Three-Way Decision Based on Three-Way Preference Measures and Three-Level Dominance Relations in Interval-Valued Systems

Three-way decision (3WD) is a cognitive methodology for decision making, and it becomes valuable for interval-valued systems. For this topic, preference measures and dominance relations between intervals act as two pivotal factors, but their existing results (including the recent D-type measure and partial-overall relation) still have advancement space. In interval-valued systems, an S-type measure is proposed to constitute three-way preference measures, while three-level dominance relations are established, so a criss-cross network of knowledge granulations emerges to motivate systematic 3WD methods. At first, the S-type preference measure is proposed by using the sigmoid function, it exhibits good learning semantics and mathematical properties, and its supplement and improvement lead to formulate three-way preference measures for applications. 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 are utilized to construct three-level dominance relations, and thus vertical-horizontal condition granulations appear to generate multiple 3WD models on preference decision classes. Finally, all 3WD strategies based on criss-cross dominance relations are comprehensively compared and selected via classification error rates; as validated by data experiments, the S-type measure and its hierarchical relations become effective and optimal for 3WD, and the new 3WD approaches outperform the existing ways based on the D-type measure and partial-overall relation. This study systematically makes a serial improvement of preference measures and a hierarchical construction of dominance relations, so it optimally promotes 3WD applications in terms of interval-valued systems.