Algebraic Product is the Only t-Norm for Which Optimization Under Fuzzy Constraints is Scale-Invariant

Authors

Juan Carlos Figueroa Garcia, Universidad DistritalFollow
Martine Ceberio, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

10-2013

Comments

Technical Report: UTEP-CS-13-50

Published in Proceedings of the Sixth International Workshop on Constraints Programming and Decision Making CoProd'2013, El Paso, Texas, November 1, 2013, pp. 8-11.

Abstract

In many practical situations, we need to optimize under fuzzy constraints. There is a known Bellman-Zadeh approach for solving such problems, but the resulting solution, in general, depends on the choice of a not well-defined constant M. We show that this dependence disappears if we use an algebraic t-norm (and-operation) a * b, and we also prove that the algebraic product is the only t-norm for which the corresponding solution is independent on M.