Partiality

Authors

Title

Status, Abstract

Gunther Schmidt

Relational Measures and Integration
.pdf .bib

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
Gunther.Schmidt@UniBw.de
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.

Authors	Title	Status, Abstract
Gunther Schmidt	Relational Measures and Integration .pdf .bib	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 Gunther.Schmidt@UniBw.de	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.