Fuzzy evidence theory and Bayesian networks for process systems risk analysis

Abstract

Quantitative risk assessment (QRA) approaches systematically evaluate the likelihood, impacts, and risk of adverse events. QRA using fault tree analysis (FTA) is based on the assumptions that failure events have crisp probabilities and they are statistically independent. The crisp probabilities of the events are often absent, which leads to data uncertainty. However, the independence assumption leads to model uncertainty. Experts’ knowledge can be utilized to obtain unknown failure data; however, this process itself is subject to different issues such as imprecision, incompleteness, and lack of consensus. For this reason, to minimize the overall uncertainty in QRA, in addition to addressing the uncertainties in the knowledge, it is equally important to combine the opinions of multiple experts and update prior beliefs based on new evidence. In this article, a novel methodology is proposed for QRA by combining fuzzy set theory and evidence theory with Bayesian networks to describe the uncertainties, aggregate experts’ opinions, and update prior probabilities when new evidences become available. Additionally, sensitivity analysis is performed to identify the most critical events in the FTA. The effectiveness of the proposed approach has been demonstrated via application to a practical system.     

Expert systems in histopathology. IV. The management of uncertainty.

Expert systems deal with data that are categorical and conceptual, that represent elements of fuzzy sets and that often, by themselves, do not allow an unequivocal decision. The management of uncertainty in expert systems thus becomes a crucial issue. It involves defining measures of uncertainty and procedures for combining accumulating evidence in a manner that properly considers the dependence structure of diagnostic clues. Probability theory offers valuable procedures for uncertainty assessment; however, their practical application in the domain of quantitative histopathology and histopathologic diagnosis can be problematic.     

An extended multi-objective mixed integer programming for water resources management through possibility theory

In this study, we develop an extended multi-objective mixed integer programming (EMOMIP) approach for water resources management under uncertainty, in which the parameters are fuzzy random variables while the decision variables are interval variables. Furthermore, some alternatives are considered to retrieve the difference between the quantities of promised water-allocation targets and the actual allocated water. Then, the proposed EMOMIP for the problem is solved by a new method using fuzzy random chance-constrained programming based on the idea of possibility theory. This method can satisfy both optimistic and pessimistic decision makers simultaneously. Finally, a real example is given to explain the proposed method.     

Reasoning in uncertainties. An analysis of five strategies and their suitability in pathology

In reasoning systems, uncertainty plays a crucial part, especially for those fields in which judgements are essential, as in pathology. Uncertainty has several aspects, such as prevalence of diseases, occurrence of findings and the sensitivity and predictive value of findings. For the functioning of a reasoning system, two aspects are crucial: (1) the internal representation of the uncertainty and (2) the way in which the uncertainty is propagated in the reasoning process when combining formal statements. Five well-known reasoning strategies (Bayes' probability theory, MYCIN's certainty factor model, fuzzy set theory, the theory of Dempster-Shafer and Pathfinder's scoring mechanism) are compared, with particular attention to: (1) Under what conditions will the model function? In particular, what information is to be specified a priori to the system? (2) Can the different aspects of uncertainty be dealt with as separate entities? (3) How are unknown uncertainties dealt with? (4) How is evidence in favor of a hypothesis combined with evidence against it? (5) How does the model treat the simultaneous occurrence of more than one disorder, that is, how does the model support reasoning with compound hypotheses? It is preliminarily concluded that the different aspects of uncertainty are expressed as separate entities only in Pathfinder and probability theory. Hence, the other models do not accurately represent uncertain knowledge. Also, such theoretically attractive models as the Bayes, MYCIN and Dempster-Shafer theory can only function properly under the tight condition of mutual exclusiveness of hypotheses, which is not always suited for broader areas of pathology. They may, however, be suited for smaller areas, with a limited number of defined diseases and a limited number of features. All models but the Bayes model lack a predictable performance since there is no (or only a partial) underlying theory to guarantee minimization of the overall error.     

Fuzzy systems vegetation theory

Fuzzy systems vegetation theory is a comprehensive framework for the expression of vegetation theory and conceptual models, as well as the development of vegetation analyses. It is applicable to vegetation/environment relations, vegetation dynamics, and the effects of environmental dynamics on vegetation composition. Fuzzy systems vegetation theory is a fuzzy set generalization of dynamical systems theory and incorporates a formal logic and mathematics. This paper presents the elements of fuzzy systems vegetation theory and discusses the relationship of the fuzzy systems theory to the geometric concepts generally employed in vegetation theory.     

