Extension of a class of decomposable measures using fuzzy pseudometrics

Authors:
Dong Qiu;Weiquan Zhang;Cheng Li
Affiliations:
College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Nanan, Chongqing 400065, PR China;School of Information Engineering, Guangdong Medical College, Dongguan, Guangdong 523808, PR China;School of Mathematics, Shandong University, Jinan, Shandong 250100, PR China
Venue:
Fuzzy Sets and Systems
Year:
2013

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Abstract

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.