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Smooth associative operations on finite ordinal scales

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1 Author(s)
Fodor, J. ; Dept. of Biomath. & Inf., Szent Istvan Univ., Budapest, Hungary

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

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Fuzzy Systems, IEEE Transactions on  (Volume:8 ,  Issue: 6 )