Research On Matroids And Conflict Analysis Based On S-Approximation Spaces

S-approximation space is a new theory to deal with uncertainties in recent years.It provides a new method for knowledge representation and knowledge processing by defining a knowledge mapping and a decision mapping respectively,which broadens the application range of rough set models.This paper intends to study matroids and conflict analysis based on S-approximation spaces.The main contents are as follows:1.As an important mathematical structure on finite sets,matroids have been widely used in rough sets research in recent years.But almost all these works are carried out on the rough set models that take inclusion relation as knowledge processing means.S-approximation space model provides a unified knowledge processing means,therefore this paper studies the matroidal structures constructed on S-approximation spaces.Firstly,we define the upper and lower approximation numbers based on knowledge and decision mappings.And we point out that the upper approximation numbers(resp.lower approximation numbers)of S_min-approximation spaces(resp.S_max-approximation spaces)are nondecreasing submodular functions.According to the method of constructing matroids with nondecreasing submodular functions,we construct matroids on S-approximation spaces by approximation numbers,called S-matroids.Secondly,this paper redefines S-matroids from the viewpoint of circuits,and investigates the relation between the rank function of an S-matroid and its corresponding approximation number.Finally,we introduce the order on S-matroids via the two orders defined on S-approximation spaces,and answer the question whether S-matroids can also be constructed on the intersection,union,or complement spaces of S-approximation spaces.2.As a tool to deal with uncertainty,rough set models are particularly suitable for the task of conflict analysis.However,rough set models with inclusion relation as knowledge procession,have poor adaptability to complex and changeable conflict situations.S-approximation space model provides a unified knowledge processing method,which is highly adaptable to conflict situations.Therefore,this paper investigates the application of S-approximation space method in conflict analysis.Firstly,based on the model of three-way conflict analysis proposed by Yao,this paper generalizes three-valued situation tables to multiset-valued situation tables on[-1,+1],and proposes a model of conflict analysis on multiset-valued situation tables.We also give the concepts of three alliances and three conflicts.Secondly,according to decision-theoretic rough sets and the decision principle of Bayesian least risks,this paper theoretically calculates the threshold values needed to partition three alliances and three conflicts.Finally,based on the reformulated S-approximation space framework,we use the tri-partion of agent set(resp.pair agents set)determined by a single issue as knowledge mapping to define the approximation of agent sets(resp.pair agents sets),and uses the tri-partion of issue set determined by a single agent(or a single pair agents)as knowledge mapping to define the approximation of issue sets.And by choosing specific decision mappings,multiset-valued conflicts situations are analyzed.In summary,based on the new knowledge processing method of S-approximation spaces,this paper constructs matroids on S-approximation spaces,and uses S-approximation space method to study multiset-valued conflict situations.These works make it possible for future research to choose knowledge processing methods based on rough sets and according to the requirements of theory and application,which has certain theoretical significance and application value.