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Ordinal Sums In Interval-Valued Fuzzy Set Theory

Author

Listed:
  • GLAD DESCHRIJVER

    (Department of Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling Research Unit, Krijgslaan 281 (S9), B-9000 Gent, Belgium)

Abstract

Interval-valued fuzzy sets form an extension of fuzzy sets which assign to each element of the universe a closed subinterval of the unit interval. This interval approximates the "real", but unknown, membership degree. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. A method for constructing t-norms that satisfy the residuation principle is by using the ordinal sum theorem. In this paper, we construct the ordinal sum of t-norms on$\mathcal{L}^I$, where$\mathcal{L}^I$is the underlying lattice of interval-valued fuzzy set theory, in such a way that if the summands satisfy the residuation principle, then the ordinal sum does too.

Suggested Citation

  • Glad Deschrijver, 2005. "Ordinal Sums In Interval-Valued Fuzzy Set Theory," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 1(02), pages 243-259.
    • Handle: RePEc:wsi:nmncxx:v:01:y:2005:i:02:n:s1793005705000172
    DOI: 10.1142/S1793005705000172
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