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Domination of aggregation operators and preservation of transitivity. (English) Zbl 1053.03514

Summary: Aggregation processes are fundamental in any discipline where the fusion of information is of vital interest. For aggregating binary fuzzy relations such as equivalence relations or fuzzy orderings, the question arises which aggregation operators preserve specific properties of the underlying relations, e.g., \(T\)-transitivity. It is shown that preservation of \(T\)-transitivity is closely related to the domination of the applied aggregation operator over the corresponding t-norm \(T\). Furthermore, basic properties for dominating aggregation operators, not only in the case of dominating some t-norm \(T\), but dominating some arbitrary aggregation operator, are presented. Domination of isomorphic t-norms and ordinal sums of t-norms are treated. Special attention is paid to the four basic t-norms (minimum t-norm, product t-norm, Łukasiewicz t-norm, and the drastic product).

MSC:

03E72 Theory of fuzzy sets, etc.
68T37 Reasoning under uncertainty in the context of artificial intelligence
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