Fuzzy Rough Set Models Over Two Universes And Multi-granulation

Rough set theory, proposed by Polish matmatician Z.Pawlak in1982, is an approachto deal with the uncertainty problems. However, the fuzzy set theory proposed byAmerica Zadeh in1965is the other way to handle the fuzzy phenomenon which declaimthat there is fuzzy phenomenon except the classical phenomenon and the fuzziness,except the classical. So the research by combining the rough set theory and the fuzzy settheory has become the one of the most spotlights in recent years.The paper proposes several fuzzy rough set models and discusses the uncertainty ofthe knowledge from the view of the universes and granular computing, using the fuzzyset as the research object. The main ideas of this paper are listed as follows:1. With the view of universe, the new rough set models which are rough fuzzy setmodel in a generalized approximation space, rough set model in a fuzzyapproximation space and rough fuzzy set model in a fuzzy approximation spacebased over two different universes are constructed. Furthermore, by employ anexample in real life to illustrate the applications and effective of these models.2. With the view of granular computing, the single granulation (i.e., a single dominaterelation) rough set in ordered information system is extended to themulti-granulation (i.e., multiple dominate relations) rough set models (MGRS)based on ordered information system. The study can deal with the problem how tohandle in many conditions.3. Based on fuzzy phenomenon in real life, construct the multi-granulation fuzzy roughset models based on ordered information system and the properties of these modelsare investigated. What’s more, the relationships among these and fuzzy rough setmodels based on ordered information system are disused.4. The model of the multi-granulation rough set based on triangular norm is proposedand the properties and the relationships between the T-upper and-lowerapproximation operators also studied.5. The models of multi-granulation fuzzy rough set models over two universes areproposed, and these properties of these operators are investigated. Moreover, byemploying an example to illustrated the application of these models in practice.Finally, the relationships among these and fuzzy rough set models over twouniverses are disused.