In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

Original scientific paper New generation electricity network called Smart Grid is a recently conceived vision for a cleaner, more efficient and cheaper electricity system. One of the major challenges of electricity network is that generation and consumption should be balanced at every moment. This paper introduces a new concept for controlling the demand side by the means of automatically enabl...

In the recent years, extensions of graph transformation systems with quantitative properties, such as real-time and stochastic behavior received considerable attention. In this paper, we describe the new quantitative modeling approach of probabilistic graph transformation systems (PGTSs) which incorporate probabilistic behavior into graph transformation systems. Among other applications, PGTSs ...

Electricity smart meters record consumption, on a near real-time basis, at the level of individual commercial and residential properties. From this, a hierarchy can be constructed consisting of time series of demand at the smart meter level, and at various levels of aggregation, such as substations, cities and regions. Forecasts are needed at each level to support the efficient and reliable man...

In explicit state (enumerative) model checking, state vectors are often represented in a compressed form in order to reduce storage needs, typically employing fingerprints, bithashes, or state signatures. When using this kind of techniques, it could happen that the compressed image of a nonvisited state s matches that of a visited state s′ 6= s, thus s and potentially many of its descendants ar...

Cloud computing applications must be allocated sufficient resources to comply with Service Level Agreements (SLAs). This paper considers data-driven probabilistic modeling of application resource demand for resource allocation. The modeling method is focused on peak demand and SLA violations and relies on a branch of statistics known as extreme value theory (EVT). Rigorous statistical validatio...

In this paper we consider a single item, discrete time, lot sizing situation where demand is random and its parameters (e.g., mean and standard deviation) can change with time. For the appealing criterion of minimizing expected total relevant costs per unit time until the moment of the next replenishment we develop two heuristic ways of selecting an appropriate augmentation quantity beyond the ...

We analyze the unit-demand Euclidean vehicle routeing problem, where n customers are modeled as independent, identically distributed uniform points and have unit demand. We show new lower bounds on the optimal cost for the metric vehicle routeing problem and analyze them in this setting. We prove that there exists a constant ĉ > 0 such that the iterated tour partitioning heuristic given by Haim...

Efficient and sustainable bike-sharing service (BSS) operations require accurate demand forecasting for bike inventory management rebalancing. Probabilistic provides a set of information on uncertainties in forecasting, thus it is suitable use stochastic management. Our research objective to develop probabilistic time-series BSS demand. We an RNN–LSTM-based model, called DeepAR, the station-wis...