A novel attribute reduction approach using coverage-credibility-based rough decision entropy for interval-valued data

Article type: Research Article

Authors: Liu, Xia^a | Zhang, Xianyong^{b; c; *} | Chen, Jiaxin^b | Chen, Benwei^{b; c}

Affiliations: [a] School of Primary Education, North Sichuan College of Preschool Teacher Education, Guangyuan, China | [b] School of Mathematical Sciences, Sichuan Normal University, Chengdu, China | [c] Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu, China

Correspondence: [*] Corresponding author. Xianyong Zhang. E-mail: [email protected].

Abstract:  Attribute reduction is an important method in data analysis and machine learning, and it usually relies on algebraic and informational measures. However, few existing informational measures have considered the relative information of decision class cardinality, and the fusion application of algebraic and informational measures is also limited, especially in attribute reductions for interval-valued data. In interval-valued decision systems, this paper presents a coverage-credibility-based condition entropy and an improved rough decision entropy, further establishes corresponding attribute reduction algorithms for optimization and applicability. Firstly, the concepts of interval credibility, coverage and coverage-credibility are proposed, and thus, an improved condition entropy is defined by virtue of the integrated coverage-credibility. Secondly, the fused rough decision entropy is constructed by the fusion of improved condition entropy and roughness degree. By introducing the coverage-credibility, the proposed uncertainty measurements enhance the relative information of decision classes. In addition, the nonmonotonicity of the improved condition entropy and rough decision entropy is validated by theoretical proofs and experimental counterexamples, with respect to attribute subsets and thresholds. Then, the two rough decision entropies drive monotonic and nonmonotonic attribute reductions, and the corresponding reduction algorithms are designed for heuristic searches. Finally, data experiments not only verify the effectiveness and improvements of the proposed uncertainty measurements, but also illustrate the reduction algorithms optimization through better classification accuracy than four comparative algorithms.

Keywords: Rough sets, Attribute reduction, Interval-valued decision systems, Algebraic measures and informational measures, Coverage-credibility-based rough decision entropy

DOI: 10.3233/JIFS-239544

Journal: Journal of Intelligent & Fuzzy Systems, vol. Pre-press, no. Pre-press, pp. 1-16, 2024