Attribute Reduction In Two Types Of Objective Random Information Systems

In this paper, we study the attribute reduction in objective random information system based on non-transitive relation and inconsistent objective random information system.The specific work is as follows:1. The classical rough set theory is proposed on the basis of the equivalence relation. Because in practice, the conditions for equivalence relation have limitations, many scholars put the equivalence relation outreach to general relations such as dominance relation and dominance- equivalence relation. The conditions of dominance relation are relatively loose, but the conditions for equivalence relation are too strict. So we consider the close degree of attribute values between different objects and structure non-transitive relation, the loose degree of conditions for this relation is between dominance relation and equivalence relation. Meanwhile, the random information system based on non-transitive relation is given and the attribute reduction is discussed. We further study the distribution reduction and the maximum distribution reduction in objective random information system under the non-transitive relation. Finally, using a numerical example to illustrate this reduction method is more effective.2. Knowledge reduction is one of the important problems in rough set theory. In knowledge reduction, restricted by various factors, for example the conditions are not sufficient, the information is defect or inaccurate, many information systems become inconsistent. In recent years, many scholars achieved good conclusions in study inconsistent information systems. However, in many practical problems, discussing the attribute reduction of inconsistent information systems, we don’t need to consider of all objects, but only to a certain object or a class of objects are discussed. Therefore, the μ-attribute reduction(for short μ-reduction) based on the subsets of the objects in inconsistent information system and objects in inconsistent objective random information systems under the equivalent relation and dominance- equivalent relation are given. The results are as follows:(1) The concept of μ-reduction based on the subsets of the objects in inconsistent objective information system is given. And some properties of μ-reduction, the judgement theorem and corresponding discernibility matrix with respect to the μ-reduction are obtained. Meanwhile an approach to calculate μ-reduction is provided.(2) The concept of μ-reduction is introduced to inconsistent objective random information systems. The μ-reduction based on objects in inconsistent objective random information systems under the equivalent relation and dominance- equivalent relation are discussed. Besides, the corresponding properties, the judgment theorem and calculation method of μ-reduction are obtained.