The Related Theory Of Pythagorean Fuzzy Sets And Its Application In Decision Making

Pythagorean fuzzy set,as an extension of intuitional fuzzy set,breaks through the limitation of the sum of membership degree and non-membership degree,and has more flexible information expression and modeling ability.It is widely used in uncertain information decision-making problems,and has become a research hotspot in recent years.However,the existing Pythagorean fuzzy set still has the following deficiencies in the universality of its application to decision problems:(1)The existing formula of Pythagorean fuzzy entropy does not fully consider the influence of hesitation,or ignores the nature of entropy,which leads to unreasonable decision results.(2)The Pythagorean fuzzy decision making method based on the existing distance measure and similarity does not properly deal with the information contained in the hesitation degree,or causes the loss of decision information,resulting in the distortion of decision results.(3)The scoring function calculation method used for ranking does not fully consider the limited rational behavior preference of decision-makers in the real decision-making situation,and lacks flexible and effective expression ability.This thesis is devoted to solving the above problems.The main research contents and achievements are as follows:(1)In order to improve the accuracy of decision making,this thesis presents a new Pythagorean fuzzy entropy.Firstly,the existing definition and properties of Pythagorean fuzzy entropy are pointed out and illustrated.Then,a new Pythagorean entropy and its properties are defined and proved strictly.Finally,by comparing the new Pythagorean fuzzy entropy with the existing entropy calculation formula,the effectiveness and superiority of the entropy proposed in this paper are proved.(2)To solve the problem that the decision result may be distorted based on the existing distance measure and the Pythagorean fuzzy decision method of similarity,this paper presents a new Dice measure and the calculation method of conformity similarity,which makes the decision result more scientific and interpretable.Firstly,based on the existing Pythagorean fuzzy distance measure and similarity,the rational allocation of hesitation degree is discussed.The Pythagorean fuzzy Dice measure and similarity of hesitation degree conformity allocation are proposed based on the average allocation of hesitation degree and Dice coefficient,and it is proved that they conform to the axiomatic definition.Secondly,VIKOR method based on entropy weight method and Dice measure and TOPSIS method based on conformity similarity are constructed,and applied to practical decision cases such as earthquake emergency decision and project selection,and comparative analysis is carried out,which proves the rationality and effectiveness of Dice measure and conformity similarity proposed in this paper.(3)The Pythagorean fuzzy score function based on radical factor is defined in order to fit the realistic decision-making situation and fully consider the behavioral preferences of decision-makers.Firstly,according to the psychological characteristics of bounded rationality in different situations,the radical,conservative and neutral behavior preferences of decision-makers are described by introducing radical factors.A new Pythagorean fuzzy scoring function and its ranking criteria are proposed and proved to conform to the axiomatic definition.Then,the Pythagoras fuzzy score function multi-attribute decision method based on radical factor is constructed and applied to the family car selection case.Through comparative analysis,the scientific rationality of the method is proved.