Rough Modeling Of Hesitant Fuzzy Sets And Its Application In Decision-making

Multi-criteria decision-making is an important research content of modern decision science,which widely exists in human’s production and living practice.As the decision-making environment becomes more and more complicated,in order to better analyze and evaluate the data and obtain effective decision-making information,it is very necessary to consider various uncertainties of data.On the one hand,hesitant fuzzy sets use several possible values in interval [0,1] to describe the membership degree of an object to the set.It can not only process the fuzziness,but also consider the hesitancy of decision-makers.It is an effective tool for processing the uncertainty and is very suitable for uncertain decision-making problems when the decision-makers are indecisive.On the other hand,rough sets can effectively deal with various inconsistencies and uncertainties caused by different granular descriptions in data by defining the lower and upper approximations of a set,which have been widely used in numerous uncertain decision-making fields.Therefore,the combination of hesitant fuzzy sets and rough sets is very beneficial to describe the knowledge in data systems more accurately,which can provide a new perspective for complex uncertain decision-making problems.In this paper,taking the hesitant fuzzy sets as the uncertainty description tool,we propose the rough modeling methods of hesitant fuzzy sets based on rough set theories,and further construct the multi-criteria decision-making theories and methods under hesitant fuzzy environment.The main contributions and novelties can be presented as follows:(1)We first give the definitions of hesitant fuzzy β covering and hesitant fuzzy βneighborhood,and propose the concept of hesitant fuzzy β covering rough set from the constructive aspect,further investigate the properties and relationships between the approximation operations.Then,we further discuss the axiomatic characterization of the lower and upper approximation operators.Next,we construct a VIKOR-CHFRS method to multi-criteria group decision-making problems by using hesitant fuzzy β covering rough set model.Finally,a practical example with comparison results illustrates the effectiveness and reasonability of VIKOR-CHFRS.This part of the study provides a new method for hesitant fuzzy group decicion-making by considering the effect on decicion-making of different expert opinion.Meanwhile,it extends the application ranges of rough set theory in uncertain decision-making fields.(2)From the point of risky decision-making,we first define two pairs of hesitant fuzzy relationship based on hesitant fuzzy β neighborhood,and construct two pairs of risky hesitant fuzzy covering rough set models,further discuss the properties and relationships between the two models.Then,we introduce a new comprehensive weight determination method by using the precision degree of the compact risk-aversion hesitant fuzzy covering rough set and the maximizing deviation method.Next,we construct a γ-RHF-TOPSIS method to multi-criteria decision-making which generalizes the TOPSIS method in hesitant fuzzy β covering approximation space.Finally,a real decision-making problem is used to demonstrate its effectiveness,reasonability and extensibility.This part of the study not only solves the shortcomings of not realzing the complete ranking for traditional hesitant fuzzy TOPSIS in a hesitant fuzzy β covering approximation space,but also provides a theoretical foundation for decision-makers when facing multiple possible choices in uncertain decision-making.(3)In order to meet the different decision-making requirements,we first propose the concepts of hesitant fuzzy β minimal description and hesitant fuzzy β maximal description,and give four kinds of hesitant fuzzy neighborhood operators,further discuss the relative properties and relations.Then,we construct four hesitant fuzzy β covering rough set models,and further discuss the properties,relations and uncertainty measures of these models.Next,by combining the second kind of hesitancy fuzzy β covering rough set model with TODIM method,we construct an NO-CHF-TODIM method to multi-criteria decision-making under hesitancy fuzzy environment.Finally,we verify the rationality,effectiveness and wide applicability of the method through the applications of college teachers’ professional title evaluation.This part of study can effectively avoid the deficiency of other methods that can only sort the alternatives,which can reasonably classify the objects,so it can provide an important theoretical basis for classification decision-making under uncertain environment.(4)We first construct a novel probabilistic hesitant fuzzy rough set model on the basis of normalized probabilistic hesitant fuzzy sets,and then enrich the theoretical results from the properties and uncertainty measures of model.Subsequently,we propose the concept of fuzziness of a probabilistic hesitant fuzzy rough sets and develop a fuzziness-based objective weight determination method.Further,we construct an extended PROMETHEE-PHFRS method to multi-criteria decision-making problems based on probabilistic hesitant fuzzy rough sets.Finally,we analyze the effectiveness and rationality of the method through two practical decision-making problems(medical diagnosis and supplier selection)along with experimental comparisons.This part of the study is very beneficial to improve the objectivity and scientificity of decision results by considering the effect on decicion-making of subjective preferences under complex decision environment.Meanwhile,it provides an important theoretical foundation for probabilistic hesitant fuzzy decision-making problems and has a meaningful application value.This paper aims to build rough models of hesitant fuzzy sets.On the one hand,based on hesitant fuzzy β covering,the new hesitant fuzzy covering rough set models are proposed,and the related properties,axiomatic characteristics and uncertainty measure are further discussed.On the other hand,starting from the operations of probabilistic hesitant fuzzy sets,a new probabilistic hesitant fuzzy rough set model is built and the related properties and uncertainty measure are investigated.The work of this paper extends deeply the rough set theories to hesitant fuzzy environment,which provides strong theoretical foundation and technical support for constructing more practical multi-critera decision-making methods.