Research On Rough Programming Method Based On Relationship Effect

Programming problems are widely encountered in such fields as economics,politics,military,and medicine.These problems have been a heavily researched topic in academic research and have several typical theories and methods.There often exist different forms of uncertainty under real decision environments and decision requests,such as randomness,fuzziness,and roughness,indicating that the decision result has no absolute optimality.Therefore,seeking a satisfactory decision scheme under certain preferences is an important research topic,among them,the research on stochastic programming and fuzzy programming is relatively mature,the theoretical research in rough set and data mining has become more and more mature.but the research on rough programming are at the starting stage,the main problem is the lack of formal description based on structural features.Firstly this paper introduces decision method and rough set theory,especially,the concept and properties of rough set theory.Based on this,the paper analyzes the essential characteristics of rough programming problem combined with reality,and presents its general descriptive form,especially discusses solving method of rough programming as the key issues.1)Using dividing as the basic description strategy of relevance and based on the basic effect of the objects and the relationship effects of related objects,we construct the rough programming model based on the relationship effect(denoted by BERC-RPM for short);and then Aiming at solving the problem of positive effect BERC-RPM,we give the concept of comprehensive value based on the upper(lower)approximation effect,we also give the steps of solving BERC-RPM by using comprehensive value based on the upper(lower)approximation effect;Finally we analyze the characteristics of BERC-RPM through a concrete case.2)Using covering as the basic description strategy of relevance and based on the basic effect of the objects and the cooperative effects of related objects,we construct a rough programming model based on the cooperative effect(denoted as BCE-RPM).Furthermore,we propose the concept of the effect average operator and the upper(lower)approximation cooperative effect value,and we subsequently provide several corresponding solution steps for the BCE-RPM with the upper(lower)approximation cooperative effect value as the basic object factor.Finally,we analyze the characteristics of the BCE-RPM through a concrete case.All of these findings indicate that BERC-RPM and BCE-RPM has good structural characteristics and can easily merge decision preferences into the decision making process.BERC-RPM and BCE-RPM has wide application prospects in the field of resource management,system optimization,and others.