Elsevier

Fuzzy Sets and Systems

Volume 5, Issue 1, January 1981, Pages 83-107
Fuzzy Sets and Systems

Representation theorems for L-fuzzy quantities

https://doi.org/10.1016/0165-0114(81)90035-XGet rights and content

Abstract

In this paper representation theorems are given for L-fuzzy quantities, which permit a better understanding of fuzziness. In particular representation theorems due to Negoita and Ralescu [17] and to Sherwood and Taylor [23] are extended to the scope of complete and Brouwerian lattices.

References (28)

  • G. Grätzer

    Lattice Theory

    (1971)
  • P.R. Halmos

    Measure Theory

    (1950)
  • U. Höhle

    Stochastische Topologien als Wahrscheinlichkeitsmaße auf Potenzmengen

    Dissertation Karlsruhe

    (1973)
  • D.A. Kappos

    Probability algebras and stochastic spaces

    (1969)
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