Belief, plausibility, and probability measures on interval-valued type 2 fuzzy sets

  • Authors:

  • I. Burhan Türkşen

  • Affiliations:

  • Knowledge/Intelligence Systems Laboratory, Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, M5S 3B8 Canada

  • Venue:
  • International Journal of Intelligent Systems - Granular Computing and Data Mining
  • Year:
  • 2004

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Abstract

Belief (Bel), plausibility (Pl), and probability (P) measures can be formulated on interval-valued type 2 fuzzy sets with their representation in terms of α-level (crisp) sets. Recently, it was shown that interval-valued type 2 fuzzy sets naturally arise with modified and restricted multivalued maps of Dempster. An analogy to Dempster's upper and lower probabilities, upper and lower beliefs, and Pl and P measures can be determined over interval-valued type 2 fuzzy sets. It is shown that the application of appropriate t-norms over α-values of α-level crisp sets in combination with the axiom of Bel measure entails appropriate weights for the overlapping α-level (crisp) set conjunctions where Bel measure is applicable. © 2004 Wiley Periodicals, Inc.