Construction Of Pythagorean Fuzzy Logic-based Cognitive Map Model

As an artificial intelligent model and soft computing method,fuzzy cognitive map(FCM)has been a research hotspot in recent years,which has been widely applied in project management,supplier selection,risk evaluation and medical diagnosis,etc.As FCM is a combination of fuzzy logic and neural network,with the development of fuzzy set theory and fuzzy logic,FCM models should be further extended to accommodate new fuzzy decision making environments.Recently,scholars have extended the traditional FCM and proposed a new FCM in intuitionistic fuzzy environment,i.e.intuitionistic fuzzy cognitive Map,IFCM.However,the harsh constraint of intuitionistic fuzzy sets that the sum of membership degree and the degree of hesitancy should be no more than on restricts appropriate expressions of decision makers' ideas,causing information distortion,and limiting the range of application of IFCM as well.To overcome the drawbacks of IFCM,this paper investigates FCM in Pythagorean fuzzy environment,and proposes the Pythagorean fuzzy cognitive map(PFCM).As an extension of intuitionistic fuzzy set,Pythagorean fuzzy set has laxer constraint.Hence,PFCM provides more freedom and flexibility for decision making experts and so that PFCM have wider range of application.There are questions in the process of establishing PFCM:(1)how to aggregate decision makers' opinion appropriately in Pythagorean fuzzy environment;(2)how to re-define the structure and inference mechanism of PFCM.Therefore,the main works of this paper are as followings:(1)Investigation of Pythagorean fuzzy decision making information aggregation methods.In order to eliminate the negative influences of unreasonable decision values on the final result,based on Pythagorean fuzzy interaction operational rules and power average operator,a series of Pythagorean fuzzy aggregation operators are proposed,and a novel Pythagorean fuzzy information aggregation method is presented.(2)Construction of cognitive maps model in Pythagorean fuzzy environment.When the causal relationship between concepts are expressed by Pythagorean fuzzy information,the PFCM-I is proposed.When both the concepts and the causal relationship between them are expressed by Pythagorean fuzzy information,the PFCM-II is developed.Further,the structure and inference mechanism of these two types of PFCM are studied.(3)Investigation of application of PFCM in medical diagnosis.Taking Pneumonia risk assessment as an example,the structures of the two PFCM models,the transformation of experts' opinion,the aggregation of decision makers' ideas,the inference process and calculation results are provided.The validity and superiorities of the newly proposed models are illustrated by comparing with other fuzzy cognitive maps.