Abstract: Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.
Abstract: This paper proposes rough set models with three
different level knowledge granules in incomplete information system
under tolerance relation by similarity between objects according to
their attribute values. Through introducing dominance relation on the
discourse to decompose similarity classes into three subclasses: little
better subclass, little worse subclass and vague subclass, it dismantles
lower and upper approximations into three components. By using
these components, retrieving information to find naturally hierarchical
expansions to queries and constructing answers to elaborative queries
can be effective. It illustrates the approach in applying rough set
models in the design of information retrieval system to access different
granular expanded documents. The proposed method enhances rough
set model application in the flexibility of expansions and elaborative
queries in information retrieval.
Abstract: In this paper, we generalize some propositions in [C.Z. Wang, D.G. Chen, A short note on some properties of rough groups, Comput. Math. Appl. 59(2010)431-436.] and we give some equivalent conditions for rough subgroups. The notion of minimal upper rough subgroups is introduced and a equivalent characterization is given, which implies the rough version of Lagranges Theorem.