Solvability of a Bounded Parametric System in Max-?ukasiewicz Algebra

Martin Gavalec and Zuzana Němcová
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Martin Gavalec: Faculty of Informatics and Management, University of Hradec Králové, 50003 Hradec Králové, Czech Republic
Zuzana Němcová: Faculty of Informatics and Management, University of Hradec Králové, 50003 Hradec Králové, Czech Republic

Mathematics, 2020, vol. 8, issue 6, 1-16

Abstract: The max-?ukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the ?ukasiewicz 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 correctness of the algorithm has been verified. The presented polynomial algorithm consists of three parts depending on the entries of the transition matrix and the required state vector. The results are illustrated by numerical examples. The presented results can be also applied in the study of the max-?ukasiewicz systems with interval coefficients. Furthermore, ?ukasiewicz arithmetical conjunction can be used in various types of models, for example, in cash-flow system.

Keywords: max-min algebra; fuzzy max-T algebra; ?ukasiewicz triangular norm; max-?ukasiewicz algebra; parametric solvability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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