In a multi-unit market, a seller brings multiple units of a good and tries to sell them to a set of buyers equipped with monetary endowments. While a Walrasian equilibrium does not always exist in this model, natural relaxations of the concept that retain its desirable fairness properties do exist. We study the dynamics of (Walrasian) envy-free pricing algorithms in this environment, showing th...

We consider the problem of sharing pooled risks among n economic agents endowed with non-necessarily monotone monetary functionals. In this framework, results of characterization and existence of optimal solutions are easily obtained as extension from the convex risk measures setting. Moreover, the introduction of the best monotone approximation of non-monotone functionals allows us to compare ...

The signed fuzzy measures are considered and some of their properties are shown. There is introduced the revised monotone functional and there are given conditions for its asymmetric Choquet integral-based representation.

It has been shown (see [10]), that there are strongly MARTIN-LÖFε-random ω-words that behave in terms of complexity like random ωwords. That is, in particular, the a priori complexity of these ε-random ω-words is bounded from below and above by linear functions with the same slope ε. In this paper we will study the set of these ω-words in terms of HAUSDORFF measure and dimension. Additionally w...

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 measur...

Extending the concept of level measure μ({f⩾a}) we introduce a generalized based on family conditional aggregations operators. As recent research direction, aggregation operators extend in order to model dependence function set. Generalized measures then provide new insight into behaviour level-dependent (monotone) and related processes. We investigate detail several basic properties measure, i...

In the field of multicriteria decision analysis, the most distinctive characteristic of the monotone measure, or called the nonadditive measure, the fuzzy measure, the capacity, is that it can adequately and flexibly describe the interactions between the decision criteria. Traditionally, the interaction described with the monotone measure can be measured by the various kinds of the probabilisti...

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}...