Pythagorean Fuzzy Decision Making Methods Based On Novel Measures

Compared to the intuitionistic fuzzy sets,the Pythagorean fuzzy sets can provide the decision makers with more freedom to express their evaluation information and greater ability to model information in multi-attribute decision making process.Analyzing and solving the problem of multi-attribute decision making based on Pythagorean fuzzy information has become a hot research topic in recent years.However,the Pythagorean fuzzy decision making methods based on measures still have some shortcomings:(1)The MULTIMOORA method is better than some of the existing decision making methods.However,it has not been improved to process Pythagorean fuzzy sets in current research results;(2)There exist some research results on the correlation coefficient for Pythagorean fuzzy sets,but sometimes they fail to deal with the problems of disease diagnosis and cluster analysis;(3)The traditional weight determination methods based on the existing entropy measures can not accurately calculate the weights of attribute sometimes,which have an impact on the accuracy of decision results.This paper is devoted to solving the above problems and carries out the following research contents:(1)To extend the Pythagorean fuzzy sets theory,this paper proposes the Pythagorean fuzzy MULTIMOORA decision making method and applies it to solve the problem of Solid State Disk products selection.Firstly,in order to solve the defects of the existing distance measures of Pythagorean fuzzy sets,based on the Dice similarity and Jaccard similarity,the novel Pythagorean fuzzy Dice distance measures and Jaccard distance measures are proposed to measure the difference between two Pythagorean fuzzy sets.Then,in order to solve the defects of the existing score functions of Pythagorean fuzzy sets,a novel Pythagorean fuzzy score function based on determinacy degree and indeterminacy degree is put forward for approximately representing Pythagorean fuzzy sets.Afterwards,the original MULTIMOORA method is extended by using the Dice distance and novel score function,and a novel Pythagorean fuzzy MULTIMOORA model is proposed to solve the multi-attribute decision making problems under the Pythagorean fuzzy sets information context.Finally,the Pythagorean fuzzy MULTIMOORA decision making method is compared with the existing Pythagorean fuzzy TOPSIS method and the Pythagorean fuzzy aggregation operator method.(2)To better solve the problems related to medical diagnosis and cluster analysis,this paper proposes some novel directional correlation coefficients of Pythagorean fuzzy sets to solve the problems of disease diagnosis and cluster analysis.Firstly,to tackle the drawbacks of the existing correlation coefficients of Pythagorean fuzzy sets,some novel directional correlation coefficients are put forward to compute the relationship between two Pythagorean fuzzy sets by taking four parameters of the Pythagorean fuzzy sets into consideration,which are the membership degree,non-membership degree,strength of commitment,and direction of commitment.Then,two practical examples are given to show the application of the proposed directional correlation coefficient in the disease diagnosis,and the application of the proposed weighted directional correlation coefficient in the cluster analysis.Finally,they are compared with the previous correlation coefficients that have been developed for Pythagorean fuzzy sets.(3)To improve the accuracy of decision results,this paper proposes a novel weight determination model.Combining with the traditional AQM method,the Pythagorean fuzzy AQM decision making method is proposed and applied to solve the evaluation problem of the Internet of Things platforms.Firstly,in order to solve the defects of the existing cross entropy measures of Pythagorean fuzzy sets,based on the divergence measures,the novel Pythagorean fuzzy cross entropy measures are proposed to measure the difference of fuzzy information contained in two Pythagorean fuzzy sets.Then,in order to solve the defects of the existing entropy measures of Pythagorean fuzzy sets,by calculating the cross entropy between the Pythagorean fuzzy set and the crisp set,the novel Pythagorean fuzzy uncertainty measures are proposed to measure the uncertainty of Pythagorean fuzzy sets.Afterwards,based on the cross entropy measure and uncertainty measure,a novel weight determination model is proposed and combined with the traditional AQM method,the Pythagorean fuzzy AQM decision method is proposed to solve the evaluation problem of Internet of Things platforms.Finally,the novel weight determination model proposed in this paper and the traditional weight determination model are compared and analyzed respectively with TOPSIS method and AQM method.