This paper considers a multi-objective portfolio selection problem imposed by gaining of portfolio, divided yield and risk control in an ambiguous investment environment, in which the return and risk are characterized by probabilistic numbers. Based on the theory of possibility, a new multi-objective portfolio optimization model with gaining of portfolio, divided yield and risk control is propo...

This paper presents a novel reliable hierarchical location-allocation model where facilities are subject to the risk of disruptions. Based on the relationship between various levels of system, a multi-level multi-flow hierarchy is considered. The heterogeneous probabilistic disruptions are investigated in which the constructed facilities have different site-dependent and independent failure rat...

Probabilistic automata (PA) [20] have been successfully applied in the formal verification of concurrent and stochastic systems. Efficient model checking algorithms have been studied, where the most often used logics for expressing properties are based on PCTL [11] and its extension PCTL [4]. Various behavioral equivalences are proposed for PAs, as a powerful tool for abstraction and compositio...

Verification of PCTL properties of MDPs with convex uncertainties has been investigated recently by Puggelli et al. However, model checking algorithms typically suffer from state space explosion. In this paper, we address probabilistic bisimulation to reduce the size of such an MDPs while preserving PCTL properties it satisfies. We discuss different interpretations of uncertainty in the models ...

Applications of probabilistic grammatical inference are limited due to time and space consuming constraints. In statistical language modeling, for example, large corpora are now available and lead to managing automata with millions of states. We propose in this article a method for pruning automata (when restricted to tree based structures) which is not only efficient (sub-quadratic) but that a...

Complex probabilistic temporal behaviours need to be guaranteed in robotics and various other control domains, as well as in the context of families of randomized protocols. At its core, this entails checking infinite-state probabilistic systems with respect to quantitative properties specified in probabilistic temporal logics. Model checking methods are not directly applicable to infinite-stat...

This paper is a first attempt to describe the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which provides precise information on the structure of such a word. With each Sturmian word of slope α, we associate particular sequences of factor lengths which have a given “position” with respect to the sequence of continuants of α...

A guarantee is only as good as its assumptions. Three group membership areas defy firm, practical guarantees: transient faults, reintegration, and large groups. We show why these areas are problematic, discuss current approaches, and illustrate alternative approaches that may lead to a more dependable system. Ultimately, designs should be tested against a comprehensive fault model, and a probab...

A formalization of the Threshold Theory, called the Probabilistic Threshold Model, is introduced. According to the Threshold Theory semantic categorization decisions come about through the placement of a threshold criterion along a dimension that represents items’ similarity to the category representation. The adequacy of this theory is assessed by applying the Probabilistic Threshold Model to ...