Uncertainty Theory Based Partitioning for Cyber-Physical Systems with Uncertain Reliability Analysis

Reasonable partitioning is a critical issue for cyber-physical system (CPS) design. Traditional CPS partitioning methods run in a determined context and depend on the parameter pre-estimations, but they ignore the uncertainty of parameters and hardly consider reliability. The state-of-the-art work proposed an uncertainty theory based CPS partitioning method, which includes parameter uncertainty and reliability analysis, but it only considers linear uncertainty distributions for variables and ignores the uncertainty of reliability. In this paper, we propose an uncertainty theory based CPS partitioning method with uncertain reliability analysis. We convert the uncertain objective and constraint into determined forms; such conversion methods can be applied to all forms of uncertain variables, not just for linear. By applying uncertain reliability analysis in the uncertainty model, we for the first time include the uncertainty of reliability into the CPS partitioning, where the reliability enhancement algorithm is proposed. We study the performance of the reliability obtained through uncertain reliability analysis, and experimental results show that the system reliability with uncertainty does not change significantly with the growth of task module numbers.

A vehicular traffic congestion predictor system using Mamdani fuzzy inference

The process of traffic control systems significantly relies on the immediate detection of breakdown states. As a result of their crisp (non-fuzzy) based calculation procedures, conventional traffic estimators and predictors cannot effectively model traffic states. In fact, these methods are characterized by exact features, while traffic is defined by uncertain variables with vague properties. Furthermore, typical numerical methodologies have constraints on evaluating the overall system status in heterogeneous and convoluted networks mainly due to the absence of reliable and real-time data. This study develops a fuzzy inference system that uses data from the Hungarian freeway networks for predicting the severity of congestion in this complex network. Congestion severity is considered the output variable, and traffic flow along with the length and the number of lanes of each section are assigned as input variables. Seventy-five fuzzy production rules were generated using accessible datasets, percentile distribution, and experts' consensus. The MATLAB fuzzy logic toolbox simulates the designed model and analysis steps. According to available resources, the results demonstrate linkages among input variables. Analyses are also used to construct intelligent traffic modeling systems and further service-related planning.

Difference double sequence of complex uncertain variables defined by Orlicz function

In this paper, we introduce the difference double sequence of complex uncertain variables defined by Orlicz function. We study some of their properties like solidness, symmetricity, and completeness and prove some inclusion results.

A New Formula for Calculating Uncertainty Distribution of Function of Uncertain Variables

As a mathematical tool to rationally handle degrees of belief in human beings, uncertainty theory has been widely applied in the research and development of various domains, including science and engineering. As a fundamental part of uncertainty theory, uncertainty distribution is the key approach in the characterization of an uncertain variable. This paper shows a new formula to calculate the uncertainty distribution of strictly monotone function of uncertain variables, which breaks the habitual thinking that only the former formula can be used. In particular, the new formula is symmetrical to the former formula, which shows that when it is too intricate to deal with a problem using the former formula, the problem can be observed from another perspective by using the new formula. New ideas may be obtained from the combination of uncertainty theory and symmetry.

On rough convergence of complex uncertain sequences

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. The main purpose of this paper is to introduce rough convergence of complex uncertain sequences and study some convergence concepts namely rough convergence in measure, rough convergence in mean, rough convergence in distribution of complex uncertain sequences. Lastly some relationship between them have been investigated.

Management of Uncertainty in Reservoir Modelling for an Onshore Carbonate Reservoir in the Middle East: A Case Study

As part of a reservoir modelling study for an onshore oil field in the Middle East, our study implemented a workflow with the objective to evaluate the impact of uncertainty on the long-term development scenario. The presence of several geological uncertainties characterized the field: many faults with uncertainty in juxtaposition and conductivity, lateral distribution of permeability in high permeability layers, and uncertainty on the rock typing. A deterministic geological model was available. There were also many dynamic uncertainties. The workflow started with an identification of uncertain variables, both from the static and the dynamic point of view, through an integrated team approach supported by a previous reservoir synthesis (Major Field Review). Subsequently, a screening analysis allowed identifying the relative impact of uncertain variables. After selecting the uncertainties with the largest impact on recovery, use of an experimental design methodology with a space-filling design resulted in alternative history matches. Statistical analysis of forecasts yielded probability density functions and low and high estimates of ultimate recovery. Forty-five uncertain variables, including both static and dynamic uncertainties, characterized the production profiles. Screening allowed reducing these to 11 main uncertain variables. A Wootton, Sergent, Phan-Tan-Luu (WSP) space-filling design yielded 162 simulation runs. Only five out of these corresponded to acceptable history matches. This number being statistically insignificant, a reexamination of the uncertainty ranges followed by a narrowing, allowed obtaining 45 history matches (out of 198 runs). The obtained spread in the cumulative oil production was narrow, with a slightly skewed distribution around the base case (closer to P90 than to P10). The study resulted in an estimation of final uncertainty in reserves that is smaller than the typical uncertainty found in post-mortem analysis of oil field development projects. Other reservoir studies in the company and in literature, employing a similar workflow, yielded outcomes with a similar bias. To tackle this issue, as a way forward we suggest history matching of multiple geological scenarios, either with multiple deterministic cases (min, base, max) or with an ensemble history matching loop including structural model generation, in-filling, and dynamic parameter uncertainty.

