Chance Theory Research Articles

AUTOMATED SYSTEM FOR TOPICAL DIAGNOSTICS IN CLINICAL NEUROLOGY

The ability to determine the localization of nervous system disorders plays a central role in neurological diagnosis. Undoubtedly, the introduction of computer tomography and magnetic resonance imaging into medical practice was the significant advance in clinical diagnostics. However, neurovisualization often requires reinforcement with a description of disease clinical manifestations. The article describes the possibilities of the program developed by the authors for recognizing the most probable localization of the nervous system affected area and evaluating the available symptoms and signs in the chance theory terms of specific disease presence.

Uncertain random shortest path problem

The shortest path is an important problem in network optimization theory. This paper considers the shortest path problem under the situation where weights of edges in a network include both uncertainty and randomness and focuses on the case that the weights of edges are expressed by uncertain random variables. Some optimization models based on chance theory are proposed in order to find the shortest path which fully reflects uncertain and random information. This paper proposes also an intelligent algorithm to calculate the shortest path for an uncertain random network. A numerical example is given to illustrate its effectiveness.

Aviation Risk Analysis: U-bowtie Model Based on Chance Theory

Risk analysis is a crucial component in any aviation application. The conventional risk analysis schemes for systems encompassing large amounts of data are based on the probability theory. However, in some practical systems, the components of complex systems may have few or even zero samples, in which case the risk cannot be evaluated simply via statistics. This paper proposes a novel aviation risk analysis scheme based on the chance theory, which is a generation of both probability theory and uncertainty theory. In this paper, a U-bowtie model is first established according to the graphic structure and step-wise analysis process. A risk belief metric is utilized, and the risk variable is modified by a logic algorithm based on the operational law of chance theory. Then, several risk belief formulas are built for different respective system configurations; the risk of output events in the U-bowtie model can be calculated via the corresponding formulas. Additionally, the most contributed basic event and the most effective measurement can be obtained through sensitivity analysis. The effectiveness of the proposed scheme is validated by a case study. The results presented here may represent an innovative approach to managing risk in larger classes of complex systems.

Reliability analysis of structures based on a probability‐uncertainty hybrid model

AbstractThe traditional reliability analysis method based on probabilistic method requires probability distributions of all the uncertain parameters. However, in practical applications, the distributions of some parameters may not be precisely known due to the lack of sufficient sample data. The probabilistic theory cannot directly measure the reliability of structures with epistemic uncertainty, ie, subjective randomness and fuzziness. Hence, a hybrid reliability analysis (HRA) problem will be caused when the aleatory and epistemic uncertainties coexist in a structure. In this paper, by combining the probability theory and the uncertainty theory into a chance theory, a probability‐uncertainty hybrid model is established, and a new quantification method based on the uncertain random variables for the structural reliability is presented in order to simultaneously satisfy the duality of random variables and the subadditivity of uncertain variables; then, a reliability index is explored based on the chance expected value and variance. Besides, the formulas of the chance theory‐based reliability and reliability index are derived to uniformly assess the reliability of structures under the hybrid aleatory and epistemic uncertainties. The numerical experiments illustrate the validity of the proposed method, and the results of the proposed method can provide a more accurate assessment of the structural system under the mixed uncertainties than the ones obtained separately from the probability theory and the uncertainty theory.

Tail value-at-risk in uncertain random environment

Chance theory is a rational tool to be used in the systems which contain not only uncertainty but also randomness. In this paper, the concept of tail value-at-risk in uncertain random risk analysis is proposed and some theorems are provided for its calculation. Moreover, the tail value-at-risk is applied as the right-tail in the parallel system, series system, standby system, k-out-of-n system and structural system.

