Imprecise Research And Application Of Path Based On Rough Classification

Rough set theory as an effective mathematical method which can deal with imprecise, incomplete anduncertain data, has been successfully applied in many fields. It has become an important intelligentinformation processing technology. Due to research on imprecise path is less, however, it exists objectivelyin real life, so research on imprecise path is a new research subject of rough set theory. At the same time, arough assessment system is obtained by extend the approximation space. Based on the mathematicalframework, the environment of researching on imprecise path is established. Resarching a mathematicalmodel of specific problems which can be described by a rough assessment system.Then it proceeds from aS-rough fuzzy relation that is produced by roughing a fuzzy relation S on M, the in-depth study of S-roughfuzzy path. The main structure of this paper is organized as follows.Firstly, by adding a binary relation and a number of assessment factors into an approximation space, arough assessment system is obtained. Based on the assessment factors, the concepts of the weight and thecomprehensive weight are defined, which leads to the comprehensive lower value of an edge set. So, a pathcan be optimized by making use of the comprehensive lower value, also an algorithm called pathoptimization algorithm is formed. Moreover, by a rough assessment system which describes supplyrelationships between enterprises, a mathematical model of practical problems is constructed. Supply pathsare therefore optimized, which is a result of applying path optimization algorithm to the supply paths. Thisdemonstrates the validity of the algorithm.Secondly, according to a rough assessment system as the mathematical framework, the concepts ofsingle factor lower value, the average weight and optimal path are defined. Path optimization algorithmbased on an single assessment factor is discussed by making use of the single factor lower value. It need tobe sorted each evaluation factor, then gradually according to this sort to achieve the path optimizationprocess. Finally it verifies the validity and feasibility of the algorithm by an example.Thirdly, By the methods of rough a fuzzy relation, S-rough fuzzy relation is introduced, and on thebasis of the S-rough fuzzy relation the S-rough fuzzy path is constructed. Focusing on studying theproperties of S-rough fuzzy path, and presenting a method to measure S-rough fuzzy path. Then, further discussing a determining method of the S-rough fuzzy path and its applications.