A Method for Data Classification Based on Discernibility Matrix and Discernibility Function

A method for data classification will influence the efficiency of classification. Attributes reduction based on discernibility matrix and discernibility function in rough sets can use in data classification, so we put forward a method for data classification. Namely, firstly, we use discernibility matrix and discernibility function to delete superfluous attributes in formation system and get a necessary attribute set. Secondly, we delete superfluous attribute values and get decision rules. Finally, we classify data by means of decision rules. The experiments show that data classification using this method is simpler in the structure, and can improve the efficiency of classification.

Reduction Algorithms Based on Discernibility Matrix:The Ordered Attributes Method

In this paper, we present reduction algorithms based on the principle of Skowron's discernibility matrix - the ordered attributes method. The completeness of the algorithms for Pawlak reduct and the uniqueness for a given order of the attributes are proved. Since a discernibility matrix requires the size of the memory of U2, U is a universe of objects, it would be impossible to apply these algorithms directly to a massive object set. In order to solve the problem, a so-called quasi-discernibility matrix and two reduction algorithms are proposed. Although the proposed algorithms are incomplete for Pawlak reduct, their opimal paradigms ensure the completeness as long as they satisfy some conditions. Finally we consider the problem on the reduction of distributive object sets.

Generalized binary discernibility matrix for attribute reduction in incomplete information systems

To extract and express the knowledge hidden in information systems, discernibility matrix and its extensions were introduced and applied successfully in many real life applications. Binary discernibility matrix, as a representative approach, has many interesting superior properties and has been rapidly developed to find intuitive and easy to understand knowledge. However, at present, the binary discernibility matrix is mainly adopted in the complete information system. It is a challenging topic how to achieve the attribute reduction by using binary discernibility matrix in incomplete information system. A form of generalized binary discernibility matrix is further developed for a number of representative extended rough set models that deal with incomplete information systems. Some useful properties and criteria are introduced for judging the attribute core and attribute relative reduction. Thereafter, a new algorithm is formulated which supports attribute core and attribute relative reduction based on the generalized binary discernibility matrix. This algorithm is not only suitable for consistent information systems but also inconsistent information systems. The feasibility of the proposed methods was demonstrated by worked examples and experimental analysis.

Investigation on AQ11, ID3 and the Principle of Discernibility Matrix

The principle of discernibility matrix serves as a tool to discuss and analyze two algorithms of traditional inductive machine learning, AQ11 and ID3. The results are: (1) AQ11 and its family can be completely specified by the principle of discernibility matrix; (2) ID3 can be partly, but not naturally, specified by the principle of discernibility matrix; and (3) The principle of discernibility matrix is employed to analyze Cendrowska sample set, and it shows the weaknesses of knowledge representation style of decision tree in theory.

Extended Rough Set Model Based on Prior Probability and Valued Tolerance Relation

Based on equivalence relation,the classical rough set theory is unable to deal with incomplete information systems.In this case,an extended rough set model based on valued tolerance relation and prior probability obtained from incomplete information systems is firstly founded.As a part of the model,the corresponding discernibility matrix and an attribute reduction of incomplete information system are then proposed.Finally,the extended rough set model and the proposed attribute reduction algorithm are verified under an incomplete information system.

Second Attribute Algorithm Based on Tree Expression

One view of finding a personalized solution of reduct in an information system is grounded on the viewpoint that attribute order can serve as a kind of semantic representation of user requirements. Thus the problem of finding personalized solutions can be transformed into computing the reduct on an attribute order. The second attribute theorem describes the relationship between the set of attribute orders and the set of reducts, and can be used to transform the problem of searching solutions to meet user requirements into the problem of modifying reduct based on a given attribute order. An algorithm is implied based on the second attribute theorem, with computation on the discernibility matrix. Its time complexity is O（n^2 × m） （n is the number of the objects and m the number of the attributes of an information system）. This paper presents another effective second attribute algorithm for facilitating the use of the second attribute theorem, with computation on the tree expression of an information system. The time complexity of the new algorithm is linear in n. This algorithm is proved to be equivalent to the algorithm on the discernibility matrix.

Design of a new type of integrated classifier for network intrusion detection systems

Based on the analysis of the network intrusion detection model,a new design scheme for the integrated classifier is proposed.The attribute reduction algorithm of the discernibility matrix is used for the optimization design of reducing nodes of input and hidden layers.The experi-mental test result shows that this design is valid.