Equivalent conditions for laws of large numbers for T-related L-R fuzzy numbers

  • Authors:

  • Dug Hun Hong;Chul H. Ahn

  • Affiliations:

  • School of Mechanical and Automotive Engineering, Catholic University of Daegu, 330 Keumrak 1-ri Hayang-up, Kyongsan, Kyungbuk 712-702, South Korea and Department of Applied Mathematics, Sejong Uni ...;School of Mechanical and Automotive Engineering, Catholic University of Daegu, 330 Keumrak 1-ri Hayang-up, Kyongsan, Kyungbuk 712-702, South Korea and Department of Applied Mathematics, Sejong Uni ...

  • Venue:
  • Fuzzy Sets and Systems - Theme: Basic concepts
  • Year:
  • 2003

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Abstract

In this paper, we give some necessary and sufficient conditions for laws of large numbers for sequence of mutually T-related L-R fuzzy numbers when T is an continuous Archimedean t-norm and diameter of support of the fuzzy numbers is not uniformly bounded. We also consider some necessary and sufficient conditions for laws of large numbers for L-R fuzzy random numbers, and generalize earlier results of Fullér (Fuzzy Sets and Systems 45 (1992) 299-303), Triesch (Fuzzy Sets and Systems 58 (1993) 339-342) and Hong and Lee (Fuzzy Sets and Systems 121 (2001) 537-543).