Abstract
In this paper we provide a full characterization of functions G:[0,y¯]2→[0,y¯] satisfying the distributivity equation G(a∘b,a∘c)=a∘G(b,c) for any a,b,c with a fixed binary operation ∘:[0,y¯]2→[0,y¯] generalizing minimum and maximum, where y¯∈(0,∞]. The above functional equation with an admissible function G and ∘ being minimum [resp. maximum] has appeared when studying properties of minitive [resp. maxitive] homogeneity for the recently introduced upper n-Sugeno integral.
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