Research On Double-quantitative Decision Model Under Hesitant Fuzzy Environment

Data processing has become increasingly difficult due to the diverse forms of consumpution in the information age.In order to describe the research object more accurately and embody diversified ideas,Torra proposed the concept of hesitant fuzzy set in 2009.The membership function of hesitation fuzzy set is composed of a set of possible values between 0 and 1,which is another new tool to describe uncertainty information after the concept of intuitionistic fuzzy set.It can vividly describe people's hesitation state in the decision-making process.Up to now,the theoretical and applied research on hesitant fuzzy sets mainly focuses on data analysis and processing,multi-attribute decision making and other related fields,and has obtained a large number of research results.This paper will continue to study the related theories and applications of hesitant fuzzy sets on the basis of the existing results.Firstly,the hesitant fuzzy information system is established under the hesitant fuzzy environment,then the hesitant fuzzy relation is defined,and the belief attribute reduction and plausibility attribute reduction methods of this information system are proposed respectively.Following this,the graded and variable precision hesitant fuzzy rough set model are discussed in the hesitant fuzzy information system.Finally,according to the minimum risk decision-making rules,two double-quantitative decision-making analysis models combining relative quantitative information and absolute quantitative information are studied.The innovation of this paper is as follows:1.The hesitant fuzzy relation is established by defining the hesitant fuzzy information system.In addition,some important properties of hesitant fuzzy relation are proposed and verified.2.In order to extract necessary information and delete redundant information in hesitant fuzzy information system,the internal(external)significance measures are introduced.Furthermore,the belief reduction model and plausibility reduction model in the information system are studied,and two corresponding concrete algorithms are designed,and the feasibility of the two algorithms is verified by an example.3.Based on the hesitant fuzzy information system,the conditional probability measure of hesitant fuzzy is defined.Two single quantitative decision models,i.e.graded hesitant fuzzy rough set and variable precision hesitant fuzzy rough set,are established in combination with score function.And then their related properties are studied.Finally,an example and the corresponding algorithm design are used to verify the rationality of its related properties and deepen the understanding of two single-quantitative decision models.4.On the basis of graded and variable precision hesitant fuzzy rough set model,the conjunctive logic operator and disjunctive logic operator are used to fuse the relative quantitative information and absolute quantitative information respectively.The double-quantitative decision analysis model based on conjunctive logic operator and the double-quantitative decision analysis model based on disjunctive logic operator under hesitant fuzzy environment are further studied,and their corresponding decision rules and internal relations are discussed.In the end,four kinds of decision analysis models are compared and analyzed with an illustrative case to verify the feasibility of two double-quantitative decision analysis models.It is concluded that the doublequantitative decision analysis model has fault tolerance mechanism.