Skill Level Reduction and Necessary and Sufficient Conditions of Forward-Graded(Backward-Graded) Knowledge Structure in Fuzzy Formal Context
FENG Danlu1, LI Jinjin1,2, LI Zhaowen3, ZHOU Yinfeng4, YANG Taoli1
1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000; 2. Fujian Key Laboratory of Granular Computing and Application, Minnan Normal University, Zhangzhou 363000; 3. Guangxi College and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000; 4. School of Mathematics and Statistics, Shaanxi Normal University, Xian 710119
Abstract：Fuzzy skill mapping is a pathway to construct knowledge structure. However, applying the basic local independence model to the forward-graded(backward-graded) knowledge structure results in unrecognizable problem. Therefore, under the premise of fuzzy skill mapping, two problems are solved in this paper: excessive time consumption in skill reduction and searching for the necessary and sufficient conditions of the forward-graded(backward-graded) knowledge structure. Firstly, based on the fuzzy skill context, a pair of operators is constructed, and the simple closure space is acquired directly through the fuzzy skill concept lattice determined by the pair of operators. At the same time, the minimum skill proficiency corresponding to each knowledge state is obtained. Secondly, the concept of skill level reduction is proposed. Redundant skill level is reduced by label skill reduction, and the algorithm of skill level reduction is provided. In addition, the necessary and sufficient conditions for inducing forward-graded(backward-graded) simple closure space from fuzzy skill mapping are presented, along with an algorithm for obtaining the forward-graded problem set and the backward-graded problem set. Finally, comparative experiments on five UCI datasets verify the feasibility and effectiveness of the proposed algorithm, and the forward-graded problem set and the backward-graded problem set are obtained.
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2023, Vol. 36 
