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Keywords:
Non-Contradiction and Excluded-Middle principles; aggregation operators; strong negations
Non-Contradiction and Excluded-Middle principles; aggregation operators; strong negations
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 non-standard 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 (w.r.t.) some given strong negation, as well as for those satisfying the laws w.r.t. any strong negation. The results obtained are applied to some of the most important known classes of aggregation operators.
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