YINYANG BIPOLAR LATTICES AND L-SETS FOR BIPOLAR KNOWLEDGE FUSION, VISUALIZATION, AND DECISION
YinYang bipolar sets, bipolar lattice, bipolar L-crisp sets, and Bipolar L-fuzzy sets are presented for bipolar information/knowledge fusion, visualization, and decision. First, a bipolar lattice B is defined as a 4-tuple (B, â, &, â) in which every pair of elements has a bipolar lub (blub â), a bipolar glb (bglb &), and a cross-pole glb (cglb â). A bipolar L-set (crisp or fuzzy) B = (B-, B+) in X to a bipolar lattice BL is defined as a bipolar equilibrium function or mapping B : X â BL. A strict bipolar lattice B is defined as a 7-tuple (B, â¡, â, â, &, -, Â¬, â) that delegates a class of isomorphic bounded and complemented bipolar lattices. A refined and generalized 9-set axiomatization is presented on a class of strict bipolar lattices. The notions of bipolar L-relations and equilibrium relations are introduced as bipolar L-sets. Remarkably, YinYang bipolar L-sets lead to a bipolar universal modus ponens (BUMP) which presents a unified non-linear bipolar generalization of classical modus ponens and builds a bridge from a linear, static, and closed world to a non-linear, dynamic, and open world of equilibria, quasi-equilibria, and non-equilibria for bipolar information/knowledge fusion, visualization, and decision. A number of potential applications are outlined.
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