Abstract: Relation between tolerance class and indispensable attribute and knowledge dependency in rough set model with tolerance relation is explored. After giving definitions and concepts of knowledge dependency and knowledge dependency degree for incomplete information system in tolerance rough set model by distinguishing decision attribute containing missing attribute value or not, the result of maintaining reflectivity, transitivity, augmentation, decomposition law and merge law for complete knowledge dependency is proved. Knowledge dependency degrees (not complete knowledge dependency degrees) only satisfy some laws after transitivity, augmentation and decomposition operations. An algorithm to solve attribute reduction in an incomplete decision table is designed. The correctness is checked by an example.
Abstract: Some invariant properties of incomplete information systems homomorphism are studied in this paper. Demand conditions of tolerance class, attribute reduction, indispensable attribute and dispensable attribute being invariant under homomorphism in incomplete information system are revealed and discussed. The existing condition of endohomomorphism on an incomplete information system is also explored. It establishes some theoretical foundations for further investigations on incomplete information systems in rough set theory, like in information systems.
Abstract: Some extended rough set models in incomplete information system cannot distinguish the two objects that have few known attributes and more unknown attributes; some cannot make a flexible and accurate discrimination. In order to solve this problem, this paper suggests an improved limited tolerance rough set model using two thresholds to control what two objects have a relationship between them in limited tolerance relation and to classify objects. Our practical study case shows the model can get fine and reasonable decision results.
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: In rough set models, tolerance relation, similarity
relation and limited tolerance relation solve different situation
problems for incomplete information systems in which there exists a
phenomenon of missing value. If two objects have the same few
known attributes and more unknown attributes, they cannot
distinguish them well. In order to solve this problem, we presented two
improved limited and variable precision rough set models. One is
symmetric, the other one is non-symmetric. They all use more
stringent condition to separate two small probability equivalent objects
into different classes. The two models are needed to engage further
study in detail. In the present paper, we newly form object classes with
a different respect comparing to the first suggested model. We
overcome disadvantages of non-symmetry regarding to the second
suggested model. We discuss relationships between or among several
models and also make rule generation. The obtained results by
applying the second model are more accurate and reasonable.
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: The information systems with incomplete attribute
values and fuzzy decisions commonly exist in practical problems. On
the base of the notion of variable precision rough set model for
incomplete information system and the rough set model for
incomplete and fuzzy decision information system, the variable rough
set model for incomplete and fuzzy decision information system is
constructed, which is the generalization of the variable precision
rough set model for incomplete information system and that of rough
set model for incomplete and fuzzy decision information system. The
knowledge reduction and heuristic algorithm, built on the method and
theory of precision reduction, are proposed.