A functional limit theorem for the partial maxima of a long memory stable sequence produces a limiting process that can be described as a β-power time change in the classical Fréchet extremal process, for β in a subinterval of the unit interval. Any such power time change in the extremal process for 0 < β < 1 produces a process with stationary max-increments. This deceptively simple time change...

We introduce bi-capacities as a natural generalization of capacities (or fuzzy measures) through the identity of Choquet integral of binary alternatives with fuzzy measures. We examine the underlying structure and derive the Möbius transform of bi-capacities. Next, the Choquet and Sugeno integrals w.r.t bicapacities are introduced. It is shown that symmetric and asymmetric integrals are recover...

We provide a survey of recent developments about capacities (or fuzzy measures) and ccoperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of ...

In this note we prove that if M is a 3-manifold and ' t : M ! M is a C 2 , volume-preserving Anosov ow, then the time-1 map ' 1 is stably ergodic if and only if ' t is not a suspension of an Anosov diieomorphism.

We consider finite-state Markov chains driven by a P-stationary ergodic invertible process σ : Ω → Ω, representing a random environment. For a given initial condition ω ∈ Ω, the driven Markov chain evolves according to A(ω)A(σω) · · ·A(σn−1), where A : Ω → Md is a measurable d × d stochastic matrix-valued function. The driven Markov chain possesses P-a.e. a measurable family of probability vect...

Based on the Choquet integral and the generalized Shapley function, two new induced Atanassov’s interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov’s interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov’s interval-val...

Bi-capacities are a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wide variety of decision behaviours. After a short presentation of the basis structure, we introduce the Shapley value and the interaction index for capacities. Afterwards, the case of bi-capacities is studied with new axiom...

This paper first shows that when colleges’ preferences are substitutable there does not exist any stable matching mechanism that makes truthful revelation of preferences a dominant strategy for every student. The paper introduces student types and captures colleges’ preferences for affirmative action via type-specific quotas: A college always prefers a set of students that respects its type-spe...