A Generalized Orthopair Fuzzy Decision Making Method Based On Aggregate Operator And Measure Theory

Multi-attribute decision making is a very important part of decision making,which is the process of selecting the best solution from a series of alternatives based on expert judgment.The proper representation of decision information is the prerequisite and basis for obtaining reasonable decision results.The fuzzy set proposed by Zadeh in 1965 is a powerful tool for describing and dealing with uncertainty problems.However,fuzzy sets contain only the degree of satisfaction,and only the degree of elements belongs to the fuzzy set is retained.With the increasing complexity of decision problems,many scholars have proposed the extension of intuitionistic fuzzy sets,hesitant fuzzy sets and pythagorean fuzzy sets based on fuzzy sets to suit the practical needs.In order to further meet the requirements of practical applications,Yager proposed generalized orthogonal fuzzy sets(q-ROFS),whose membership degree μ and nonmembership degree v,satisfy the conditions μ~q+v~q≤1(q≥1) of the intuitionistic fuzzy sets and pythagorean fuzzy sets,the q-rung orthopair fuzzy sets can represent the evaluation information with the sum of the squares of the membership and nonmembership degrees exceeding one by changing the values,which allows decision makers to express the evaluation information more freely.This allows decision makers to express evaluation information more freely,and also provides convenience for handling complex fuzzy information.In recent years,q-rung orthopair fuzzy sets have become one of the research hotspots.The commonly used decision methods include hierarchical analysis,TOPSIS method,VIKOR method and so on.Integration operators and measure theory are common tools for fusion of fuzzy information.The existing integration operators mainly include(weighted)arithmetic average operator,(weighted)geometric average operator,ordered(weighted)average operator,ordered(weighted)geometric operator,mixed ordered weighted average operator,(weighted)Bonferroni average operator,(weighted)Maclaurin symmetric average operator,Heronian average operator,Choquet fuzzy integral fusion operator,etc.The existing measure theories include similarity measure,distance measure,association measure,entropy measure,divergence measure,inclusion measure,etc.These decision methods and theories have been widely used in pattern recognition,medical diagnosis,engineering management,risk assessment and other fields.In this paper,we investigate decision making methods in generalized orthogonal fuzzy environments,using distance measures and integration operators as tools,and our main research work is as follows.(1)A new q-rung orthopair fuzzy distance measure is definedA new q-rung orthopair fuzzy distance measure is defined.Since the q-rung orthopair fuzzy fuzzy Hamming distance only considers the absolute distance between the data,and sometimes the direction of the data needs to be considered in some practical problems,our proposed distance measure compensates for the shortcomings of the generalized orthogonal fuzzy Hamming distance in some problems.The proposed measure satisfies the good properties and is combined with TOPSIS method to solve the multi-attribute decision problem of mouthpiece selection.(2)The q-rung orthopair Maclaurin symmetric averaging operator based on the confidence level is studied.Since the Maclaurin symmetric averaging operator takes into account the interrelationship between attributes,considering the confidence level of experts can reduce the influence of unreasonable evaluation values given by decision makers on the decision results in the decision-making process.The q-rung orthopair fuzzy Maclaurin symmetric averaging operator based on confidence level and the q-rung orthopair fuzzy weighted Maclaurin symmetric averaging operator based on confidence level are established.The q-rung orthopair fuzzy Maclaurin symmetric averaging operator decision model based on confidence level is established,and the practicality of the method is verified by the example of purchasing computer hard disk.(3)The q-rung orthopair fuzzy set of cosine functions into operators is studiedThe q-rung orthopair fuzzy number of cosine function is defined,so that the fuzzy evaluation information of experts can be expressed more freely and adequately.The properties and algorithms of the cosine q-rung orthopair fuzzy numbers are studied,and then the cosine q-rung orthopair fuzzy arithmetic mean and geometric mean operators are defined,and finally the multi-attribute decision making method based on the cosine q-rung orthopair fuzzy operators is applied to the site selection problem of a company.