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Transitive decomposition of fuzzy preference relations: the case of nilpotent minimum

Susana Díaz, Susana Montes, Bernard De Baets (2004)

Kybernetika

Transitivity is a fundamental notion in preference modelling. In this work we study this property in the framework of additive fuzzy preference structures. In particular, we depart from a large preference relation that is transitive w.r.t. the nilpotent minimum t-norm and decompose it into an indifference and strict preference relation by means of generators based on t-norms, i. e. using a Frank t-norm as indifference generator. We identify the strongest type of transitivity these indifference and...

Transitivity and partial order

Jiří Klaška (1997)

Mathematica Bohemica

In this paper we find a one-to-one correspondence between transitive relations and partial orders. On the basis of this correspondence we deduce the recurrence formula for enumeration of their numbers. We also determine the number of all transitive relations on an arbitrary n -element set up to n = 14 .

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