| Hesitant fuzzy set is a generalized form of fuzzy sets.It means that the membership degree of an object which belonging to a fuzzy concept has multiple values,which reflects the hesitation of decision makers.The hesitant fuzzy information system refers to the value of the object under the attribute is the hesitant fuzzy element.In this paper,we study the ranking of hesitant fuzzy elements,the attribute reduction of hesitant fuzzy ordered information system and its decision table.There are mainly innovations in the following aspects:(1)A new ranking method for hesitant fuzzy elements is proposed.Firstly,some existing ranking methods of hesitant fuzzy elements are analyzed,and some shortcomings of these ranking methods are pointed out through examples.The t-norm and t-conorm operations of hesitant fuzzy elements have been given.The t-norm value of the hesitant fuzzy element represents the pessimistic value of the hesitant fuzzy element,and the t-conorm value represents its optimistic value.Then a new possibility is proposed by using the t-norm value and t-conorm value of hesitant fuzzy element,and the property of this possibility is studied,which proves that the probability satisfies reflexivity,symmetry and transmission under certain conditions.Finally,based on this possibility,a new ranking method for hesitant fuzzy elements is proposed.Based on the new ranking method of hesitant fuzzy element,a hesitant fuzzy multi-attribute decision making method is proposed,the possibility and effectiveness of which are illustrated by an example.(2)For the hesitant fuzzy ordered information system,a new dominance relation is defined by introducing a threshold based on the new possibility of hesitant fuzzy elements.The properties of the dominant relation are given,besides,the attribute reduction method for the hesitant fuzzy ordered information system is discussed,which guarantees the dominant relation unchanged.Based on the dominant class and the dominant class,the definition of the dominance between objects is given,and a ranking method of objects in the hesitant fuzzy ordered information system under this dominance is discussed.(3)Based on the proposed dominance relation,the attribute reduction method of hesitant fuzzy ordered decision table is discussed.Firstly,the upper approximation and the lower approximation and correlation properties of the ordered decision classes are given.The decision theorem and reduction method of the attribute reduction of the coordinated hesitant fuzzy ordered decision table are proved.Aiming at inconsistent and hesitant fuzzy ordered decision table,its distribution reduction is discussed,and a method of using discernibility matrix to find distribution reduction is presented.Finally,the proposed method is analyzed and verified via a practical case. |
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