Calculation models of reliability of petroleum reservoirs

Raising of problem. From the point of view of reliability most building constructions can be examined after a decouplig as a system with logically successive connection of elements. For the normal functioning of such system all its elements must be capable of working. The refuse of even one element results in the refuse of all system. In case of independence of refuses of separate elements probability of faultless work of the system is easily determined by well-known rule of increase of probabilities. If the refuses of elements of the examined system are statistically dependent, then it is adequate to represent dependence of reliability of all system indexes on probabilistic descriptions of its elements considerably more difficult. The well-known in the theory of chances going near the decision of this task is based on the synthesis of functions (integral or closenesses) of joint probability of works completely of separate elements of the system distribution. However for the decision of practical tasks such approach is extremely uncomfortable and not used actually. In this article the questions of design of reliability of steel reservoirs indexes are examined for oil products on the basis of hypothesis of the "weakest link". Purpose of the article - to show legitimacy of application of hypothesis of the "weakest link" at development of models of estimation of reliability of petroleum reservoirs being in exploitation. Conclusions. The gotten results confirm legitimacy of application of hypothesis of the "weakest link" at the design of reliability of steel reservoirs indexes for standing oil product storing. Offer models allow to get the complex probabilistic estimation of the technical state of reservoirs. The parameters of these models can be corrected from data of model inspections, that promotes exactness of estimation in every special case. In addition, these models can be used as prognosis models on the stage of planning of reservoirs and as case frames by reliability in the period of exploitation of these building. The models considered in the total can serve as an effective enough mathematical instrument at research of problems of reliability and longevity of petroleum reservoirs.

A new model and algorithm for uncertain random parallel machine scheduling problem

The paper presents a new model for uniform parallel machine scheduling problem with uncertainty and randomness simultaneously for processing times of jobs based on chance theory. The objective of the model is to minimize expected completion time. The constraint of the model is that uncertain random completion time of scheduling is less than or equal to expected completion time. The model is transformed to a crisp non-deterministic polynomial hard mathematical programming model based on chance theory. Firstly, simulation techniques of the objective function and the left chance constraint are proposed. Then, two heuristic methods to solve the crisp model are presented. Finally, they are integrated into two hybrid intelligent algorithms for searching the quasi-optimal schedule. Besides, the effectiveness of the model and its hybrid intelligent algorithms are verified by a numerical example generated randomly.

Uncertain Urn Problems and Ellsberg Experiment

The basic urn problem is to determine the probability of drawing one colored ball from an urn with known composition of differently colored balls. If the composition is unknown, then it is called uncertain. This paper designs some uncertain urn problems in order to compare probability theory and uncertainty theory. It is concluded that uncertainty theory is better than probability theory to deal with uncertain urn problems. As a by-product, this paper also solves the choice problem in Ellsberg experiment by chance theory.

Renewal Reward Process With Uncertain Interarrival Times and Random Rewards

Renewal reward process is used to measure the cumulative occasional rewards up to some given time. So far, two basic types of renewal reward processes with only random parameters or with only uncertain parameters have been proposed. This paper aims at proposing a new type of renewal reward process, which has uncertain interarrival times and random rewards in the framework of the chance theory. The chance distribution of such an uncertain random renewal reward process is obtained, and the reward rate is derived. A renewal reward theorem is verified to show that the reward rate converges in distribution to an uncertain variable, which is highly related to the interarrival times and the expected values of random rewards.

Nowa metoda oceny niezawodności mechanizmów oparta na pomiarze szansy wystąpienia zdarzenia w warunkach niepewności rozmytej i losowej

The traditional reliability analysis methods based on probability theory and fuzzy set theory have been widely used in engineering practice. However, these methods are unable directly measure the uncertainty of mechanism reliability with uncertain variables, i.e., subjective random and fuzzy variables. In order to address this problem, a new quantification method for the mechanism reliability based on chance theory is presented to simultaneously satisfy the duality of randomness and the subadditivity of fuzziness in the reliability problem. Considering the fact that systems usually have multilevel performance and the components have multimode failures, this paper proposes a chance theory based multi-state performance reliability model. In the proposed method, the chance measure is adopted instead of probability and possibility measures to quantify the mechanism reliability for the subjective probability or fuzzy variables. The hybrid variables are utilized to represent the random and fuzzy parameters, based on which solutions are derived to analyze the chance theory based mechanism reliability with chance distributions. Since the input parameters of the model contain fuzziness and randomness simultaneously, an algorithm based on chance measure is designed. The experimental results on the case application demonstrate the validity of the proposed method.

