Incomplete Probabilistic Information Research Articles

Retracted: Emergency Optimization Decision-Making with Incomplete Probabilistic Information under the Background of COVID-19

Retracted: Emergency Optimization Decision-Making with Incomplete Probabilistic Information under the Background of COVID-19

Reasoning with belief functions over Belnap–Dunn logic

We design an expansion of Belnap–Dunn logic with belief and plausibility functions that allows non-trivial reasoning with contradictory and incomplete probabilistic information. We also formalise reasoning with non-standard probabilities and belief functions in two ways. First, using a calculus of linear inequalities, akin to the one presented in [23]. Second, as a two-layered modal logic wherein reasoning with evidence (the outer layer) utilises paraconsistent expansions of Łukasiewicz logic. The second approach is inspired by [3]. We prove completeness for both kinds of calculi and show their equivalence by establishing faithful translations in both directions.

The optimal emergency decision-making method with incomplete probabilistic information

Emergencies often occur irregularly, such as infectious diseases, earthquakes, wars, floods, the diffusion and leakage of chemically toxic and harmful substances, etc. These emergencies can bring huge disasters to people, even worse, the time left for people to make critical decisions is usually very limited. When an emergency occurs, the most important thing for people is to make reasonable decisions as soon as possible to deal with the current problems, otherwise, the situation may deteriorate further. The paper proposes an emergency decision-making algorithm under the constraints of the limited time and incomplete information, the research is mainly carried out from the following aspects, firstly, we use the data structure of the hesitant fuzzy probabilistic linguistic set to collect the basic data after careful comparison, which has three advantages, (1) considering the hesitation in the decision-making process, each evaluation information is allowed to contain multiple values instead of just one value; (2) each evaluation value is followed by a probability value, which further describes the details of the evaluation information; (3) the data structure allows some probability information to be unknown, which effectively expands the application scope of the algorithm. Secondly, the maximization gap model is proposed to calculate unknown parameters, the model can distinguish alternatives with small differences. Thirdly, all the evaluation information will be aggregated by the dynamic hesitant probability fuzzy weighted arithmetic operator. Subsequently, an instance is given to illustrate the effectiveness and the accuracy of the algorithm proposed in the paper. Finally, the advantages of the proposed algorithm are further demonstrated by comparing it with other outstanding algorithms. The main contribution of the paper is that we propose the maximization gap model to obtain the unknown parameters, which can effectively and accurately distinguish alternatives with small differences.

Emergency Optimization Decision-Making with Incomplete Probabilistic Information under the Background of COVID-19

At present, the whole world is facing the serious challenge of COVID-19, and it has reached a consensus that taking appropriate measures timely is the key to prevent and control infectious diseases. This paper proposes an algorithm to solve the problem of how to choose the most appropriate alternative from numerous alternatives in the limited time from the perspective of management. First of all, we have compared various data structures for keeping the comparison results of alternatives. After comparisons, we adopt the hesitant fuzzy incomplete probabilistic linguistic preference relation matrix to save the information which can keep the first-hand valuable collected data to the maximum extent; then, we can obtain the missing values with the help of the fault tree analysis method, which can consider both subjective evaluation data and objective historical data simultaneously. Meanwhile, the fault tree analysis method can find development laws with the help of similar infectious diseases that have occurred in the past. The definition of consistency index is also introduced which can measure whether there are contradictions and the degree of contradiction in the decision results. Only those data that meet the consistency requirements can be used for decision-making and then a method is proposed to effectively reduce the degree of inconsistency. The information aggregation method will be adopted subsequently, and we can obtain the ranking of alternatives. An instance with specific execution steps is also introduced to illustrate the feasibility and efficiency of the algorithm proposed in this paper; in the end, several types of comparisons with typical algorithms proposed by other scholars are carried out, and all the experimental results show that the algorithm proposed in this paper is effective and innovative in some aspects.

