The Analysis Of Aggregation Operators Based On Hesitant Fuzzy Information

Multiple criteria decision making(MCDM)problems exist in every aspect of modern society with its essence which is that the decision makers intend to select or sort the best choice from a number of alternatives by using several known decision information.In real life,owing to the limitation of decision makers and the uncertainty of the objective factors,it is hard for decision makers to make accurate assessment;they always hesitate about some evaluation values.In order to solve this problem,Torra put forward the hesitant fuzzy set.Up to now,many experts have investigated the decision methods under hesitant fuzzy environment,but the evaluation values of the studies were accurate.In many cases,it is difficult to give accurate values to evaluations.For more detailed depiction of decision makers' preference,interval-valued information arouses people's strong attention.Although the theory of interval-valued set has been studied,the theory of interval-valued intuitionistic hesitant fuzzy multi-criteria group decision making remains to be improved.Firstly,the background and current status of multi-criteria group decision making,hesitant fuzzy information and aggregation operators under hesitant fuzzy environment are introduced.Secondly,the definition and operational laws of hesitant fuzzy set,dual hesitant fuzzy set and interval-valued intuitionistic hesitant fuzzy set are summarized.Fuzzy measure,Choquet integral and Quasi-Choquet averaging are generalized at the same time.The paper develops the interval-valued intuitionistic hesitant fuzzy Quasi-Choquet geometric operator based on Archimedean t-conorm,Archimedean t-norm and Quasi-Choquet averaging mean.The operator can aggregate interval-valued intuitionistic hesitant fuzzy values,where interactive or inter-dependent characteristics among input arguments are taken into consideration.Then,some desirable properties of interval-valued intuitionistic hesitant fuzzy Quasi-Choquet geometric operator are proposed.Thirdly,the family of the interval-valued intuitionistic hesitant fuzzy operators is shown,it provides a flexible and useful method for decision makers to make assessments.Further,the proposed aggregation operators based on compromise ratio method,the extended technique for order preference by similarity to ideal solution(TOPSIS)method and extended Euclidean distance are used for these interval-valued intuitionistic hesitant multi-criteria group decision making problems.Finally,conclusions and remarks about the current work and further research are given.