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Summary.Two emergent properties in aggregation theory are investigated, namely horizontal maxitivity and comonotonic maxitivity (as well as their dual counterparts) which are commonly defined by means of certain functional equations. We completely describe the function classes axiomatized by each of these properties, up to weak versions of monotonicity in the cases of horizontal maxitivity and minitivity...
In [6] the authors introduced the notion of quasi-polynomial function as being a mapping f : Xn → X defined and valued on a bounded chain X and which can be factorized as $${f(x_1,\ldots,x_n)=p(\varphi(x_1),\ldots,\varphi(x_n))}$$ , where p is a polynomial function (i.e., a combination of variables and constants using the chain operations $${\wedge}$$ and $${\vee}$$ ) and $${\varphi}$$...
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