Variable Precision Rough Set Based Knowledge Discovery In Ordered Information Systems

Resulting from objective facts and following the cognitive process, we use majoritysupport of variable precision to generalize rough set approach in this thesis. The classicaldominance-based rough set theory can’t tolerate error and mistake in data. To overcomethis limitation, variable precision method is employed to study the dominance-basedvariable precision rough set and the model based attribute reduction theory. By takingcurrently existing multi-granulation rough set as foundations, discussions on generalizedmulti-granulation rough set, granulation weighted multi-granulation rough set, thecombination of multi-granulation and variable precision are implemented separately. Theinnovative points are arranged in the following:1. The theory on variable precision ordered information system is enriched andperfected. We redefine the inclusion degree on Cantor set and draw the variable precisionmethod into ordered information system to study the properties, features of measures andthe attribute reduction theory. Meanwhile, algorithm and program are provided to acquirerough approximation operators and attribute reductions. Detailed interpretations andverifies are explained by cases.2. Discussions on the generalized multi-granulation rough set are put into effect. Bythe defining of support characteristic function, whether an object supports a concept or notunder single granulation is presented. Thus, the objects are selected in sense of multiplegranulations. Basic properties, characteristics of measures, consistence of informationsystems and attribute reduction under multi-granulation are studied further in thegeneralized multi-granulation rough set model. Moreover, acquiring of attribute reductionsin the generalized multi-granulation rough set model is performed by Matlab programing.3. Granulation weighted multi-granulation rough set is studied. Granulation weightand support characteristic function are used to define granulation weightedmulti-granulation rough set. Basic properties and uncertainty measures are investigated indepth. Thus, the different affections of granulations on knowledge representation arereflected. Programs are designed to calculate granulation weights and the approximationsets. Furthermore, examples are arranged to show interpretations.4. The combination of multi-granulation and variable precision is elaborated. Variableprecision method is introduced on the basis of multi-granulation and essential propertiesare discussed. Simultaneously, granulation weighted multi-granulation rough set is also integrated with variable precision. Granulation weighted variable precision rough set andgranulation weighted ordered variable precision rough set are defined and the propertiesare studied. As further research, a case is employed to verify the work investigated.