Interval data

• Snehashish Chakraverty: Mathematical Methods in Interdisciplinary Sciences
• Ramon E. Moore, R. Baker Kearfott, Michael J. Cloud: Introduction to interval analysis
• Phd thesis Alves
• Wojciech Chmiel, Iwona Skalna & Stanisław Jędrusik: Intelligent route planning system based on interval computing. Multimedia Tools and Applications volume 78, pages4693–4721(2019)
• Billard

C:\Users\batagelj\Documents\papers\2020\zametki\interval.pdf

25.6.2020 Intervals on R₀⁺ form a semiring for + and x ; I guess also for min and + .

X = [x1,x2], Y = [y1,y2]

X + Y = [x1+y1, x2+y2]

X . Y = [x1.y1, x2.y2], x1,y1 >= 0

min(X,Y) = [min(x1,y1), min(x2,y2)] ? minimal paths

d1(X,Y) = |x2-y2| + |x1-y1|

d2(X,Y) = (x2-y2)² + (x1-y1)², ? center = [ave(x1), ave(x2)]

dm(X,Y) = max(|x2-y2|, |x1-y1|)