YIN YANG EQUILIBRIUM RELATIONS ―A MATHEMATICAL MODEL FOR BIPOLAR PARTITIONING AND COORDINATION

摘要

This work generalizes classical binary relations to (yin yang) bipolar relations, classical equivalence relations to bipolar equilibrium relations, and classical unipolar sets to bipolar sets which consists of coalition sets, conflict sets, and harmony sets. A relational strength in a bipolar relation consists of both a negative pole and a positive pole. A number of theorems are proved that build analytical bridges from equilibrium (bipolar) relations back to equivalence relations. These theorems provide an analytical basis for bipolar partitioning. A bipolar partitioning algorithm is presented which can identify disjoint coalition subsets not involved in a conflict, disjoint coalition subsets involved in a conflict, disjoint conflict subsets, and disjoint harmony subsets from the set X. Thus, equilibrium relations provide a unique structure for bipolar data and knowledge fusion, bipolar clustering, conflict resolution, and multiagent coordination.