| Biometrics and Process Control, (2009) | |||||||||||||
Abstract | |||||||||||||
| A general framework for studying the transitivity of reciprocal relations is presented. The key feature is the cyclic evaluation of transitivity: triangles (i.e. any three points) are visited in a cyclic manner. An upper bound function acting upon the ordered weights encountered provides an upper bound for the ‘sum minus 1 ’ of these weights. Commutative quasi-copulas allow to translate a general definition of fuzzy transitivity (when applied to reciprocal relations) elegantly into the framework of cycletransitivity. Similarly, a general notion of stochastic transitivity corresponds to a particular class of upper bound functions. Special attention is given to selfdual upper bound functions. Keywords: Cycle-transitivity, reciprocal relations, self-dual upper bound function, t-conorm. 1 | |||||||||||||
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