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Cycle-free cuts of mutual rank probability relations

Karel De Loof; Bernard De Baets; Hans De Meyer — 2014

Kybernetika

It is well known that the linear extension majority (LEM) relation of a poset of size $n \geq 9$ can contain cycles. In this paper we are interested in obtaining minimum cutting levels $α_{m}$ such that the crisp relation obtained from the mutual rank probability relation by setting to $0$ its elements smaller than or equal to $α_{m}$ , and to $1$ its other elements, is free from cycles of length $m$ . In a first part, theoretical upper bounds for $α_{m}$ are derived using known transitivity properties of the mutual rank probability...

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