Journal
IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS
Volume 33, Issue 2, Pages 295-307Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSMCB.2003.810444
Keywords
bipolar cognitive mapping; bipolar logic and equilibrium relations; bipolar sets and partitioning; equilibrium energy and stability; international relations; online analytical mining (OLAM); online analytical processing (OLAP); strategic decision support
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Bipolar logic, bipolar sets, and equilibrium relations are proposed for bipolar cognitive mapping and visualization in online analytical processing (OLAP) and online analytical mining (OLAM). As cognitive models,, cognitive maps (CMs) hold great potential for clustering and visualization. Due to the lack of a formal mathematical basis, however, CM-based OLAP and OLAM have not gained popularity. Compared with existing approaches, bipolar cognitive mapping has a number of advantages. First,,bipolar CMs are formal logical models as well as cognitive models. Second, equilibrium relations (with polarized reflexivity, symmetry, and transitivity), as bipolar generalizations and fusions of equivalence relations, provide a theoretical basis for bipolar visualization and coordination. Third, an equilibrium relation or CM induces bipolar partitions that distinguish disjoint coalition subsets not involved in any conflict, disjoint coalition subsets involved in a conflict, disjoint conflict subsets, and disjoint harmony subsets. Finally, equilibrium energy analysis leads to harmony and stability measures for strategic decision and multiagent coordination. Thus,this work bridges a gap for CM-based clustering and visualization, in OLAP and OLAM. Basic ideas are illustrated with example CMs in international relations.
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