A Novel Approach of Weighted Support Vector Machine with Applied Chance Theory for Forecasting Air Pollution Phenomenon in Egypt

The particulate matter air pollutant of diameter less than 10 micrometers (PM[Formula: see text]), a category of pollutants including solid and liquid particles, can be a health hazard for several reasons: it can harm lung tissues and throat, aggravate asthma and increase respiratory illness. Accurate prediction models of PM[Formula: see text] concentrations are essential for proper management, control, and making public warning strategies. Therefore, machine learning techniques have the capability to develop methods or tools that can be used to discover unseen patterns from given data to solve a particular task or problem. The chance theory has advanced concepts pertinent to treat cases where both randomness and fuzziness play simultaneous roles at one time. The main objective is to study the modification of a single machine learning algorithm — support vector machine (SVM) — applying the chance weight of the target variable, based on the chance theory, to the corresponding dataset point to be superior to the ensemble machine learning algorithms. The results of this study are outperforming of the SVM algorithms when modifying and combining with the right theory/technique, especially the chance theory over other modern ensemble learning algorithms.

Epistemic theories of objective chance

Epistemic theories of objective chance hold that chances are idealised epistemic probabilities of some sort. After giving a brief history of this approach to objective chance, I argue for a particular version of this view, that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. The main argument for this view is the demonstration that it entails all of the commonly-accepted properties of chance. For example, this analysis entails that chances supervene on the physical facts, that the chance function is an expert probability, that the existence of stable frequencies results from invariant chances in repeated experiments, and that chances are probably close to long-run relative frequencies in repeated experiments. Despite these virtues, epistemic approaches to chance have been neglected in recent decades, on account of their conflict with accepted views about closely related topics such as causation, laws of nature, and epistemic probability. However, existing views on these topics are also very problematic, and I believe that the epistemic view of chance is a key piece of this puzzle that, once in place, allows all the other pieces to fit together into a new and coherent way. I also respond to some criticisms of the epistemic theory that I favour.

El azar como espacio positivo de indeterminación en la asimilación tomista de la física de Aristóteles

“Chance as a Positive Space of Indetermination in the Thomistic Assimilation of Aristotle’s Physics”. This article analyzes Thomas Aquinas’s assimilation of the Aristotelian theory of chance. The analysis highlights Thomas Aquinas’s unequivocal acceptance of Aristotelian philosophy, as well as the issues regarding which he abandoned the Aristotelian position by offering a new interpretation related to the role of chance in the context of the created cosmos. All in all, the confluence of these two great systems of thought –Aristotelian thought and late Medieval Christianity– provided new ways to understand nature, by expanding the scope of physics from the absolutely determined to the anomalous and irregular.

Loss of a chance theory: an analysis of the favorable jurisprudential arguments to its acceptance in Brazil.

Loss of a chance theory: an analysis of the favorable jurisprudential arguments to its acceptance in Brazil.

Air Pollution Forecasting Model Based on Chance Theory and Intelligent Techniques

A novel approach of weighted support vector regression (WSVR) technique with applied chance theory was proposed to build a robust forecasting model, called the chance weighted support vector regression (chWSVR) model. In order to forecast the particulate matter air pollutant of diameter less than 10 micrometers (PM10) one hour advance in the Greater Cairo Metropolitan Area (GCMA) in Egypt. The chance theory has advanced concepts pertinent to treat cases where both randomness and fuzziness play simultaneous roles at one time. The basic idea based on the proposed chWSVR model is assigning the chance weight value of the target variable, based on the chance theory, to its corresponding dataset point to become minimized in the objective function making that point more significant during the training process. Measuring data were collected and reprocessed from four monitoring stations located in GCMA and relative to the springs during the period from 2007 to 2010. The results of such model compared to similar ones built by other machine learning techniques, Random Forest and Bootstrap aggregating techniques. In all stations, comparing such models revealed that the proposed chWSVR model findings were promising in the forecasting of PM10hourly concentration.

