Three-way Decision And Attribution Reduction Based On Multi-adjoint Fuzzy Rough Sets

A pair of triangular norm and implication operator are used to construct the approximate operator in traditional fuzzy rough set,which does not consider the attribute difference.However,several adjoint triples are used to construct the approximate operator in multi-adjoint fuzzy rough set,which precisely reflects the user preferences.Multi-adjoint fuzzy rough sets model currently has become an interesting research topic.This thesis mainly focuses on the following aspects:Firstly,a new method to the weight of attribute is proposed,which is used to popularize multi-adjoint fuzzy rough sets.Family of adjoint pairs are considered to construct the lower and upper approximations in multi-adjoint fuzzy rough sets.The user may represent explicit preferences among the objects in a decision system by associating a particular adjoint triple with any pair of objects.And the concept of weighted reduction is proposed and a weighted reduction algorithm is formulated,in which the weight vector represents importance of attributes.The algorithm is an extension of the reduction algorithm based on discernibility.Finally,we testify the accuracy of the theory through two experiments.Secondly,decision-theoretic rough set provides a new perspective to handle decisionmaking problems under uncertainty and risk.Three-way decision with decision-theoretic rough sets,generated by Bayesian decision theory,is a typical risk decision method.Cost is proposed into multi-adjoint fuzzy rough sets model and cost-sensitive multi-adjoint fuzzy rough sets model is defined,which considers problems more practically,all sidedly.Three-way decision is formulated and loss function is constructed with the optimistic probability in cost-sensitive multi-adjoint fuzzy rough sets.Corresponding three-way decision model is constructed,and the three-way decision is induced in order to make decisions with the minimum loss risk.Thirdly,multi-adjoint intuitionistic fuzzy rough set is proposed,and three-way decision is formulated in multi-adjoint intuitionistic fuzzy rough sets.The optimistic multiadjoint intuitionistic fuzzy rough set is defined in order to deal with the complicated calculation of intuitionistic fuzzy value.As the determination of loss function is one of the key steps in the decision process,then the loss function is calculated by using the degree of membership and the degree of nonmembership.The event objects are assessed through the loss functions.Next,we construct corresponding three way decision model,and induce the three-way decision in order to make decisions with the minimum risk of loss and get the risk of the corresponding decision.The structure of the expected loss function synthetically considers the support degree and the nonsupport degree,which can effectively reflect the real life situation and meet users' preferences.Finally,an example of medical diagnosis is employed to verify the effectiveness of the proposed model.