method is applied to some examples,such as plant site selection,green supplier selection,market investment,etc.And the validity of the proposed method is illustrated by verifying these examples.The main research contents are as follows:(1)The present situation of trapezoidal fuzzy set theory and trapezoidal fuzzy multi-attribute method and its application are analyzed.The research content,purpose and significance of this paper are expounded.The basic knowledge of multiple attribute decision making is summarized.(2)For the problem of intuitionistic trapezoidal fuzzy multiple attribute decision making with unknown attribute weights.The Hamming distance of intuitionistic trapezoidal fuzzy numbers is given.An optimization model is built according to the idea of maximizing deviation.And we use the method of TOPSIS to calculate for each plan and degree and distance of positive and negative ideal scheme.By comparison the size of the degree scheme for the sorting.Based on the attribute weights are unknown intuitionistic trapezoidal fuzzy multiple attribute decision making method of steps is presented.Finally,an example is given to show the effectiveness of this method.And a new method for intuitionistic trapezoidal fuzzy multiple attribute decision making with unknown weight is proposed.(3)For Pythagorean trapezoidal fuzzy multiple attribute decision making problem,its aggregation operator is calculated.Then the expected value of Pythagorean trapezoidal fuzzy number is assumed according to the expected value of intuitionistic trapezoidal fuzzy number.The scoring function and the exact function of fuzzy number of Pythagorean trapezoid are improved.The sizes of the new score function and the original score function are obtained by the aggregation operator,and the schemes are sorted.The fuzzy multiple attribute decision method of the Pythagorean trapezoidal fuzzy numbers' ranking according to the score is given.Finally,an example is given to verify that the original score function is the same as the new score function,which shows the effectiveness of the proposed method.(4)For the interval-valued Pythagorean trapezoidal fuzzy multiple attribute decision making problem.Since no scholars have defined the distance between the interval-valued Pythagorean trapezoidal fuzzy numbers,many scholars rank their schemes by the size of the score function.In this paper,we define and prove its Hamming distance.The TOPSIS method is combined with it,and its fuzzy multiple attribute decision method is proposed,and the decision steps are given.Finally,the method is applied to an example,and the result of this method is the same as that of sorting by the size of score function,which proves the effectiveness of this method.