Ordination on the basis of fuzzy set theory

Fuzzy set theory is an extension of classical set theory where elements of a set have grades of membership ranging from zero for non-membership to one for full membership. Exactly as for classical sets, there exist operators, relations, and mappings appropriate for these fuzzy sets. This paper presents the concepts of fuzzy sets, operations, relations, and mappings in an ecological context. Fuzzy set theory is then established as a theoretical basis for ordination, and is employed in a sequence of examples in an analysis of forest vegetation of western Montana, U.S.A. The example ordinations show how site characteristics can be analyzed for their effect on vegetation composition, and how different site factors can be synthesized into complex environmental factors using the calculus of fuzzy set theory.In contrast to current ordination methods, ordinations based on fuzzy set theory require the investigator to hypothesize an ecological relationship between vegetation and environment, or between different vegatation compositions, before constructing the ordination. The plotted ordination is then viewed as evidence to corroborate or discredit the hypothesis.I am grateful to Dr R. D. Pfister (formerly USDA Forest Service) for kind permission to publish data from a Forest Service study.I would like to gratefully acknowledge the helpful comments and criticisms of Drs. G. Cottam, J. D. Aber, T. F. H. Allen, E. W. Beals, I. C. Prentice, C. G. Lorimer, and two anonymous reviewers.Taxonomic nomenclature follows Hitchcock & Cronquist (1973).I would like to thank the Dean of the College of Letters and Sciences, University of Wisconsin—Madison, for a fellowship which supported this research, and the Department of Botany for computer funds to perform the analyses.     

On the use of possibility theory in uncertainty analysis of life cycle inventory

Purpose  

The purpose of this paper is to enhance the mathematical and physical understanding of practitioners of uncertainty analysis of life cycle inventory (LCI), on the application of possibility theory. The main questions dealt with are (1) clear definition of the terms—“necessity–possibility,” “probability,” “belief–plausibility,” and of their mutual relationships; (2) what justifies the substitution of classical probability for possibility; (3) mutual comparison of, and transformations in both senses between probability and possibility uncertainty measures; (4) how to construct meaningful input possibility measures from available probabilistic/statistic information; and (5) comparative analysis of the solutions of the problem of data uncertainty propagation in LCI, afforded, respectively, by probabilistic Monte Carlo simulation and possibilistic fuzzy interval arithmetic.     

粗糙集模糊聚类分析法在昆虫分类研究中的应用

本文根据昆虫图像,对半翅目、鳞翅目、鞘翅目的28种昆虫提取的形状参数、叶状性、球状性等7项数学形态特征进行了粗糙集模糊聚类分析。在粗糙集处理的基础上,分别进行7指标和3指标（相对约简）两种不同的模糊聚类分析法相比较。结果显示,在作为目级阶元分类指标时,各项特征的重要性依次为：(似圆度、偏心率)＞（亮斑数、球状性、圆形性）＞（叶状性、形状参数）;粗糙集分类正确率优于模糊聚类分析法;粗糙集处理后的3指标分类正确率优于未处理的7指标分类正确率。结论认为,粗糙集理论在昆虫依据数学形态特征进行分类方面与统计分析方法相比更有优势,粗糙集滤过指标后再进行模糊聚类法分析在昆虫分类研究上具有重要意义。     

Optimal applicator placement in hepatic radiofrequency ablation on the basis of rare data

In this paper, a numerical procedure to determine an optimal applicator placement for hepatic radiofrequency ablation incorporating uncertain material parameters is presented. The main focus is set on the treatment of subjective and rare data-based information. For this purpose, we employ the theory of fuzzy sets and model uncertain parameters as fuzzy quantities. While fuzzy modelling has been established in structural engineering in the recent past, it is novel in biomedical engineering. Incorporating fuzzy quantities within an optimisation task is basically innovative. In our context, fuzzy modelling allows us to determine an optimal applicator placement that maximises the therapy success under the given uncertainty conditions. The applicability of our method is demonstrated by means of an example case.     

Paternal age and Down syndrome.

The frequency of Down syndrome (DS) in infants of older fathers has been examined in two sets of data. The effect of maternal age was controlled by single years of age. Lack of tight control has been an important weakness of other studies on this subject. Data obtained in metropolitan Atlanta by an intensive case-ascertainment program showed no overall excess of DS infants born to older fathers. Nor was there evidence of such an effect in recent birth certificate data made available by the National Center for Health Statistics. The Atlanta data suggest an increased number of DS infants born to older fathers who had children by women less than or equal to 34 years. However, there was a small deficiency of DS infants born to older fathers by women greater than or equal to 35 years. The possibility of a paternal-age effect remains open, but the available data suggest that, if it exists, it is quite small.     

