A full function-based calculus of directed and undirected intervals: Markov's interval arithmetic revisited (Q2387788)

The authors define an interval-type entity \[ [\underline a,\overline a]_F=\{f \mid f \text{ continuous in }[0,1],\,f([0,1])\subseteq [\underline a,\overline a]\} \] and further define related classes by requiring \(f\) to be nondecreasing/nonincreasing, \(f([0,1])=[\underline a,\overline a]\), etc., until they get a family closed under intersection on which they define arithmetic operations. They show that these generalized interval operations lead to Kaucher's interval arithmetic and Markov's directed intervals.