Murofushi, Toshiaki A note on upper and lower Sugeno integrals. (English) Zbl 1094.28012 Fuzzy Sets Syst. 138, No. 3, 551-558 (2003). The Sugeno integral for functions measurable with respect to a paving \({\mathcal A}\) (system of subsets of a universe \(X\) containing the empty set) and fuzzy measures on \({\mathcal A}\) (monotone \({\mathcal A}\to [0,1]\) set functions vanishing at the empty set) is introduced and discussed, and extended for arbitrary \(X\to [0,1]\) functions in two ways: as an upper and a lower Sugeno integral (compared with the standard extensions to an upper and a lower measure in the classical measure theory). Some properties are discussed and illustrated by an example. Reviewer: Radko Mesiar (Bratislava) Cited in 1 Document MSC: 28E10 Fuzzy measure theory 06F30 Ordered topological structures Keywords:fuzzy measures; Sugeno integral PDFBibTeX XMLCite \textit{T. Murofushi}, Fuzzy Sets Syst. 138, No. 3, 551--558 (2003; Zbl 1094.28012) Full Text: DOI References: [1] Denneberg, D., Non-Additive Measure and Integral (1997), Kluwer: Kluwer Dordrecht [2] Kandel, A.; Byatt, W. J., Fuzzy sets, fuzzy algebra, and fuzzy statistics, Proc. IEEE, 66, 1619-1639 (1978) [3] Murofushi, T.; Sugeno, M., A theory of fuzzy measurerepresentation, the Choquet integral and null sets, J. Math. Anal. Appl., 159, 532-549 (1991) · Zbl 0735.28015 [4] M. Sugeno, Theory of fuzzy integrals and its applications, Doctoral Thesis, Tokyo Institute of Technology, 1974.; M. Sugeno, Theory of fuzzy integrals and its applications, Doctoral Thesis, Tokyo Institute of Technology, 1974. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.