IDEAS home Printed from https://ideas.repec.org/a/wsi/ijitdm/v05y2006i01ns0219622006001885.html
   My bibliography  Save this article

Yinyang Bipolar Fuzzy Sets And Fuzzy Equilibrium Relations: For Clustering, Optimization, And Global Regulation

Author

Listed:
  • WEN-RAN ZHANG

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

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.

Suggested Citation

  • Wen-Ran Zhang, 2006. "Yinyang Bipolar Fuzzy Sets And Fuzzy Equilibrium Relations: For Clustering, Optimization, And Global Regulation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 19-46.
    • Handle: RePEc:wsi:ijitdm:v:05:y:2006:i:01:n:s0219622006001885
    DOI: 10.1142/S0219622006001885
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219622006001885
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219622006001885?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijitdm:v:05:y:2006:i:01:n:s0219622006001885. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijitdm/ijitdm.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.