The Approach To Probabilistic Decision-theoretic Rough Set Based On Interval-valued Fuzzy Information System

With the vigorous development of the society,people are facing the different types,the multiple types and the top-ranking update speed of data set in information age.The interval-valued fuzzy information system(IVFIS),which is composed of uncertain fuzzy interval forms,has become one of the hotspots in the current research of information technology.At the same time,how to excavate valuable information from IVFIS is also a major challenge in the field of artificial intelligence.Rough set theory,as a mathematical theory for dealing with uncertain problems,is extended to the theory of granular computing and three-way decisions and the defined upper and lower approximation sets defined are used to characterize uncertain information.Because rough set haven't fault tolerance mechanism,with the need of study,scholars have developed more models such as the decision-theoretic rough set(DTRS)proposed by Yao,which is mainly used in practical decision-making problems.The semantic interpretation of this model is to accept things in the positive region,to refuse things in the negative domain divided by the upper and lower approximate set.The boundary domain represents the delayed decision-making.On the base of DTRS,the graded rough set(GRS)and multi-granulation rough set(MGRS),this paper firstly study the attribute reduction of IVFIS and the purpose is to remove the influence of redundant information on knowledge acquisition process and final result.Secondly,considering the probability and the real-valued and interval-valued loss functions,we establish fuzzy probability decision-theoretic rough set and interval-valued fuzzy probability decision-theoretic rough set in IVFIS,respectively.Finally,this article investigates the graded multi-granulation rough set(GMGRS).The main innovations are as follows:1.In the inconsistent IVFIS,we establish distribution reduction,the maximum distribution reduction and the partial consistent reduction method of IVFIS by defining the distribution function,the maximum distribution function and the partial consistent function.How to obtain the simplest information and get the optimal solution is reported in this paper.The related mathematical properties are studied in depth and the relationship among different attribute reductions in IVFIS is discussed.Finally,the IVFIS distribution reduction,the maximum distribution reduction and the partial consistent reduction are calculated based on the definition method and discernibility matrix method.Through the comparison and analysis of algorithm,it is concluded that the discernibility matrix method simplifies the complexity of time and space.2.The decision of IVFIS is changed to the decision-making under the approximate space and the new similarity relation among objects is defined by the absolute index method.Under the environment permit,we convert IVFIS into fuzzy approximate space and interval-valued fuzzy approximate space.Then considering the probability and loss function in real-valued and interval-valued under the approximation space,we set up two models include fuzzy probability decision-theoretic rough set of IVFIS and interval-valued fuzzy probability decision-theoretic rough set of IVFIS respectively.In the decision-making process,the degree of risk is controlled by threshold ? and ?.In addition,the latter model is more consistent with the characteristics of decisions in the uncertainty measure than the former.Finally,a case is made to make a decision on IVFIS,and the validity and value of the proposed model are expounded.3.Based on multi granularity and graded rough set theory,three types of graded multi-granulation rough set based on IVFIS are constructed based.Namely,optimistic graded multi-granulation rough set(OGMGRS),pessimistic graded multi-granulation rough set(PGMGRS)and generalized graded multi-granulation rough set(GGMGRS).Some basic structures and properties of models are studied.And the connections of the upper and lower approximation operators of models are established.The scheme is decided by the graded multi-granulation approximation operators and the various rough regions which defined in multiple dominance relations.Finally,a new order relation-? geometric average ranking for IVFIS is introduced to demonstrate the practicality and feasibility of the model by means of examples.