Bipolar fuzzy cognitive mapping and bipolar visualization for OLAP/OLAM

Bipolar fuzzy sets and bipolar fuzzy cognitive maps (FCMs) are introduced for online analytical processing (OLAP) and online analytical mining (OLAM). As cognitive models CMs hold great potential for visualization in OLAP and OLAM. Due to the lack of formal mathematical basis, however, CM-based OLAP and OLAM have not become popular. Compared with existing approaches, bipolar fuzzy sets and CMs have a number of advantages. First, they are formal logical as well as cognitive models. Secondly, strict bipolarity leads to the notions of fuzzy equilibrium that provides a theoretical basis for bipolar information or knowledge fusion, clustering, and coordination. Thirdly, a fuzzy equilibrium relation or FCM induces bipolar fuzzy clusters that distinguish fuzzy coalition, fuzzy conflict and fuzzy harmony subsets. Fourthly, equilibrium energy and stability analysis provides perspectives and support for strategic decision-making. Basic ideas are illustrated with FCMs in international relations.