Self-dual types of cycle-transitivity

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.

• Type: Conference
• Year: 2003
• Where: EUSFLAT
• Authors: Bernard De Baets, Hans De Meyer, Bart De Schuymer
• Keywords: EUSFLAT 2003, EUSFLAT 2007, Reciprocal Relations, Stochastic Transitivity Corresponds, Upper Bound Functions