Robustness of Interval Monge Matrices in Fuzzy Algebra

Máté Hireš, Monika Molnárová and Peter Drotár
Additional contact information
Máté Hireš: Department of Computers and Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia
Monika Molnárová: Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia
Peter Drotár: Department of Computers and Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia

Mathematics, 2020, vol. 8, issue 4, 1-16

Abstract: Max–min algebra (called also fuzzy algebra) is an extremal algebra with operations maximum and minimum. In this paper, we study the robustness of Monge matrices with inexact data over max–min algebra. A matrix with inexact data (also called interval matrix) is a set of matrices given by a lower bound matrix and an upper bound matrix. An interval Monge matrix is the set of all Monge matrices from an interval matrix with Monge lower and upper bound matrices. There are two possibilities to define the robustness of an interval matrix. First, the possible robustness, if there is at least one robust matrix. Second, universal robustness, if all matrices are robust in the considered set of matrices. We found necessary and sufficient conditions for universal robustness in cases when the lower bound matrix is trivial. Moreover, we proved necessary conditions for possible robustness and equivalent conditions for universal robustness in cases where the lower bound matrix is non-trivial.

Keywords: robustness; fuzzy algebra; interval matrices; Monge matrices; inexact data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/4/652/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/4/652/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:4:p:652-:d:349766

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().