Research on the Approach of Knowledge Acquisition in Expert Systems based on Rough Sets Theory

The research on expert systems has been a hotspot. In order to resolve the problems about knowledge acquisition in complete and incomplete knowledge representation systems, the algorithm of knowledge acquisition based on rough set theory is proposed. Let the knowledge representation system be a decision table, the useful knowledge can be obtained by simplification of the decision table. The algorithm of computation of condition attributes’ reductions and the algorithm of computation of reduction of decision rule are researched to simplify the decision table. When there are missing values in knowledge representation systems, the missing data should be completed by the algorithm of missing values’ completion firstly. This algorithm of knowledge acquisition based on rough set theory can obtain a minimal set of decision rules which can be used to reason in expert systems. The approach of knowledge acquisition can be used to simplify uncertain and incomplete knowledge representation systems. Introduction With the development of the application system of the artificial intelligence and the knowledge engineering, the expert system [1] has been a hot area. It was successfully applied in many domains. With the enhancement of demand, many questions such as the knowledge acquisition [2,3] and the uncertain knowledge reasoning are exposed. Rough sets theory [4] was proposed by Z. Pawlak in 1982. The theory provides a new tool for dealing with classification of fuzzy, inaccurate or incomplete information. The main idea of the theory is that rules of decision and classification can be obtained by reduction of knowledge remaining the classification ability of information system unchanged. In this paper, a model of an expert system based on rough sets theory as shown in fig. 1 is given, and the knowledge acquisition mechanism based on the model will be researched in detail. An improved algorithm of knowledge acquisition from complete knowledge representation system based on rough sets theory and an improved algorithm of missing values’ completion in incomplete knowledge representation system will be proposed. Knowledge representation system [5] can be formulated as a pair ) , ( A U S = .U is a nonempty and finite set called the universe. A is a nonempty and finite set of primitive attributes. Every primitive attribute a A ∈ is a function : a U Va → (Va is the set of values of a , called the domain of a ). If u U ∈ , a A ∈ and a v Va ∈ , the knowledge representation system will been called complete knowledge representation system, otherwise the knowledge representation system is a incomplete data Data pre processing Knowledge representation system knowledge acquisition Reason machine Fig.1 a model of expert systems based on rough sets theory User interface 2nd International Conference on Electrical, Computer Engineering and Electronics (ICECEE 2015) © 2015. The authors Published by Atlantis Press 1265 knowledge representation system. Let , C D A ⊂ (where , C D called condition and decision attributes respectively), the knowledge representation system with distinguished condition and decision attributes will be called a decision table, and will be denoted ( , , , ) S U A C D = . Knowledge Acquisition from Complete Knowledge Representation Systems Based on Rough Sets Theory The process of knowledge acquisition in expert systems based on rough sets theory is actually simplification of knowledge representation systems [6]. Simplification of Knowledge representation system is simplified as follow. Let ( , , , ) S U A C D = be a knowledge representation system. If { } ( ) ( ) C a C POS D POS D − = , the attribute a is dispensable in knowledge representation system, otherwise the attribute a is indispensable. If all attributes a C ∈ are indispensable, the knowledge representation system is independent. Let R C ⊆ . If ( ) ( ) R C POS D POS D = and the decision table ' ( , , , ) S U R D R D =  is independent, R which can be denoted ( , ) RED C D is a reduction of condition attributes in the knowledge representation system, ' S is a reduction of the decision table ( , , , ) S U A C D = . The set of all indispensable attributes in condition attributes will be called the core of the decision table, and will be denoted ( , ) CORE C D . ( , ) ( , ) CORE C D RED C D =  . Let θ ψ → be a RD -rule and a R ∈ , If ( ) / R a s s θ ψ θ ψ ∧ = − ∧ , the attribute a is dispensable in the ruleθ ψ → , otherwise the attribute a is indispensable. If all attributes a R ∈ are indispensable, the rule θ ψ → is independent. If ' R R ⊆ , / ' R θ ψ → and / ' S s R θ ψ θ ψ ∧ = ∧ , / ' R θ ψ → is a reduction of RD -rule:θ ψ → . The set of all indispensable attributes of RD -rule:θ ψ → will be called the core of the rule and will be denoted ( ) CORE θ ψ → . The approach to simplification of knowledge representation systems [7] presented in this paper consists of the following steps: (1) Computation of condition attributes’ reductions; (2) Elimination of duplicate rows in the decision table ' ( , ( , ) , ( , ), ) S U RED C D D RED C D D =  (remark: rows do not represent here description of any real objects); (3) Computation of reduction of every rule in the knowledge representation system. The Approach to Simplify Knowledge Representation Systems (1) The algorithm of computation of condition attributes’ reductions Computation of condition attributes’ reductions [8,9] has been proved to be a Non-deterministic Polynomial Complete problem. In order to improve the efficiency of knowledge acquisition, a lot of researches on approaches to compute reductions of condition attributes have focused on the approximate reduction of attributes. In this paper, a algorithm of approximate reduction based on the importance of attributes will be proposed. Let ( , , , ) S U A C D = be a decision table, R C ⊆ , and a C R ∈ − , the importance of attributes a which will be denoted tan ( , , ) impor ce a R D can be formulated as follows: { } ( ) ( ) { } | | | | tan ( , , ) | | | | R a R R R a POS D POS D impor ce a R D U U γ γ = − = − 