YINYANG BIPOLAR FUZZY SETS AND FUZZY EQUILIBRIUM RELATIONS: FOR CLUSTERING, OPTIMIZATION, AND GLOBAL REGULATION

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, GA, 30460-7997, USA

International Journal of Information Technology & Decision Making (IJITDM), 2006, vol. 05, issue 01, 19-46

Abstract: Based on the notions of bipolar lattices andL-sets, YinYang bipolar fuzzy sets and fuzzy equilibrium relations are presented for bipolar clustering, optimization, and global regulation. While a bipolarL-set is defined as a bipolar equilibrium functionLthat maps a bipolar object setXover an arbitrary bipolar latticeBasL:X ⇒ B, this work focuses on the unit square latticeBF= [-1, 0] × [0, 1]. A strong or weak bipolar fuzzy equilibrium relation in a bipolar setXis then defined as a reflexive, symmetric, and bipolar interactive (or transitive) fuzzy relationμR: X ⇒ BF. Three types of bipolar α-level sets are presented for bipolar defuzzification and depolarization. It is shown that a fuzzy equilibrium relation is a non-linear bipolar generalization and/or fusion of multiple similarity relations, which induces disjoint or joint bipolar fuzzy subsets including quasi-coalition, conflict, and harmony sets. Equilibrium energy and stability analysis can then be utilized on different clusters for optimization and global regulation purposes. Thus, this work provides a unified approach to truth, fuzziness, and polarity and leads to a holistic theory for cognitive-map-based visualization, optimization, decision, global regulation, and coordination. Basic concepts are illustrated with a simulation in macroeconomics.

Keywords: Bipolar fuzzy sets; fuzzy equilibrium relations; depolarization and defuzzification; bipolar fuzzy clustering; energy and stability; bipolar optimization and global regulation; macroeconomics (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0219622006001885

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