Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra

Abstract

The max-Lukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the Lukasiewicz triangular norm. The behavior of such a system in time depends on the solvability of the corresponding bounded parametric max-linear system. The aim of this study is to describe an algorithm recognizing for which values of the parameter the given bounded parametric max-linear system has a solution---represented by an appropriate state of the fuzzy system in consideration. Necessary and sufficient conditions of the solvability have been found and a polynomial recognition algorithm has been described. The results are illustrated by numerical examples. The presented results can be also applied in the study of the max-Lukasiewicz systems with interval coefficients.