In this paper we introduce the notion of conditional monotonicity and from it the concepts of conditional monotonicity given a vector of degenerated intervals and conditional monotonicity given a constant vector of functions to the setting of intervals endowed with admissible orders. This work is a step after the contribution of Sesma-Sara et al., where these monotonicities were introduced in terms of the (non linear partial) \textit{Kulisch-Miranker order}. Besides, whereas Sesma-Sara et. al defined weak/directional monotonicities by using points in euclidean plane, we use just intevals. The paper also proposes the notions of conditional monotonicity with respect to a function $ G $ and a parameter $\Lambda$ for intervals -- the interval counter-part of $g$-monotonicity proposed by Santiago et. al in 2021 -- and pre-aggregations IV-functions. The paper shows some properties, how some interval implications behave with respect to such new monotonicities and the relationships between abstract homogeneity and these notions. keywords: Interval Valued Functions; Admissible orders; Conditional monotonicity; Weak/Directional/G-weak monotonicity; Pre-aggregation functions; Abstract homogeneity.
翻译:在本文中,我们引入了条件单一性的概念,并且从中引入了条件单一性的概念,而Sesma-Sara等人的概念,从中我们引入了条件单一性的概念,而从中我们定义了条件单一性的概念,因为一个矢量的间隔和条件单一性,因为一个矢量的矢量在设定具有可受理命令的间隔时具有不变的矢量。这项工作是在Sesma-Sara等人的贡献之后迈出的一步,在Sesma-Sara等人的贡献中,这些单一性是在(非线性部分)\ textit{Kulisch-Miranker 顺序中引入的。此外,Sesma-Sara et. et al定义了条件单一性概念的弱点/直接性单一性概念,而我们只是使用非静态的函数。本文还提出了与一个函数($G)和一个参数($\Lambda)的间隔性参数(美元)有关的有条件单一性概念概念概念概念概念 -- -- 圣地亚哥等人等人在2021年建议的间断断段之间建议的间隔间隙点和四级函数。 本文显示了一些特性,对于这种单一性单一性概念和抽象共性关系和共性关系之间的间隔影响如何表现; 数值序列/单质/单数;调的公式/单质/单质/单质/单质性函数; ;