The Extension Of Hesitant Fuzzy Rough Set Model And Its Application

Rough set theory and hesitant fuzzy set theory are two important mathematical tools for dealing with uncertainty and fuzziness.After several years of development,these two theories have been promoted one after another.At the same time,the fusion of the two theories has also developed rapidly,and subsequently hesitated fuzzy rough sets and their various forms of promotion have been proposed.Based on the existing research results,this paper studies the generalized form of hesitant fuzzy rough sets.Firstly,based on the hesitant fuzzy set,a new extension method is proposed.Based on this extension method,new intersection and union operations,new inclusion relations,and new rough hesitation fuzzy sets are established.Based on the study of the enhanced rough hesitant fuzzy set.Secondly,the similarity and inclusion degree are studied for hesitant fuzzy sets,and then a new hesitant fuzzy rough set model is established by using the inclusion degree and similarity.Then,it is applied to the attribute reduction of hesitant fuzzy systems to solve the uncertain decision problem.The details are as follows:(1)A new continuation method is proposed for hesitant fuzzy elements with different lengths.That is,the mean value of all possible membership values of the hesitant fuzzy element is used to complement,and the hesitation fuzzy element and the hesitant fuzzy set new intersection and union operations are given based on the extension method,and the hesitation fuzzy element is used respectively.The maximum and minimum values of the mean and hesitant fuzzy elements define a new inclusion relationship;in the Pawlak approximation space,a new rough hesitant fuzzy set is established based on the equivalence relation and the newly defined union and intersection operations;on this basis,research The enhanced rough hesitant fuzzy set: Firstly,how to approximate the fuzzy set in the Pawlak approximation space is studied.The existing mean fuzzy set and rough fuzzy set are used to establish the new upper approximation set and lower approximation set of the fuzzy target,ie the enhanced upper,the next approximation set.Compared with the existing rough fuzzy set and mean fuzzy set,it is concluded that the approximate space has higher precision under certain conditions,and the new approximate set has better closeness to the target set.Furthermore,numerical examples are given to illustrate the superiority of the newly proposed upper and lower approximation operators.Next,the heuristic fuzzy set approximation set is studied and compared.(2)Firstly,the concept of inclusion in fuzzy set is extended to hesitant fuzzy set by the heuristic fuzzy set,and some calculation formulas and axiomatic definitions of hesitant fuzzy inclusion are given.Secondly,hesitant fuzzy inclusion is given based on hesitant fuzzy partition.The concept of approximate space is established,and the hesitant fuzzy rough set model based on inclusion degree is established.Some basic properties of approximation operator are discussed.Finally,an attribute reduction method based on inclusion degree is given in hesitation fuzzy approximation space.This method can obtain the corresponding decision rules while obtaining the most approximate set,and illustrates the feasibility and effectiveness of the algorithm.(3)By using the axiomatic definition of hesitation fuzzy set similarity,the new continuation method of the hesitant fuzzy element is used to complete the similarity formula of the hesitant fuzzy element and the hesitant fuzzy set.Then,in the general hesitant fuzzy approximation space,the fuzzy relation matrix between the objects in the hesitant fuzzy approximation space is obtained by using the similarity between hesitant fuzzy elements,and then the fuzzy similarity matrix is transformed into the fuzzy equivalence matrix by the transitive closure method of the fuzzy set.Based on this,a hesitant fuzzy rough set model is established in the information system by using fuzzy equivalence relations.The classification reduction and kernel calculation and its decision theorem at a given similar level are discussed.For the hesitant fuzzy decision system,the relative reduction and its optimal decision rule are obtained at a given level of similarity.