Research On Multi-attribute Rough Sets And Soft Rough Sets

Rough set theory was proposed by Poland scientist Pawlak in1991. It is a new method todeal with incomplete and uncertain knowledge. Rough set theory is based on the assumptionthat there is a certain amount of information associated with every object of the universe.Rough set theory is widely used in fields like pattern recognition, information processing andfeature selection. Rough set theory is an extension of set theory, it uses equivalence relationbased upper approximation and lower approximation to describe a subset of the universe.Although traditional rough set theory is very useful for dealing with uncertainty andvagueness. It is restricted to one attribute set. Thus the performances of rough sets theory indealing with multi-attributes problems in applications are limited.Recently, soft set theory as a general method to deal with uncertain data is widely used infields like decision-making problems. It is first introduced by Molodtsov. One advantage ofsoft set theory is that it is free from the inadequacy of the parameterization tools like fuzzysets theory and probability. Classical soft set theory is based on complete information, butthere are many reasons that may lead to incomplete soft sets. Furthermore, because of thespecial parameter domain of soft sets, traditional ways used to deal with incompleteinformation system need to be extended to deal with incomplete sot sets. Weighted-averagemethod can be used to predicted unknown parameter values in soft sets. However, not enoughinformation in soft sets has been made use of. The accuracy of prediction for unknownparameter values using weighted-average method in incomplete soft sets will be low whenfew parameter values have been known already.In complete soft sets, it is very meaningful to combine rough sets and soft sets to dealwith incomplete problem. Until now research on soft rough sets are mainly based on soft setsdefined by equivalence relation, which greatly limit the applications of soft rough sets. In thepaper the following work have mainly been done:First, in this paper we have built a multi-attribute rough sets model, by establishing anapproximation space of multi-attributes. Multi-attribute rough sets theory can deal withproblems with more than one attribute sets. We studied multi-attribute rough sets model basedon keeping partitions induced by different attribute sets. The operators between two subsets ofthe universe are researched and proofs are also given. Moreover, basic properties of more than two subsets of the universe are investigated. Multi-attribute rough set theory is extended tomore than one attribute set, furthermore, relationship between multi-attribute rough set theoryand classical rough set theory is discussed. Finally, an example is used to demonstrate thetheory’s practical applications.Second, in the paper the problem of parameter reductions in soft sets is studied,moreover, the advantages and disadvantages of using the existing methods to predictparameter value are analyzed. The object-parameter method which makes full use of theinformation of relationships between objects and relationships between parameters isproposed. The proposed object-parameter method has more advantages than other methodswhen there are few known parameter values. Thus it can predict parameter values with higheraccuracy and provide support in decision-making problems.Finally, dominance relation which can reduce the influence of inconsistency in somedegree is discussed in the paper. Parameter importance definition based on dominance relationis given and clustering method in soft sets is investigated. The paper also defined clusteringbased soft rough sets theory. At last, operations and accuracy in soft rough sets are researched.