Weakly Linear Independent and Gondran-Minoux in Semiring Min-plus Interval
Izmah Ashfayel Hikmah

Department of Mathematics, Faculty of Mathematics and Natural Science, University of Sebelas Maret Surakarta, Indonesia

Abstract

In linear algebra it is known semiring min-plus or R_min, with R is the set of all real numbers with the minimum operation and the addition operation. Research related to min-plus algebra and its application has been developed by several researchers. The development of min-plus algebra, is also known as interval min-plus algebra. The purpose of this research is to determine the concept of linearly dependent and weakly linear independent, Gondran-Minoux, tropical, and the relationship between them in the semiring min-plus interval. Based on Rosenmann^s research, max-plus algebra and min-plus algebra are isomorphic. Using the appropriate analogy in the semiring max-plus interval we will define the concepts of Gondran-Minoux linear independent and tropical linear independent in the semiring min-plus interval. The results show that if a set of P is tropical linearly independent, then P also linearly independent in Gondran-Minoux, if a set P is linearly independent in Gondran-Minoux, then P is also weakly linearly independent, and if a set P is tropically independent, then P is also weakly linearly independent.

Keywords: Min-plus interval algebra- linear freedom- Gondran-Minoux- tropical

Topic: Mathematics