Copula-based approach coupling information diffusion distribution for slope reliability analysis

Uncertain probability distributions and interdependencies of geotechnical parameters have profound impacts on slope reliability analysis, especially under incomplete probabilistic information. In this paper, a copula-based approach coupling information diffusion (ID) distribution is proposed to reduce such uncertainties. Firstly, ID theory is introduced to establish marginal distribution of strength parameter. Copulas are subsequently performed to characterize the corresponding dependence structure and link the proposed ID margins. At last, equivalent samples are simulated and plugged into Monte Carlo simulation (MCS) to estimate slope reliability. The effect of the proposed method is validated by a slope case. Results show that the proposed ID algorithm holds remarkable superiority in estimating the marginal distribution with considering random volatility of geotechnical parameter. For slope reliability, both marginal distributions and interdependencies of geotechnical parameters barely affect the factor of safety (FS) but significantly impact failure probability (pf). Unreasonable estimation of probability distribution may lead to large deviation in calculation of slope failure probability. Comparably, the proposed copula-based approach coupling ID distribution can give a reasonable and robust reliability results with considering random volatility.

Optimal Estimation of Shear Strength Parameters Based on Copula Theory Coupling Information Diffusion Technique

In geotechnical reliability analysis, random volatility in marginal distributions of shear strength parameters has been rarely considered. Unfortunately, conventional marginal distribution models cannot characterize real probability distribution accurately, leading to considerable dispersion with incomplete probabilistic information. In this paper, an estimation methodology is proposed based on copula theory coupling information diffusion technique. Firstly, information diffusion distribution is extended to represent one-dimensional marginal distributions of shear strength parameters. Secondly, copula theory is employed to characterize the dependence structures among the parameters. Eventually, equivalent sample is yielded by information diffusion distribution that has been already established. A case study in Singapore is implemented to enunciate and validate the competence of the proposed method. The performances of the candidate copulas coupling different marginal distributions are further discussed. Results indicate that information diffusion distribution can efficiently capture the random volatility of real distributions of shear strength parameters and hold remarkable superiority in modeling marginal distributions. The equivalent sample, estimated by information diffusion technique in conjunction with Gaussian copula, has considerable consistency with original data. The proposed method can provide a reference to reliability analysis in geotechnical engineering.

Reliability analysis with consideration of asymmetrically dependent variables: Discussion and application to geotechnical examples

The consideration of multivariate models in the reliability analysis is quite essential from practical perspective. In principle, complete information regarding the joint probability distribution function should be known in prior to the analysis. However, in real practice, only the marginal distribution and covariance matrix are known in most cases. Such incomplete probabilistic information could lead to dubious results if dependences are not fully catered. Asymmetric dependence is one of these factors influencing the quality of reliability analysis. In this paper, the influences of asymmetric dependences to the reliability problem are investigated. The copula theory as well as the concept of asymmetric dependences is briefly introduced. The techniques of constructing asymmetric copulas are, thereafter, provided in details. Geotechnical problem is selected in this study as examples in the reliability analysis. Based on the given information, a group of symmetric and asymmetric copulas are selected to model the dependences between cohesion and friction angle, the parameters more commonly used to characterize soil strength. The reliability analysis of a continuous spread footing and an infinite slope are then presented to demonstrate the influence of asymmetric dependences on reliability. The results showed that the failure probabilities of the investigated geotechnical problems are very sensitive to the adopted dependence structure, either symmetrically or asymmetrically. The commonly applied one parameter symmetric copulas, such as Archimedean copulas, may underestimate the failure probabilities. Furthermore, the asymmetric copulas are more powerful in characterizing the tail dependences structures of variables especially for asymmetric dependent variables.

The strength analysis and probabilistic design of a bogie frame with incomplete probabilistic information

A bogie frame is a key component of high-speed rail; higher requirements of the safety and stability of the bogie frame are put forward with the continuous improvement of the train speed. In this study, we first performed a strength analysis of a bogie frame according to the JIS E 4207 standard by using finite element method. Then, we did a reliability analysis of the bogie frame. The reliability problems are defined as strength reliability and resonant frequency reliability, which indicate the structural safety and stability of the bogie frame. The reliability estimation is realized by experimental design, artificial neural network and stochastic perturbation theory. Additionally, reliability- based sensitivity indices were derived to measure the parameter importance of random input variables. An illustrative example of the bogie frame with incomplete probabilistic information was used to demonstrate the applications of the proposed method for reliability and reliability-based sensitivity estimation in terms of strength and resonant frequency reliability. The results indicate that vertical loads and the material density have more of an impact on reliability than other variables of the bogie frame.

