Three-way decision based on three-way preference measures and three-level dominance relations in interval-valued systems

Abstract

Interval-valued systems facilitate data decision, and their preference measures and dominance relations become pivotal for three-way decision (3WD). However, the recent D-type preference measure and partial-overall dominance relation between intervals respectively exhibit the weak representation and incomplete hierarchy, so corresponding results need further development. Aiming at interval-valued systems, an S-type measure is proposed to constitute three-way preference measures, and three-level dominance relations are established, so criss-cross knowledge granulations motivate systematic 3WD models and applications. First, the S-type preference measure is proposed from the sigmoid function, it exhibits good learning semantics and mathematical properties, and its supplementation and improvement induce three-way preference measures. Then, by three-level constructions, three-way preference measures are applied for sorting and classification, and the S-type measure exhibits decision effectiveness and recognition superiority. Furthermore, hierarchical three-way preference measures induce three-level dominance relations, and vertical-horizontal condition granulations generate multiple 3WD models on preference decision classes. Finally, all 3WD strategies from criss-cross dominance relations are comprehensively compared and selected via classification error rates; by data experiments, the S-type measure and its hierarchical relations become effective and optimal for 3WD, and the corresponding 3WD approaches outperform the existing methods from the D-type measure and partial-overall relation.