Research On Three-way Decision Models Of Multi-granulation Support Intuitionistic Fuzzy Rough Sets

Three-way decisions are a "three divides and conquers" decision-making model that conforms to human cognitive process,and it provides a reasonable solution for handling uncertain decision problems.It also takes into account the uncertainty and cost loss in decision-making process,which is in line with the cognitive process and selection habits of human thinking and decision-making.It is a hotspot worthy of in-depth research.When several conflicting attribute information are involved in uncertainty decisionmaking,support intuitionistic fuzzy sets use membership degree,non-membership degree and support degree to intuitively and scientifically describe uncertainty of things.Considering the inherent properties and external influence of the object,the uncertainty problems are studied and the decision precision is improved.However,most of the current researches on the uncertainty problems are based on a single granularity structure,which cannot meet the needs of complex fuzzy environment decision-making.Multi-granulation rough sets can deal with the fuzzy problems of multiple granularity structures.Combining them can effectively handle uncertain decision problems.Therefore,using support intuitionistic fuzzy set theory from the perspective of multi-granulation and multi-level to study three-way decisions and expand relevant research has certain research value and significance.In this paper,support intuitionistic fuzzy rough sets and support intuitionistic fuzzy probability are defined by studying support intuitionistic fuzzy sets.From the perspective of multi-granulation analysis,we propose multi-granulation support intuitionistic fuzzy rough set models and multi-granulation support intuitionistic fuzzy probability rough set models.In order to effectively and accurately make decisions on uncertain information and reduce the losses caused by erroneous decisions,the correlative three-way decision models are established by combining three-way decision theory.The related properties of these models were discussed,and the validity of these models was verified by examples.The main research work of this paper is as follows:(1)In view of the problem that multiple conflicting attribute information in multi-attribute decision-making makes it difficult for decision makers to make decision judgments,a multi-granulation support intuitionistic fuzzy rough set model is constructed by combining support intuitionistic fuzzy sets with multi-granulation rough sets,and the related properties are discussed.The fitting function is defined by t-norm and t-conorm,and we propose a multi-attribute decision-making solving method of multi-granulation support intuitionistic fuzzy rough sets.At the same time,a new score function and accuracy function are defined to sort the decision results,the corresponding decision rules are extracted,the algorithm is designed and an example is analyzed.The results show that this method enables decision makers to select the optimal decision-making scheme according to actual needs when dealing with conflicting multi-attribute decision-making problems.(2)Aiming at the influence of various uncertain factors on decision-making,support intuitionistic fuzzy sets are introduced for three-way decisions to research this topic from the perspective of multi-granulation.First,on the basis of multi-granulation support intuitionistic fuzzy rough sets,a variable multi-granulation support intuitionistic fuzzy rough set model is constructed by introducing parameter ? to constrain the disjunction and conjunction operations among multiple support intuitionistic fuzzy relations.Then,the concepts of similarity measure,positive ideal solution,negative ideal solution and conditional probability based on multi-granulation support intuitionistic fuzzy rough sets are defined,and relevant three-way decision models are established.Finally,a score function and an accuracy function are constructed to derive the decision rules,and related algorithm is given.The effectiveness of the proposed models is verified by an example.(3)Based on support intuitionistic fuzzy sets,the definitions of support intuitionistic fuzzy probability and multi-granulation support intuitionistic fuzzy probability approximate spaces are given.Four support intuitionistic fuzzy probabilities are proposed according to different operation combinations between multiple granularities.The type ?,type ?,type ? and type ? multi-granulation support intuitionistic fuzzy probabilistic rough set models are constructed by using Bayesian theory to calculate thresholds ? and ?,and the relevant properties of these models are discussed.Combining with three-way decision theory,four kinds of three-way decision models are constructed,and an example is given to verify and compare the effectiveness of these models.This paper mainly researches three-way decision theory by combining support intuitionistic fuzzy sets with multi-granulation rough sets.It enriches three-way decision theory,expands application range of support intuitionistic fuzzy sets and multi-granulation rough sets theories,and provides a new direction and method for the study of uncertain decision-making problems.