Relational measures and integration

  • Authors:

  • Gunther Schmidt

  • Affiliations:

  • Institute for Software Technology, Department of Computing Science, Universität der Bundeswehr München, Neubiberg, Germany

  • Venue:
  • RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
  • Year:
  • 2006

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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.