Generalized Hesitant Fuzzy Soft Set And Its Applications In Decision Making

Rough set theory,fuzzy set theory and soft set theory are three important mathematical tools for dealing with uncertainty problems.After recent years of development,these three theories have been generalized.Meanwhile,some hybrid model of hesitant fuzzy soft sets and soft fuzzy rough sets based on the three theories have also gained a rapid development.According to the existing research results,the further studies of hesitant fuzzy soft sets and soft fuzzy rough sets are given in this thesis.Firstly,the generalized hesitant fuzzy soft sets have been defined and its property has been discussed based on the hesitant fuzzy soft sets.Secondly,two generalized hesitant fuzzy soft set similarity measurement methods are constructed to apply to the practical problems.Finally,soft hesitant fuzzy rough set model is proposed by generalizing the soft fuzzy rough set model.The detailed content of dissertation is as following:(1)Studying in the generalized hesitant fuzzy soft set.Based on hesitant fuzzy soft set and generalized fuzzy soft set,hesitant fuzzy membership degree is given to the parameter set of hesitant fuzzy soft set and the model of generalized hesitant fuzzy soft set is defined,in addition,the generalized soft hesitant fuzzy subset is proposed.An extension of model of generalized hesitant fuzzy soft set is defined,which can convert the generalized hesitant fuzzy soft set with different parameter quantities into the generalized hesitant fuzzy soft set with the same parameter quantity.Later,some basic operations of union,intersection and complement are studied and fundamental properties of generalized hesitant fuzzy soft sets are discussed as well.Finally,a practical example is given to illustrate the effectiveness of the definition.(2)The similarity measures I of generalized hesitant fuzzy soft set is given for the problem of the similarity measures of generalized hesitant fuzzy soft set.At first,three kinds of inclusion degree of hesitant fuzzy sets are constructed based on the similarity measure formula of hesitant fuzzy set.Then,three kinds of similarity measures of the generalized hesitant fuzzy soft set are provided by using the three kinds of inclusion degree of hesitant fuzzy sets.Later,according to the axiomatic definition of similarity measures of the hesitant fuzzy soft set,the axiomatic definition of similarity measures of the generalized hesitant fuzzy soft set is given,and similarity measure formula of the generalized hesitant fuzzy soft set is constructed by using the three kinds of similarity degree formulas of hesitant fuzzy sets,at the same time,these formulas are proved.Finally,a decision method is constructed by using the similarity measurement of generalized hesitant fuzzy soft set,and the decision-making method is applied to the problems of environmental governance.(3)The similarity measures II of generalized hesitant fuzzy soft set is given for the problem of the similarity measures of generalized hesitant fuzzy soft set.At first,the axiomatic definition of the generalized hesitate fuzzy soft set contains degrees is given based on the axiomatic definition of hesitant fuzzy set contains degrees,and the inclusion degreesformula of generalized hesitate fuzzy soft set has been structured by the three hesitant fuzzy set contains degrees formula.Later,started with the inclusion degree of generalized hesitant fuzzy soft set,the similarity formula of generalized hesitant fuzzy soft set is constructed,whose computing method is also applicable to the generalized hesitant fuzzy soft set with different parameter sets.At last,the similarity II of generalized hesitant fuzzy soft set is applied to the clustering analysis case about city hygienic evaluation,the example illustrates the effectiveness of the proposed control method.(4)First of all,hesitant fuzzy rough set in double domains of discourse is proposed to discuss about its properties.Secondly,soft hesitant fuzzy rough set is investigated,and the upper approximate as well as lower approximate operator of soft hesitant fuzzy rough set is given to discuss about its properties.Then,a soft hesitant fuzzy rough set based decision algorithm is constructed to apply to the decision problem of purchasing automobile.At last,the relationship between model of soft hesitant fuzzy rough set and model of generalized hesitant fuzzy soft set is discussed so as to describe the practical significance of two models in automobile transaction.