Smooth associative operations on finite ordinal scales

Authors:
J. Fodor
Affiliations:
Dept. of Biomath. & Inf., Szent Istvan Univ., Budapest
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2000

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Abstract

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