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Article

Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra

Faculty of Informatics and Management, University of Hradec Králové, 50003 Hradec Králové, Czech Republic
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Mathematics 2020, 8(6), 1026; https://doi.org/10.3390/math8061026
Received: 26 April 2020 / Revised: 14 June 2020 / Accepted: 19 June 2020 / Published: 23 June 2020
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2020)
The max-Łukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the Łukasiewicz 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-Łukasiewicz systems with interval coefficients. Furthermore, Łukasiewicz arithmetical conjunction can be used in various types of models, for example, in cash-flow system. View Full-Text
Keywords: max-min algebra; fuzzy max-T algebra; Łukasiewicz triangular norm; max-Łukasiewicz algebra; parametric solvability max-min algebra; fuzzy max-T algebra; Łukasiewicz triangular norm; max-Łukasiewicz algebra; parametric solvability
MDPI and ACS Style

Gavalec, M.; Němcová, Z. Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra. Mathematics 2020, 8, 1026. https://doi.org/10.3390/math8061026

AMA Style

Gavalec M, Němcová Z. Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra. Mathematics. 2020; 8(6):1026. https://doi.org/10.3390/math8061026

Chicago/Turabian Style

Gavalec, Martin; Němcová, Zuzana. 2020. "Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra" Mathematics 8, no. 6: 1026. https://doi.org/10.3390/math8061026

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