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Yinyang Bipolar Lattices Andl-Sets For Bipolar Knowledge Fusion, Visualization, And Decision

Author

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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)

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.

Suggested Citation

  • Wen-Ran Zhang, 2005. "Yinyang Bipolar Lattices Andl-Sets For Bipolar Knowledge Fusion, Visualization, And Decision," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 621-645.
    • Handle: RePEc:wsi:ijitdm:v:04:y:2005:i:04:n:s0219622005001763
    DOI: 10.1142/S0219622005001763
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    Cited by:

    1. Wen-Ran Zhang & Karl E. Peace & Hyo-Joo Han, 2016. "YinYang bipolar dynamic organizational modeling for equilibrium-based decision analysis: Logical transformation of an indigenous philosophy to a global science," Asia Pacific Journal of Management, Springer, vol. 33(3), pages 723-766, September.

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