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Article
Bipolar Fuzzy Sets
IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (1998)
  • Wen-Ran Zhang, Georgia Southern University
Abstract
A bipolar fuzzy set theory has been introduced for bipolar reasoning in the space. Two types of bipolar α-level cut have been proposed. Resolutions of the two types of level sets were examined and the relationships were established. The bipolar fuzzy set theory combines polarity and fuzziness into unified model and provides a theoretical basis for bipolar clustering, decision analysis, and coordination. Based on bipolar crisp and fuzzy relations, crisp and fuzzy equilibrium relations can be defined as a bipolar reflexive, symmetric, and transitive crisp or fuzzy bipolar relation. While equivalence relations induce fuzzy clusters, equilibrium relations lead to coalition, conflict, harmony, and neutral crisp or fuzzy sets.
Keywords
  • Bipolar fuzzy sets,
  • Bipolar reasoning,
  • Equivalence relations,
  • Equilibrium relations
Disciplines
Publication Date
December, 1998
Citation Information
Wen-Ran Zhang. "Bipolar Fuzzy Sets" IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (1998) p. 835 - 840
Available at: http://works.bepress.com/wen-ran_zhang/14/