Siswanto; Suparwanto, Ari; Rudhito, M. Andy Strongly regular matrices and simple image set in interval max-plus algebra. (English) Zbl 1408.15011 JP J. Algebra Number Theory Appl. 38, No. 1, 63-78 (2016). Summary: Suppose that \(\mathbb R\) is the set of real numbers and \(\mathbb R_{\varepsilon} = \mathbb R \cup \{\varepsilon \}\) with \(\varepsilon = -\infty\) Max-plus algebra is the set \(\mathbb R_{\varepsilon}\) that is equipped with two operations, maximum and addition. Matrices over max-plus algebra are matrices whose elements belong to \(\mathbb R_{\varepsilon}\). The set \(I(\mathbb R)_{\varepsilon} = \{ x= [\underline x, \bar x] \underline x, \bar x \in \mathbb R, \varepsilon < \underline x \leq \bar x \} \cup \{\varepsilon\}\) with \(\varepsilon = [\varepsilon,\varepsilon]\) is equipped with maximum and addition operations is known as interval max-plus algebra. Matrices over interval max-plus algebra are matrices whose elements belong to \(I(\mathbb R_{\varepsilon})\). The research about image set, strongly regular matrix and simple image set in max-plus algebra have been done. In this paper, we investigate image set, strongly regular matrix and simple image set in interval max-plus algebra. Cited in 1 Document MSC: 15A80 Max-plus and related algebras 15A15 Determinants, permanents, traces, other special matrix functions 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 15A30 Algebraic systems of matrices Keywords:image set; strongly regular matrix; simple image set PDFBibTeX XMLCite \textit{Siswanto} et al., JP J. Algebra Number Theory Appl. 38, No. 1, 63--78 (2016; Zbl 1408.15011) Full Text: DOI Link