Keywords: Monotone measure Atom Weak null-additivity Regularity Sugeno integral Choquet integral a b s t r a c t In this paper, we prove some properties of atoms of weakly null-additive monotone measures. By using the regularity and weak null-additivity, a sin-gleton characterization of atoms of monotone measures on a metric space is shown. It is a generalization of previous results obtained by...

In the paper we present a new notion of stochastic monotone measure and its application to image processing. By definition, a stochastic monotone measure is a random value with values in the set of monotone measures and it can describe a choice of random features in image processing. In this case, a monotone measure describes uncertainty in the problem of choosing the set of features with the h...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

In this paper we provide the complete solution to the existence and characterisation problem of optimal capital and risk allocations for not necessarily monotone, law-invariant convex risk measures on the model space L, for any p ∈ [1,∞]. Our main result says that the capital and risk allocation problem always admits a solution via contracts whose payoffs are defined as increasing Lipschitz con...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

Monotone sets have been introduced about ten years ago by Cheeger and Kleiner who reduced the proof of non biLipschitz embeddability Heisenberg group into L1 to classification its monotone subsets. Later on, played an important role in several works related geometric measure theory issues setting. In this paper, we work arbitrary Carnot show that subsets are with locally finite perimeter local ...

Sen [6] proved that by confining voters to value restricted (acyclic) domains voting paradoxes (intransitive relations) can be avoided in aggregation by majority. We generalize this result to any neutral monotone aggregation. In addition, we show that acyclicity is neither necessary nor sufficient for transitivity for neutral non-monotone aggregation: we construct a cyclic transitive domain and...

In this paper, we investigate Egoroff's theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff's theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff's theorem for non-additive measure is formulated in full generality.

In this paper we will describe a framework that allows us to connect the problem of hedging a portfolio in finance to the existence of Pareto optimal allocations in economics. We will show the solvability of both problems is equivalent to the No Good Deals assumption. We will then analyze the case of co-monotone additive monetary utility functions and risk measures.