Status, Abstract

Gunther Schmidt

Relational Measures and Integration

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Proc. of the International Workshop RelMiCS '9

Relational Methods in Computer Science

combined with the 4th Internat. Workshop on Applications of Kleene Algebra

Revised Selected Papers, edited by Renate A. Schmidt

Lecture Notes in Computer Science

vol. 4136, (2006), 343--357

Later substantially extended together with Rudolf Berghammer and accepted as

Relational Measures and Integration in Preference Modeling

for a Special Issue of the Journal of Logic and Algebraic Programming

Department of Computing Science
Universität der Bundeswehr München
85577 Neubiberg, Germany

August 2006
Work in fuzzy modeling has recently made its way from the interval [0,1] of real numbers 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 pointfree 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.