The Chances of Propensities

This paper argues that if propensities are displayed in objective physical chances then the appropriate representation of these chances is as indexed probability functions. Two alternative formal models, or accounts, for the relation between propensity properties and their chancy or probabilistic manifestations, in terms of conditionals and conditional probability are first reviewed. It is argued that both confront important objections, which are overcome by the account in terms of indexed probabilities. A number of further advantages of the indexed probability account are discussed, which suggest that it is promising as a general theory of objective physical chance. The paper ends with a discussion of the indexical character of the objective chances that are grounded in propensities.

Some Results of Moments of Uncertain Random Variables

Chance theory is a mathematical methodology for dealing with indeterminatephenomena including uncertainty and randomness.Consequently, uncertain random variable is developed to describe the phenomena which involveuncertainty and randomness.Thus, uncertain random variable is a fundamental concept in chance theory.This paper provides some practical quantities to describe uncertain random variable.The typical one is the expected value, which is the uncertain version of thecenter of gravity of a physical body.Mathematically, expectations are integrals with respect to chance distributionsor chance measures.In fact, expected values measure the center of gravity of a distribution; they aremeasures of location. In order to describe a distribution in brief terms thereexist additional measures, such as the variance which measures the dispersionor spread, and moments.For calculating the moments of uncertain random variable, some formulas are provided through chance distribution and inverse chance distribution. The main results are explained by using several examples.

The maximum flow problem of uncertain random network

The maximum flow problem is an important problem of network optimization and it covers a wide range of engineering and management applications. The goal of the problem is to find the maximum amount of flow from the source to the sink in a network. This paper investigates two models of the maximum flow of an uncertain random network under the framework of chance theory. The expected value constrained maximum flow and chance constrained maximum flow models with uncertain random arc capacities are proposed. We prove that there exists an equivalence relationship between the uncertain random maximum flow models and the deterministic maximum flow models. Furthermore, some important properties of the models are analyzed, and two algorithms are proposed. Finally, as an illustration, a numerical example is presented to show the effectiveness of the models and algorithms.

Day-ahead optimal dispatch for wind integrated power system considering zonal reserve requirements

Large-scale integration of renewable power presents a great challenge for day-ahead dispatch to manage renewable resources while provide available reserve for system security. Considering zonal reserve is an effective way to ensure reserve deliverability when network congested, a random day-ahead dispatch optimization of wind integrated power system for a least operational cost is modeled including zonal reserve requirements and N−1 security constraints. The random model is transformed into a deterministic one based on the theory of chance constrained programming and a determination method of optimal zonal reserve demand is proposed using the minimum confidence interval. After solving the deterministic model, the stochastic simulation is conducted to verify the validity of solution. Numerical tests and results on the IEEE 39 bus system and a large-scale real-life power system demonstrate the optimal day-ahead dispatch scheme is available and the proposed method is effective for improving reserve deliverability and reducing load shedding after large-capacity power outage.

Explaining (One Aspect of) the Principal Principle without (Much) Metaphysics

According to David Lewis’s Principal Principle, our beliefs about the objective chances of outcomes (typically) determine our rational credences in those outcomes. Lewis influentially argues that any adequate metaphysics of objective chance must explain why the Principal Principle holds. Since no theory of chance is widely agreed to have met this burden, I suggest we change tack. On the view I develop, a central aspect of the Principal Principle holds not because of what objective chances are but rather because of the explanatory role that objective chances play for the rational agents who believe in them.