Research And Application Of Multi-granulation Rough Intuitionistic Hesitant Fuzzy Set Models

Intuitionistic hesitant fuzzy set theory is an extension theory of intuitionistic fuzzy set and hesitation fuzzy set.It uses multiple membership degrees and non-membership degrees to express the fuzziness of uncertain things,which provides a more comprehensive and reasonable method for describing fuzzy information.As another mathematical method to deal with imprecise and uncertain knowledge,rough sets relies on a binary relationship to express knowledge,which has limitations in dealing with complex and uncertain information.Multi-granulation rough sets contain multiple binary relations,which can deal with multi-dimensional complex fuzzy information system.To solve the problem that effective information cannot be obtained directly from intuitionistic hesitant fuzzy decision information system,this paper introduces multi-granulation rough set theory into the system,and proposes multi-granulation rough intuitionistic hesitant fuzzy set to deal with fuzzy information.On the basis of the multi-granulation rough intuitionistic hesitant fuzzy set,four optimal granularity selection algorithms based on different states are designed to solve the attribute reduction problem in intuitionistic hesitant fuzzy decision information system.In order to make decision-making judgments for the objects in the intuitionistic hesitant fuzzy decision information system,four algorithms for extracting three-way decision rules are proposed based on three-way decision theory.Both of these algorithms use examples to further verify the effectiveness,and apply them to the applicant evaluation system to help companies select talents.The main research work of this paper includes the following three aspects:(1)In order to obtain the optimal granulations after reduction from the intuitionistic hesitant fuzzy decision information system with multiple attributes,firstly,on the basis of intuitionistic hesitant fuzzy sets,attribute information is introduced,and the concept of rough intuitionistic hesitant fuzzy sets is given.Then four upper and lower approximation models of optimistic and pessimistic multi-granulation rough intuitionistic hesitant fuzzy sets are proposed,and the related properties are discussed.Secondly,based on the lower approximation of the pessimistic multi-granulation rough intuitionistic hesitant fuzzy set,define the granulation quality similarity degree and internal/external granulation importance degree,and the related algorithm of optimal granulation selection is designed.Finally,through the wine evaluation case,optimal granularities are calculated based on the lower and upper approximations of optimistic and pessimistic multi-granulation rough intuitionistic hesitant fuzzy sets,then analyzed results.It is verified that algorithms are effective for the reduction of intuitionistic hesitant fuzzy decision information system.(2)To investigate information in intuitionistic hesitant fuzzy decision information system and make decisions for objects,firstly,optimistic-pessimistic and pessimistic-optimistic multi-granulation rough intuitionistic hesitant fuzzy set models are proposed,then their properties are discussed.Secondly,based on optimistic,pessimistic,optimistic-pessimistic and pessimistic-optimistic multi-granulation rough intuitionistic hesitant fuzzy set models,we define the combination formula about the upper and lower approximations of multi-granulation rough intuitionistic hesitant fuzzy sets,and present a new intuitionistic hesitant fuzzy cross-entropy.Then the conditional probabilities under four cases are calculated by TOPSIS approach.Thirdly,define the intuitionistic hesitant fuzzy decision-theoretic rough sets,and corresponding three-way decision rules are given.Specifically,four kinds of three-way decision models based on proposed multi-granulation rough intuitionistic hesitant fuzzy sets are constructed,and the decision rules extraction algorithm are designed.Finally,an example demonstrates that four models can evaluate objects with different attitudes and provide decision solutions,which proves the feasibility and effectiveness of the proposed algorithms.(3)Using the optimal granulation selection algorithms and the three-way decision rule extraction algorithms proposed in this paper,and using the GUI platform in MATLAB,we develop the applicant evaluation system which has the function of screening attributes of assessment and selecting the applicants.