Transitive fuzzy orderings of fuzzy numbers (Q1121927)

In this well-organized paper a generalization of the Baas-Kwakernaak index [\textit{S. M. Baas} and \textit{H. Kwakernaak}, Automatica 13, 47-58 (1977; Zbl 0363.90010)] is presented by replacing the min operation in their definition by a t-norm. Essential properties of the thus defined induced fuzzy ordering are established. Moreover, it is shown that there are classes of fuzzy numbers such that this index defines transitive fuzzy ordering of fuzzy numbers in these classes. The obtained results are illustrated by examples.