Interval-valued Pythagorean Hesitant Fuzzy Rough Sets And Their Multi-granularity Extensions

Rough sets and fuzzy sets are both effective tools for dealing with uncertain problems.There are many independent expansion models for both of them by adding multigranularity and interval elements,such as multi-granularity rough sets models by introducing multi-granularity elements,and interval-valued Pythagorean hesitant fuzzy sets models by introducing interval elements.Furthermore,on the basis of the fuzzy rough sets constructed by the combination of the two models,the fusion expansion models of the two elements can enhance the ability of uncertain information processing.Firstly,the interval-valued Pythagorean hesitant fuzzy rough sets model is constructed by integrating the interval-valued Pythagorean hesitant fuzzy information into the rough sets analysis to realize the uncertain information fusion.Then,multi-granularity factors are introduced into the model,and a multi-granularity intervalvalued Pythagorean hesitant fuzzy rough sets model is constructed.The model is applied to the decision of the optimal work department,and the validity of the model in multi-attribute decision making is verified.The specific research contents are as follows:(1)The interval-valued Pythagorean hesitant fuzzy information is integrated into rough sets analysis,and the corresponding uncertainty modeling is carried out to realize the uncertain information fusion.Concretely,based on the interval-valued Pythagorean hesitant fuzzy relation,the model of interval-valued Pythagorean hesitant fuzzy rough set is constructed.Then the basic properties of the lower and upper approximation on the set union and cross complement operation are studied.The knowledge granular monotone properties of the approximate set are obtained.At the same time,a case study was used to illustrate the model and verify its properties.(2)The multi-granularity elements are introduced into the interval-valued Pythagorean hesitant fuzzy rough sets,and the corresponding uncertainty modeling is carried out to realize multi-source information fusion.Concretely,based on the multiple interval-valued Pythagorean hesitant fuzzy relation,the optimistic and pessimistic multi-granularity Pythagorean hesitant fuzzy rough sets model is constructed.Furthermore,the relationship between single-granularity and multi-granularity models,optimistic and pessimistic models are analyzed,and the basic properties of lower and upper approximation on set operation are studied.The model is applied to multi-attribute decision making,and its effectiveness is proved by a case study.In a word,this thesis constructs two models,namely “interval-valued Pythagorean hesitant fuzzy rough sets models” and “multi-granularity interval-valued Pythagorean hesitant fuzzy rough sets models”.The basic properties of the lower and upper approximation of the two models are studied and verified.Through the analysis of examples and the application of multi-attribute decision making,it is shown that the two models and their related properties are beneficial to the uncertainty reasoning of interval-valued information systems,and meet the demand of multi-attribute decision making in practical application.