A fuzzy ordering on multi-dimensional fuzzy sets induced from convex cones

  • Authors:
  • Yuji Yoshida;Etienne E. Kerre

  • Affiliations:
  • Faculty of Economics and Business Administration, the University of Kitakyushu, 4-2-1 Kitagata, Kokuraminami, Kitakyushu 802-8577, Japan;Department of Applied Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling, Krijgslaan 281 (S9), B-9000 Gent, Belgium

  • Venue:
  • Fuzzy Sets and Systems - Fuzzy intervals
  • Year:
  • 2002

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Abstract

A fuzzy ordering for fuzzy sets on Rn is presented by a fuzzy relation on Rn × Rn which is induced by closed convex cones. The suitability of the fuzzy order is discussed using the axioms A1-A7 in (Fuzzy Sets and Systems 118 (2001) 375). For fuzzy sets on Rn which are incomparable with respect to the fuzzy order, a method to evaluate the degree of satisfaction regarding the fuzzy order is presented by using a subsethood degree. Approximation by discrete cases is discussed for numerical calculation on the degree of the fuzzy order. Numerical examples are also given to illustrate our idea.