Probabilistic S_p-Rough Sets And Its Actuaral Model On Bayes Decision

By using the concepts of upper approximation and lower approximation to express uncertain data,Rough Set Theory has been used as a mathematical approach to describ imperfect and uncertain knowledge.In Rough Sets Theory,the uncertainty of knowledge is arose from two main aspects as following:On one hand,the directly reason,which is called conceptual uncertainty,is the binary relation and the knowledge module generated by the binary relation,namely the approximation space itself.There are no any more information in the partition,if there is only one element for each classes generated by the binary relation.More rough for each partition,more larger for each knowledge module,so there are more rough and uncertain for the knowledge from knowledge base in relation to the concept and knowledge of approximation space.Generally,entropy of information,as a good approach,is choosed to measure conceptual uncertainty.There are close connection between the grandulation of knowledge and the entropy of information,and,substantively,the grandulation of knowledge is just the deeply layer depiction on how much information there is contained.On the other hand,given the approximation space,the uncertainty of knowledge is arose from the boundary of rough set,which is called uncertainty of system and measured by employing measure of grandulation or the degree of approximate accuracy.The knowledge is absolutely certain,if the boundary of knowledge is null set.More large boundary of knowledge,more rough or vague for knowledge.Analysis method of rough set,a rising analysis method of data,which is an analysis method based on rough set,is in force on anaylsing and dealing with a varity of imperfect information,such as uncomplete,imprecise,uncertain or inconsistent information and so on.Sequentially,it can be used to mine the hidden knowledge and discover the intrinsic law.As it抯 known,the classical Pawlak sets is just a static rough set and is helpless for dealing with dynamic situation.In practice,a vatiety of information systems present always dynamic,such as finance system,risk investment system,medical treatment system and so on.Especially,for decision making system, decision makers have to make decisions when they face the continual changing of outside condition,in order to make most benefit for their company or least loss. Would all been as before metioned,the decision makers should make advanced research and take necessary action for control risk in good season,all of which ask decision makers pay attention to the changes frequently,so that makers can make optimistical decision.Singular rough set develope the Pawlak rough set and describes dynamics of system by employing the concept of element transfer which is one of the primary concepts in S-rough sets theory.The boundary of rough set may be influenced,in other words,the value of measure uncertain of knowledge may be changed,if there are elements been transferred.In fact,it抯always unknown wether there are elements been transferred,because the element transfer has randomicity.Almost all the current researches about S-rough set theory are presented on the assumption that the element transfer is an accomplished fact,but there are a fat lot of studing randomicity of element transfer.Based upon the above fact,it is necessary to measure the probability of element transfer and study its probabilitical characteristic.By mining statistic information generated by element transfer,the degree influenced by external factor is measured in virture of probability and statistics.Based upon the summarization of predecessor抯words,this dissertation presents the researches primarily as following:1.Supposed that the entroy of information of uncertainty approximation space is given,the least attribution reduction algorithm is presented.The probability(degree of confidence) of element transfer is defined and its probabilitical characteristic is discussed briefly,then the mathematical form of probabilitical Se-rough set is given and the relations are discussed among the probabilitical S_P-rough sets and S-rough sets and probabilitical rough sets.2.The characteristic of element transfer is futher discussed,and some concepts about element transfer are given,such as F-probability of state transition of element transfer,F-transition matrix,F-positively decomposed,F-inversely decomposed F-abosultely decomposed and so on,and their properties are discussed brefiely.Model of Bayes decision based on S_P- rough sets and actuarial model of Bayes decision based on S_P -rough sets are presented,then the main procedures of the two decision models are presented separately,and then the relations are discussed briefly among these models.