Smooth associative operations on finite ordinal scales
Janos C. Fodor · IEEE Transactions on Fuzzy Systems · 2000
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.