Aggregation functions are precisely the lax morphisms of quantales, supplying a unified framework that deduces prior results on metric and fuzzy metric aggregation.
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Strongly quasi-pseudometric aggregation functions are characterized by continuity at zero plus minimal zero preimage for products and by supremum topology conditions for fixed sets.
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Aggregation functions as lax morphisms of quantales
Aggregation functions are precisely the lax morphisms of quantales, supplying a unified framework that deduces prior results on metric and fuzzy metric aggregation.
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Strongly quasi-pseudometric aggregation functions
Strongly quasi-pseudometric aggregation functions are characterized by continuity at zero plus minimal zero preimage for products and by supremum topology conditions for fixed sets.