Abstract
Work in fuzzy modeling has recently made its way from the interval \([0,1]\subseteq {\mathord{\rm I \! R}}\) to the ordinal or even to the qualitative level. We proceed further and introduce relational measures and relational integration. First ideas of this kind, but for the real-valued linear orderings stem from Choquet (1950s) and Sugeno (1970s). We generalize to not necessarily linear order and handle it algebraically and in a componentfree manner. We thus open this area of research for treatment with theorem provers which would be extremely difficult for the classical presentation of Choquet and Sugeno integrals.
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© 2006 Springer-Verlag Berlin Heidelberg
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Schmidt, G. (2006). Relational Measures and Integration. In: Schmidt, R.A. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2006. Lecture Notes in Computer Science, vol 4136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11828563_23
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DOI: https://doi.org/10.1007/11828563_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37873-0
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