Aggregation operators from the ancient NC and EM point of view. (English) Zbl 1249.03101

Summary: This paper deals with the satisfaction of the well-known non-contradiction (NC) and excluded-middle (EM) principles within the framework of aggregation operators. Both principles are interpreted in a nonstandard way based on self-contradiction (as in ancient logic) instead of falsity (as in modern logic). The logical negation is represented by means of strong negation functions, and conditions are given both for those aggregation operators that satisfy NC/EM with respect to some given strong negation, as well as for those satisfying the laws with respect to any strong negation. The results obtained are applied to some of the most important known classes of aggregation operators.


03E72 Theory of fuzzy sets, etc.
03B52 Fuzzy logic; logic of vagueness
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