The construction of consistent possibility and necessity measures

  • Authors:

  • K. David Jamison;Weldon A. Lodwick

  • Affiliations:

  • Watson Wyatt & Company, 950 17th Street, Suite 1400, Denver, CO;Watson Wyatt & Company, 950 17th Street, Suite 1400, Denver, CO and Department of Mathematics, Campus Box 170, University of Colorado, P.O. Box 173364, Denver, CO

  • Venue:
  • Fuzzy Sets and Systems - Possibility theory and fuzzy logic
  • Year:
  • 2002

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Abstract

Given a general measure µ (finite or infinite), we develop possibility and necessity measures as upper and lower estimators of µ. We provide a method for constructing such fuzzy measures and show that the measure can be approximated with arbitrary closeness using fuzzy measures constructed this way. Using the extension principle, these consistent possibility and necessity measures are used to produce possibility and necessity measures on the range space of a measurable function which are consistent with the measure on the range space induced by the measurable function. This induced measure can be approximated with arbitrary closeness by extending consistent possibility and necessity measures constructed on the domain space.