{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T13:09:41Z","timestamp":1773148181727,"version":"3.50.1"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Info. Tech. Dec. Mak."],"published-print":{"date-parts":[[2006,3]]},"abstract":"<jats:p> Based on the notions of bipolar lattices and L-sets, YinYang bipolar fuzzy sets and fuzzy equilibrium relations are presented for bipolar clustering, optimization, and global regulation. While a bipolar L-set is defined as a bipolar equilibrium function L that maps a bipolar object set X over an arbitrary bipolar lattice B as L:X \u21d2 B, this work focuses on the unit square lattice B<jats:sub> F <\/jats:sub> = [-1, 0] \u00d7 [0, 1]. A strong or weak bipolar fuzzy equilibrium relation in a bipolar set X is then defined as a reflexive, symmetric, and bipolar interactive (or transitive) fuzzy relation \u03bc<jats:sub>R<\/jats:sub>: X \u21d2 B<jats:sub> F <\/jats:sub>. Three types of bipolar \u03b1-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. <\/jats:p>","DOI":"10.1142\/s0219622006001885","type":"journal-article","created":{"date-parts":[[2006,4,12]],"date-time":"2006-04-12T06:54:58Z","timestamp":1144824898000},"page":"19-46","source":"Crossref","is-referenced-by-count":39,"title":["YINYANG BIPOLAR FUZZY SETS AND FUZZY EQUILIBRIUM RELATIONS: FOR CLUSTERING, OPTIMIZATION, AND GLOBAL REGULATION"],"prefix":"10.1142","volume":"05","author":[{"given":"WEN-RAN","family":"ZHANG","sequence":"first","affiliation":[{"name":"Department of Computer Science, College of Information Technology, Georgia Southern University, P.O. Box 7997, Statesboro, GA, 30460-7997, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"295","volume":"33","author":"Zhang W.","journal-title":"IEEE Trans. SMC, Part B"},{"key":"rf2","first-page":"241","volume":"9","author":"Zhang W.","journal-title":"Int. J. 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D.\u00a0Belnap, Modern Uses of Multiple-Valued Logic, eds. G.\u00a0Epstein and J. M.\u00a0Dunn (Reidel, Dardrecht, 1997)\u00a0pp. 8\u201337."},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/1.1.41"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(71)80005-1"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1145\/321105.321107"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1111\/j.1936-4490.1997.tb00117.x"}],"container-title":["International Journal of Information Technology &amp; Decision Making"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219622006001885","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:02:40Z","timestamp":1565118160000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219622006001885"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3]]},"references-count":17,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,3]]}},"alternative-id":["10.1142\/S0219622006001885"],"URL":"https:\/\/doi.org\/10.1142\/s0219622006001885","relation":{},"ISSN":["0219-6220","1793-6845"],"issn-type":[{"value":"0219-6220","type":"print"},{"value":"1793-6845","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,3]]}}}