On conditional monotonicities of interval-valued functions. (English) Zbl 07856747
Summary: This paper introduces the concept of conditional monotonicity and other related relaxed monotonicities within the framework of intervals equipped with admissible orders. It generalizes the work of Sesma-Sara et al., who introduced weak/directional monotonicity on intervals endowed with the Kulisch-Miranker order, and the work of Santiago et al., who introduced the notion of \(g\)-weak monotonicity in the fuzzy setting. The paper also explores properties of conditional monotonicities, introduce the notion of ordinal sum for a family of functions and examines the connections between conditional monotonicity, ordinal sums and implications.
MSC:
| 03B52 | Fuzzy logic; logic of vagueness |
| 06A05 | Total orders |
| 26A48 | Monotonic functions, generalizations |
Keywords:
conditional monotonicity; admissible orders; weak/directional/\(g\)-weak monotonicity; ordinal sumReferences:
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