An intuitive notion of smoothness introduced by Godo et al. (1988) on finite chains is investigated and formulated in a more useful mathematical way. By the help of this equivalent form, which is the intermediate-value theorem, we completely characterize a class of smooth associative, increasing binary operations on a chain that also satisfy weak boundary conditions. Some important subclasses of such operations are also described.
No takes yet. Share an insight, caveat, or question.
Janos C. Fodor (2000) studied this question.