Imprecise reliability assessment of generating systems involving interval probability

Probabilistic information about random variables describing equipment's reliability is not complete when there is a lack of statistical data about failure. The traditional reliability assessment cannot deal with the incomplete probabilistic information. Interval probability is an efficient method to address the incomplete probabilistic information. The interval value of reliability indices can reflect the degree of completeness of probabilistic information. In this study, the optimisation model of generating systems’ imprecise reliability assessment (IRA) is established and the efficient unit-adding algorithm is proposed to obtain the upper and lower bounds of reliability indices. The probability density and the expectation of reliability indices are also calculated by the Monte Carlo simulation method. In the process of IRA, massive calculations of the traditional reliability are needed, therefore the recursive convolution algorithm, which is based on the outage capacity table and has the merit of high-computation efficiency, is adopted. A case study on a revised IEEE-RTS79 system shows the rationality and equity of the presented method.

Imprecise Risk Assessment of Power System

The incomplete probabilistic information can lead to imprecision. The traditional power system risk assessment can only deal with random information, but it cannot deal with the imprecise information. Interval Probability (IP) can reflect both randomness and imprecision. The risk assessment of power system based on IP is an effective method to deal with imprecision and can provide more useful information to the decision-makers. In the paper, the completeness degree of probabilistic information was depicted by IP. The nonlinear optimization models for imprecise risk assessment of generating system and composite generation-transmission system were established. And the genetic algorithm was used to obtain the upper and lower bound of reliability indices. Case study on revised IEEE-RTS79 and IEEE-RBTS system showed the rationality and equity of presented method.

Medical Heuristics and Cognitive Decision Errors: Modeling Thought Processes Through an Integrative Curriculum

OPEN ACCESSMarch 20, 2013Medical Heuristics and Cognitive Decision Errors: Modeling Thought Processes Through an Integrative Curriculum William F. Paolo, MD William F. Paolo, MD State University of New York Upstate Medical University Google Scholar More articles by this author https://doi.org/10.15766/mep_2374-8265.9375 SectionsAboutAbstract ToolsDownload Citations ShareFacebookTwitterEmail AbstractAbstractEmergency medicine (EM) residents are forced to make patient care decisions based upon incomplete probabilistic information and prior experience. Heuristics are a useful cognitive tool via which limited information is processed and cognitive solutions are rapidly identified. However, the inappropriate unconscious dependence on these cognitive shortcuts often leads to decision errors due to the inability to recognize the biasing influence of mental processing. The goal of this educational resource is the implementation of multi-layered curriculum through which EM residents learn the basics of heuristic decision-making as well as the associated cognitive errors. The target audience is EM residents of all levels. The curriculum has three essential components that are complimentary to one another. The curriculum is administered over 5 hours that are divided into three 30-minute introductory lectures, 1 hour of simulation, a written posttest, and a final 1-hour simulation. Necessary equipment includes PowerPoint capabilities and a simulation laboratory. The curriculum has been previously used by approximately 30 emergency medicine residents ranging in PGY year from 1–3. The curriculum has been met with success and has been well-received. Educational Objectives By the end of this module, the learner will be able to: Identify common cognitive errors.Demonstrate an understanding of the basics of cognitive decision theory. Sign up for the latest publications from MedEdPORTAL Add your email below FILES INCLUDEDReferencesRelatedDetails FILES INCLUDED Included in this publication: Case 1.docx Case 2.docx Instructor's Guide.docx Lecture 1.pptx Lecture 2.pptx Lecture 3.pptx Test.docx To view all publication components, extract (i.e., unzip) them from the downloaded .zip file. Download editor’s noteThis publication may contain technology or a display format that is no longer in use. Copyright & Permissions© 2013 Paolo. This is an open-access article distributed under the terms of the Creative Commons Attribution license.KeywordsDecision TheoryHeuristics Disclosures None to report. Funding/Support None to report. Loading ...

