Double-quantitative fusion of accuracy and importance: Systematic measure mining, benign integration construction, hierarchical attribute reduction

• IP-Accuracy is mined by systematic double-quantitative fusion of causality measures.
• IP-Accuracy GrC integration is constructed to gain benign granulation monotonicity.
• IP-Accuracy attribute reduction is studied to establish a hierarchical reduct system.

Uncertainty measure mining and applications are fundamental, and it is possible for double-quantitative fusion to acquire benign measures via heterogeneity and complementarity. This paper investigates the double-quantitative fusion of relative accuracy and absolute importance to provide systematic measure mining, benign integration construction, and hierarchical attribute reduction. (1) First, three-way probabilities and measures are analyzed. Thus, the accuracy and importance are systematically extracted, and both are further fused into importance-accuracy (IP-Accuracy), a synthetic causality measure. (2) By sum integration, IP-Accuracy gains a bottom-top granulation construction and granular hierarchical structure. IP-Accuracy holds benign granulation monotonicity at both the knowledge concept and classification levels. (3) IP-Accuracy attribute reduction is explored based on decision tables. A hierarchical reduct system is thereby established, including qualitative/quantitative reducts, tolerant/approximate reducts, reduct hierarchies, and heuristic algorithms. Herein, the innovative tolerant and approximate reducts quantitatively approach/expand/weaken the ideal qualitative reduct. (4) Finally, a decision table example is provided for illustration. This paper performs double-quantitative fusion of causality measures to systematically mine IP-Accuracy, and this measure benignly constructs a granular computing platform and hierarchical reduct system. By resorting to a monotonous uncertainty measure, this study provides an integration-evolution strategy of granular construction for attribute reduction.