Aggregation, non-contradiction and excluded-middle. (English) Zbl 1122.68128

Summary: This paper investigates the satisfaction of the Non-Contradiction (NC) and Excluded-Middle (EM) laws within the domain of aggregation operators. It provides characterizations both for those aggregation operators that satisfy NC/EM with respect to some given strong negation, as well as for those satisfying them with respect to any strong negation. The results obtained are applied to some of the most important known classes of aggregation operators.


68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
68T27 Logic in artificial intelligence
68T37 Reasoning under uncertainty in the context of artificial intelligence
Full Text: EuDML