Multi-attribute Information Interactive Group Decision-making Method And Application In Hesitant Fuzzy Environment

Group decision-making is a decision-making method in which multiple experts form a comprehensive index information according to a certain rule set.It is not only an important part of decision-making theory,but also can effectively gather the collective wisdom of multiple experts and play an important role in order to improve the scientific effectiveness of decision-making problems.Usually,in some practical problems,it is difficult for decision-makers to get a satisfactory decision-making scheme by integrating information only once.They often need to constantly modify and adjust the expert weight vector,and even after repeatedly integrating information,they can finally get a satisfactory decision-making scheme.This paper mainly discusses the interactive decision-making methods under the aggregation information mode of hesitant Pythagorean fuzzy number(HPFN),probabilistic hesitant fuzzy number(PrHFN)and probabilistic hesitant Pythagorean fuzzy number(PrHPFN)The specific research contents are as follows:The first part mainly introduces the background and research status of this paper.The second part mainly introduces the basic definition,related representation,operation rules and ranking method of hesitant Pythagorean fuzzy number and probability hesitant fuzzy number.The third part:In the context of hesitant Pythagorean fuzzy number,HPFN similarity is introduced by appropriately supplementing the number of elements contained in membership degree,non membership degree set and Hamming distance.According to the evaluation matrix given by experts,the similarity of hesitant Pythagorean fuzzy matrix(HPFM)is proposed,and then an interactive group decision-making method is designed.An example is given to verify the effectiveness of this method.In the fourth part:Aiming at the defects of the traditional PrHFN distance,a new Hamming distance and similarity are proposed.The concept of probability hesitation fuzzy matrix(PrHFM)similarity is introduced through the initial evaluation matrix,and a new interactive group decisionmaking method is designed according to the PrHFM similarity in the probability hesitation fuzzy environment.Finally,an example is given to verify the effectiveness of this method.In the fifth part:In the probabilistic hesitant Pythagorean fuzzy environment,the score function,Hamming distance measure,weighted distance measure and similarity are improved,the probabilistic hesitant Pythagorean fuzzy matrix(PrHPFM)similarity is given,and the interactive group decision-making method is designed according to the PrHPFM similarity.Then an example is given to verify the rationality and effectiveness of this method.