, Volume 15, Issue 2, pp 433–469

Integrals of random fuzzy sets


DOI: 10.1007/BF02607061

Cite this article as:
Krätschmer, V. Test (2006) 15: 433. doi:10.1007/BF02607061


This paper tries to give a systematic investigation of integration of random fuzzy sets. Besides the widely used Aumann-integral adaptions of Pettis- and Bochner-integration for random elements in Banach spaces are introduced. The mutual relationships of these competing concepts will be explored comprehensively, completing and improving former results from literature. As a by product dominated convergence theorems, strong laws of large numbers and central limit theorems for random fuzzy sets can be derived. They are based on weaker assumptions than previous versions from literature.

Key Words

Random fuzzy setsintegrably bounded random fuzzy setsAumann-integralPettis-integralBochner-integraldominated convergence theoremsstrong law of large numberscentral limit theorems

AMS subject classification

Primary 60D05Secondary 60F15

Copyright information

© Sociedad Española de Estadistica e Investigacion Operativa 2006

Authors and Affiliations

  1. 1.Statistics and Econometrics, Faculty of Law and EconomicsUniversity of SaarlandGermany