Sensitivity importance‐based robust optimization of structures with incomplete probabilistic information

SUMMARYRobust design optimization (RDO) is usually performed by minimizing the nominal value of a performance function and its dispersion considering equal importance to each individual gradient of the performance function. However, it is well known that all gradients are not equally important. An efficient sensitivity importance‐based RDO technique is proposed in the present study for optimum design of structures characterized by bounded uncertain input parameters. The basic idea of the proposed RDO formulation is to improve the robustness of a performance function by using a new gradient index that utilizes the importance factors proportional to the importance of the gradients of the performance function. The same concept is also extended to the constraints. To enhance the robustness of the constraints, the constraint functions are also modified by using the importance factor proportional to the importance of the associated gradient of the constraint. Because all the variables are not equally important to capture the presence of uncertainty, an improved robust solution is obtained by the proposed approach compared with the conventional RDO approach. The present formulation is illustrated with the help of three informative examples. The results are compared with the conventional RDO results to study the effectiveness of the proposed RDO approach. Copyright © 2012 John Wiley & Sons, Ltd.

Worst case risk measurement: Back to the future?

This paper studies the problem of finding best-possible upper bounds on a rich class of risk measures, expressible as integrals with respect to measures, under incomplete probabilistic information. Both univariate and multivariate risk measurement problems are considered. The extremal probability distributions, generating the worst case scenarios, are also identified. The problem of worst case risk measurement has been studied extensively by Etienne De Vijlder and his co-authors, within the framework of finite-dimensional convex analysis. This paper revisits and extends some of their results.

Representation, Propagation, and Decision Issues in Risk Analysis Under Incomplete Probabilistic Information

This article tries to clarify the potential role to be played by uncertainty theories such as imprecise probabilities, random sets, and possibility theory in the risk analysis process. Instead of opposing an objective bounding analysis, where only statistically founded probability distributions are taken into account, to the full-fledged probabilistic approach, exploiting expert subjective judgment, we advocate the idea that both analyses are useful and should be articulated with one another. Moreover, the idea that risk analysis under incomplete information is purely objective is misconceived. The use of uncertainty theories cannot be reduced to a choice between probability distributions and intervals. Indeed, they offer representation tools that are more expressive than each of the latter approaches and can capture expert judgments while being faithful to their limited precision. Consequences of this thesis are examined for uncertainty elicitation, propagation, and at the decision-making step.

Explicit neural signals reflecting reward uncertainty

The acknowledged importance of uncertainty in economic decision making has stimulated the search for neural signals that could influence learning and inform decision mechanisms. Current views distinguish two forms of uncertainty, namely risk and ambiguity, depending on whether the probability distributions of outcomes are known or unknown. Behavioural neurophysiological studies on dopamine neurons revealed a risk signal, which covaried with the standard deviation or variance of the magnitude of juice rewards and occurred separately from reward value coding. Human imaging studies identified similarly distinct risk signals for monetary rewards in the striatum and orbitofrontal cortex (OFC), thus fulfilling a requirement for the mean variance approach of economic decision theory. The orbitofrontal risk signal covaried with individual risk attitudes, possibly explaining individual differences in risk perception and risky decision making. Ambiguous gambles with incomplete probabilistic information induced stronger brain signals than risky gambles in OFC and amygdala, suggesting that the brain's reward system signals the partial lack of information. The brain can use the uncertainty signals to assess the uncertainty of rewards, influence learning, modulate the value of uncertain rewards and make appropriate behavioural choices between only partly known options.

An ignorant belief network to forecast glucose concentration from clinical databases

Ignorant Belief Networks (IBNs) are a class of Bayesian Belief Networks (BBNs) able to reason on the basis of incomplete probabilistic information and to incrementally refine the precision of the inferred probabilities as more information becomes available. In this paper, we will describe how can be used to develop a system able to forecast blood glucose concentration in patients affected by insulin dependent diabetes mellitus (IDDM). The major difference between our approach and the traditional ones is that probability distributions over the IBN are not provided by some human expert or by the current literature but they are directly extracted from a clinical database of IDDM patients. This choice capitalizes on the large amount of information generated by the daily control of blood glucose and allows the system to improve the accuracy of predictions as more information becomes available. We will show how, even with a very small subset of the information needed to specify a BBN, the IBN is able to carry out predictions about the future blood glucose concentration in a patient by explicitly taking into consideration the level of ignorance embedded in the network.