Abstract
The binary discernibility matrix, originally introduced by Felix and Ushio, is a binary matrix representation for storing discernible attributes that can distinguish different objects in decision systems. It is an effective approach for feature selection, knowledge representation and uncertainty reasoning. An original binary discernibility matrix usually contains redundant objects and attributes. These redundant objects and attributes may deteriorate the performance of feature selection and knowledge acquisition. To overcome this shortcoming, row relations and column relations in a binary discernibility matrix are defined in this paper. To compare the relationships of different rows (columns) quickly, we construct deterministic finite automata for a binary discernibility matrix. On this basis, a quick algorithm for binary discernibility matrix simplification using deterministic finite automata (BDMSDFA) is proposed. We make a comparison of BDMR (an algorithm of binary discernibility matrix reduction), IBDMR (an improved algorithm of binary discernibility matrix reduction) and BDMSDFA. Finally, theoretical analyses and experimental results indicate that the algorithm of BDMSDFA is effective and efficient.
Highlights
Decision making can be considered as the process of choosing the best alternative from the feasible alternatives
By using deterministic finite automata, we develop a quick algorithm of binary discernibility matrix simplification
By using deterministic finite automata, we propose an algorithm of binary discernibility matrix simplification using deterministic finite automata (BDMSDFA)
Summary
Decision making can be considered as the process of choosing the best alternative from the feasible alternatives. Researchers in rough set theory [9] are usually concerned with attribute reduction (or feature selection) problems of multiple attribute decision making. In the paper [20], a novel method for calculation of incremental core attribute was introduced firstly On this basis, an algorithm of attribute reduction was proposed. Our works in this paper concern on how to improve the time efficiency of algorithms of binary discernibility matrix simplification On this purpose, we construct deterministic finite automata in a binary discernibility matrix to compare the relationships of different rows (or columns) quickly. Deterministic finite automata in a binary discernibility matrix are proposed to compare the relationships of different rows (or columns) quickly Based on this method, a quick algorithm for binary discernibility matrix simplification (BDMSDFA) is proposed.
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