Ordinal sums of aggregation operators. (English) Zbl 1015.68194

De Baets, Bernard; Mesiar, Radko

Bouchon-Meunier, Bernadette (ed.) et al., Technologies for constructing intelligent systems. 2: Tools. Heidelberg: Physica-Verlag. Stud. Fuzziness Soft Comput. 90, 137-147 (2002).

Summary: In this work, aggregation operators are to be understood in their most general sense, i.e. as families of operators, one for each arity. We characterize the smallest and greatest aggregation operators with a predefined behaviour in case all arguments are taken from the same interval (belonging to a system of pairwise disjoint open intervals). Similarly, we characterize the smallest and greatest idempotent aggregation operators with a predefined idempotent behaviour. Relationships with classical ordinal sum constructions are investigated.
For the entire collection see [Zbl 0980.00013].

MSC:

68T35	Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
68U35	Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.)

Keywords:

aggregation operators