On Monotonicities of Interval Valued Functions
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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) 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 Λ 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.
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