An Uncertain APP Model with Allowed Stockout and Service Level Constraint for Vegetables

Volatile markets and uncertain deterioration rate make it extremely difficult for manufacturers to make the quantity of saleable vegetables just meet the fluctuating demands, which will lead to inevitable out of stock or over production. Aggregate production planning (APP) is to find the optimal yield of vegetables, shortage and overstock symmetry, are not conducive to the final benefit.The essence of aggregate production planning is to deal with the symmetrical relation between shortage and overproduction. In order to reduce the adverse effects caused by shortage, we regard the service level as an important constraint to meet the customer demand and ensure the market share. So an uncertain aggregate production planning model for vegetables under condition of allowed stockout and considering service level constraint is constructed, whose objective is to find the optimal output while minimizing the expected total cost. Moreover, two methods are proposed in different cases to solve the model. A crisp equivalent form can be transformed when uncertain variables obey linear uncertain distributions and for general case, a hybrid intelligent algorithm integrating the 99-method and genetic algorithm is employed. Finally, two numerical examples are carried out to illustrate the effectiveness of the proposed model.

Analysis and Prediction for Confirmed COVID-19 Cases in Czech Republic with Uncertain Logistic Growth Model

This paper presents an uncertain logistic growth model to analyse and predict the evolution of the cumulative number of COVID-19 infection in Czech Republic. Some fundamental knowledge about the uncertain regression analysis are reviewed firstly. Stochastic regression analysis is invalid to model cumulative number of confirmed COVID-19 cases in Czech Republic, by considering the disturbance term as random variables, because that the normality test and the identical distribution test of residuals are not passed, and the residual plot does not look like a null plot in the sense of probability theory. In this case, the uncertain logistic growth model is applied by characterizing the disturbance term as uncertain variables. Then parameter estimation, residual analysis, the forecast value and confidence interval are studied. Additionally, the uncertain hypothesis test is proposed to evaluate the appropriateness of the fitted logistic growth model and estimated disturbance term. The analysis and prediction for the cumulative number of COVID-19 infection in Czech Republic can propose theoretical support for the disease control and prevention. Due to the symmetry and similarity of epidemic transmission, other regions of COVID-19 infections, or other diseases can be disposed in a similar theory and method.

On Some Laws of Large Numbers for Uncertain Random Variables

Baoding Liu created uncertainty theory to describe the information represented by human language. In turn, Yuhan Liu founded chance theory for modelling phenomena where both uncertainty and randomness are present. The first theory involves an uncertain measure and variable, whereas the second one introduces the notions of a chance measure and an uncertain random variable. Laws of large numbers (LLNs) are important theorems within both theories. In this paper, we prove a law of large numbers (LLN) for uncertain random variables being continuous functions of pairwise independent, identically distributed random variables and regular, independent, identically distributed uncertain variables, which is a generalisation of a previously proved version of LLN, where the independence of random variables was assumed. Moreover, we prove the Marcinkiewicz–Zygmund type LLN in the case of uncertain random variables. The proved version of the Marcinkiewicz–Zygmund type theorem reflects the difference between probability and chance theory. Furthermore, we obtain the Chow type LLN for delayed sums of uncertain random variables and formulate counterparts of the last two theorems for uncertain variables. Finally, we provide illustrative examples of applications of the proved theorems. All the proved theorems can be applied for uncertain random variables being functions of symmetrically or asymmetrically distributed random variables, and symmetrical or asymmetrical uncertain variables. Furthermore, in some special cases, under the assumption of symmetry of the random and uncertain variables, the limits in the first and the third theorem have forms of symmetrical uncertain variables.

Uncertain time series forecasting method for the water demand prediction in Beijing

Water demand prediction is crucial for effectively planning and management of water supply systems to handle the problem of water scarcity. Taking into account the uncertainties and imprecisions within the framework of water demand forecasting, the uncertain time series prediction method is introduced for the water demand prediction. Uncertain time series is a sequence of imprecisely observed values that are characterized by uncertain variables and the corresponding uncertain autoregressive model is employed to describe it for predicting the future values. The main contributions of this paper are shown as follows. Firstly, by defining the auto-similarity of uncertain time series, the identification algorithm of uncertain autoregressive model order is proposed. Secondly, a new parameter estimation method based on the uncertain programming is developed. Thirdly, the imprecisely observed values are assumed as the linear uncertain variables and a ratio-based method is presented for constructing the uncertain time series. Finally, the proposed methodologies are applied to model and forecast the Beijing's water demand under different confidence levels and compared with the traditional time series, i.e., ARIMA method. The experimental results are evaluated on the basis of performance criteria, which shows that the proposed method outperforms over the ARIMA method for water demand prediction.