Weakly linear independent and Gondran-Minoux in semiring interval min-plus
Izmah Ashfayel Hikmah, Siswanto Siswanto Β· AIP conference proceedings Β· 2024
In linear algebra it is known semiring min-plus or β πππ = β βͺ {+β}, with β is the set of all real numbers with the minimum operation (β') and the addition operation (β).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.Interval min-plus algebra is the set πΌ(π ) πππ = {π₯ = [ π₯, π₯ ]| π₯ β β πππ | π₯ β€ π₯ β€ π₯}.Research related to min-plus algebra and its application has been developed by several researchers, but for its definition of dependent linear and independent linear still no one has researched it.The purpose of this research is to determine the concept of weakly linear dependent and weakly linear independent, linear dependent in Gondran-Minoux and linear independent in Gondran-Minoux, and the comparison between them in the semiring interval min-plus.Based on Rosenmann's research, max-plus algebra and minplus algebra are isomorphic.By using the appropriate analogy in the semiring interval max-plus, we will define the concepts of weakly linear independent, weakly linear dependent, linear dependent, and independent Gondran-Minoux in the semiring interval min-plus.