Max-min (σ-)additive representation of monotone measures
نویسندگان
چکیده
In non-additive measure and integration (or fuzzy measure and integral) one tries to generalise the issues of product measure and conditional expectation from the additive theory. In the discrete case successful attempts have been made via the max-min additive representation of the monotone measure and the corresponding integrals. The present paper intends to find, for arbitrary monotone measures, a maxmin additive representation and, under certain topological assumptions, a representation with σ-additive measures, thus providing a powerful tool for the theory of non-additive measure and integration.
منابع مشابه
Monotone Proper Interval Digraphs and Min-Max Orderings
We introduce a class of digraphs analogous to proper interval graphs and bigraphs. They are defined via a geometric representation by two inclusion-free families of intervals satisfying a certain monotonicity condition; hence we call them monotone proper interval digraphs. They admit a number of equivalent definitions, including an ordering characterization by so-called MinMax orderings, and th...
متن کاملTopology Information Condensation in Hierarchical Networks
Inspired by the PNNI protocol of the ATM Forum, this work focuses on the problem of node aggregation within peer groups and link aggregation between peer groups. It is assumed that the (large) network is already divided into peer groups. The objective is to maximally condense topology information subject to a given accuracy constraint. The QoS measures can be reduced into three distinct classes...
متن کاملInterval-valued Chebyshev, Hölder and Minkowski inequalities based on g-integrals
A natural generalization of (classical) measures are monotone set valued functions, the so called non-additive measures. Further generalization of measures are intervalvalued measures and interval-valued non-additive measures. Since interval-valued ⊕-measures, as a special case of intervalvalued non-additive measures, have been extensively applied in the mathematical representation of the vario...
متن کاملSet Sequences and Monotone Class
In this paper we first defined the partial-union sequence, the partial-intersection sequence, and the partial-difference-union sequence of given sequence of subsets, and then proved the additive theorem of infinite sequences and sub-additive theorem of finite sequences for probability. Further, we defined the monotone class of families of subsets, and discussed the relations between the monoton...
متن کاملRepresentation of increasing convex functionals with countably additive measures
We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of realvalued continuous functions and the second a sup-representation of functionals defined on spaces of real-valued measurable functions. MSC 2010: 47H07, 28C05, 28C15
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001