有界链上拟多项式函数的公理化
Axiomatizations of quasi-polynomial functions on bounded chains
摘要：
研究了凝聚理论中的两个涌现性质，即水平极大性和共单调极大性（以及它们的对偶），它们通常由某些函数方程定义.我们完全描述的功能类公理化的每一个这些属性，到弱版本的单调性的情况下，水平极大性和minitivity。在研究由这些性质的组合公理化的类时，我们引入了拟多项式函数的概念，它是多项式函数的一个自然扩张。我们给出了进一步的公理化这一类的函数方程和自然松弛的同质性和中位数分解。作为值得注意的特殊情况，我们研究这些子类的拟项函数和拟加权最大和最小的功能，并提供相应的特征。
英文摘要：
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. While studying the classes axiomatized by combinations of these properties, we introduce the concept of quasi-polynomial function which appears as a natural extension of the well-established notion of polynomial function. We give further axiomatizations for this class both in terms of functional equations and natural relaxations of homogeneity and median decomposability. As noteworthy particular cases, we investigate those subclasses of quasi-term functions and quasi-weighted maximum and minimum functions, and provide characterizations accordingly.
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