YINYANG BIPOLAR LATTICES ANDL-SETS FOR BIPOLAR KNOWLEDGE FUSION, VISUALIZATION, AND DECISION

Wen-Ran Zhang ()
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Wen-Ran Zhang: Department of Computer Science, College of Information Technology, Georgia Southern University, P. O. Box 7997, Statesboro, Georgia 30460-7997, USA

International Journal of Information Technology & Decision Making (IJITDM), 2005, vol. 04, issue 04, 621-645

Abstract: YinYang bipolar sets, bipolar lattice, bipolarL-crisp sets, and BipolarL-fuzzy sets are presented for bipolar information/knowledge fusion, visualization, and decision. First, a bipolar latticeBis defined as a 4-tuple(B, ⊕, &, ⊗)in which every pair of elements has a bipolar lub (blub ⊕), a bipolar glb (bglb &), and a cross-pole glb (cglb ⊗). A bipolarL-set (crisp or fuzzy)B = (B-, B+)inXto a bipolar latticeBLis defined as a bipolar equilibrium function or mappingB : X ⇒ BL. A strict bipolar latticeBis defined as a 7-tuple(B, ≡, ⊕, ⊗, &, -, ¬, ⇒)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 bipolarL-relations and equilibrium relations are introduced as bipolarL-sets. Remarkably, YinYang bipolarL-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.

Keywords: YinYang Bipolar Equilibria; bipolar lattice; bipolarL-crisp sets; bipolarL-fuzzy sets; Bipolar Dynamic Modus Ponens (BDMP); Bipolar Universal Modus Ponens (BUMP); BipolarL-relations; BipolarL-equilibrium relations; Information/knowledge fusion; Visualization; decision and coordination (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219622005001763

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