Hesitant Fuzzy Graphs,Hesitant Fuzzy Hypergraphs And Its Graph Decision Analysis

As a generalization of fuzzy graphs,hesitant fuzzy graphs contain the informa-tion of membership degree and hesitation degree of the object and so on.Therefore,it is more flexible and convenient to deal with the multi-attribute decision making problems that under the background of hesitant fuzzy.It has not been systemati-cally studied whether the hesitant fuzzy graphs can be used to describe the fuzzy relationship among actors in fuzzy social networks and indecision,which is caused by the differences of cognition and the complexity of thinking,of decision makers.On the basis of hesitant fuzzy graphs and fuzzy hypergraphs,the operation properties,equivalent representation and decision methods of hesitant fuzzy hypergraphs are discussed in this paper,and the decision methods of hesitant fuzzy social network is studied.Firstly,the definition of hesitant fuzzy hypergraphs is given by means of hesi-tant fuzzy sets and fuzzy hypergraphs,and some basic graph operations of hesitant fuzzy hypergraphs are studied.Secondly,some equivalence relations among hesitant fuzzy hypergraphs,analysis of hesitant fuzzy formal concept and system of hesitant fuzzy information are discussed.In view of the characteristic that granule comput-ing can deal with multi-attribute decision making problem well,the hesitant fuzzy hypergraph model based on granule computing is established in this paper,and a multi-attribute decision making algorithm based on hesitant fuzzy hypergraph mod-el is obtained,and soem examples are given.Finally,based on the hesitant fuzzy graphs,this paper defined and discussed the hesitant fuzzy social network,studied the centrality of the hesitant fuzzy social network,and concluded the Simon decision methods which satisfies all the actors in the hesitatnt fuzzy social network.