Extension of a class of decomposable measures using fuzzy pseudometrics
In this paper, we consider a topological approach to extension of t-conorm-based decomposable measures by introducing a fuzzy pseudometric structure on an algebra of sets. We prove that every non-strict continuous Archimedean t-conorm-based decomposable measure can be extended from an algebra to the completion of this algebra under the fuzzy pseudometric and then to the sigma-algebra generated by this algebra. The existence of such an extension follows very simply from the well-known Caratheodory result. However, our topological proof offers an intuitive interpretation of the extension of decomposable measures. (C) 2012 Elsevier B.V. All rights reserved.
decomposable measures non-additive measures fuzzy metric space t-norm t-conorm