The tissue organization field theory of cancer: a testable replacement for the somatic mutation theory

The somatic mutation theory (SMT) of cancer has been and remains the prevalent theory attempting to explain how neoplasms arise and progress. This theory proposes that cancer is a clonal, cell-based disease, and implicitly assumes that quiescence is the default state of cells in multicellular organisms. The SMT has not been rigorously tested, and several lines of evidence raise questions that are not addressed by this theory. Herein, we propose experimental strategies that may validate the SMT. We also call attention to an alternative theory of carcinogenesis, the tissue organization field theory (TOFT), which posits that cancer is a tissue-based disease and that proliferation is the default state of all cells. Based on epistemological and experimental evidence, we argue that the TOFT compellingly explains carcinogenesis, while placing it within an evolutionarily relevant context.     

The theory of functional systems and purposeful behavior

The role of probability forecasting in the purposive behavior under conditions of subjective uncertainty is considered in terms of the theory of functional systems. Participation of the probability forecasting in the afferent synthesis, goal formation, formation of the acceptor of action result and action program, and, finally, in the action program actualization is substantiated. The model of behavior under conditions of subjective uncertainty is advanced. It includes all the classical elements of the model of behavioral act developed by P.K. Anokhin. In order to take into account the probability aspects of behavior, the role of probability forecasting is emphasized at every stage of the system functioning. In addition to the classical elements, two novel components are introduced. These are the "memory buffer" (results of searching reactions) and the apparatus of probability decisions about changes in the action program. By the memory buffer an apparatus is meant, which gathers and stores the information about the results of many behavioral acts performed during the actualization of the action program. This information is used in the process of making a probability decision as whether to alter or not the action program after each specific behavioral act. Such an approach integrates the probability forecasting and the theory of functional systems. The theory becomes universal, i.e., applicable not only to deterministic but also to probabilistic environments.     

Spatial Uncertainty Modeling of Fuzzy Information in Images for Pattern Classification

The modeling of the spatial distribution of image properties is important for many pattern recognition problems in science and engineering. Mathematical methods are needed to quantify the variability of this spatial distribution based on which a decision of classification can be made in an optimal sense. However, image properties are often subject to uncertainty due to both incomplete and imprecise information. This paper presents an integrated approach for estimating the spatial uncertainty of vagueness in images using the theory of geostatistics and the calculus of probability measures of fuzzy events. Such a model for the quantification of spatial uncertainty is utilized as a new image feature extraction method, based on which classifiers can be trained to perform the task of pattern recognition. Applications of the proposed algorithm to the classification of various types of image data suggest the usefulness of the proposed uncertainty modeling technique for texture feature extraction.     

Periodic health examination, 1996 update: 1. Prenatal screening for and diagnosis of Down syndrome. Canadian Task Force on the Periodic Health Examination.

OBJECTIVE: To make recommendations to physicians providing prenatal care on (1) whether prenatal screening for and diagnosis of Down syndrome (DS) is advisable and (2) alternative screening and diagnosis manoeuvres. OPTIONS: "Triple-marker" screening of maternal serum levels of alpha-fetoprotein, human chorionic gonadotropin and unconjugated estriol; fetal ultrasonographic examination; amniocentesis; and chorionic villus sampling (CVS). OUTCOMES: Accuracy of detection of DS in fetuses, and risks to the mother, including psychologic distress, and to the fetus from the screening and diagnostic interventions. EVIDENCE: A MEDLINE search for relevant articles published from Jan. 1, 1966, to Mar. 31, 1994, with the use of MeSH terms "Down syndrome," "prenatal diagnosis," "screening," "prevention," "amniocentesis," "chorionic villus sampling," "ultrasonography," "anxiety," "depression" and "psychological stress" and a manual search of bibliographies, recent issues of key journals and Current Contents. VALUES: The evidence-based methods and values of the Canadian Task Force on the Periodic Health Examination were used. A high value was placed on providing pregnant women with the opportunity to determine whether they are carrying a fetus with DS and to make choices concerning the termination of the pregnancy. The economic issues involved are complex and were not considered. BENEFITS, HARMS AND COSTS: Triple-marker screening identifies an estimated 58% of fetuses with DS, but it has an estimated rate of true-positive results of 0.1% and of false-positive results of 3.7% (given a risk cut-off of one chance in 190 of DS). These rates vary with maternal age and the risk cut-off chosen. Women with a known risk of having a fetus with DS (e.g., those who have had a previous child with DS) may benefit from a reduction in anxiety after confirmation that their fetus does not have DS. Screening allows women at low risk of having a child with DS to detect fetuses with the syndrome, but may cause psychologic distress if there is a false-positive screening test result. Up to 20% of women with positive results of screening tests may decline to undergo a subsequent amniocentesis. Amniocentesis and CVS are very accurate in diagnosing DS in fetuses and have a very low rate of serious complications for the mother. Amniocentesis is associated with a 1.7% rate of fetal loss when it is performed after 16 weeks'' gestation, whereas the rate among controls is 0.7% (for a difference of 1%, 95% confidence interval 0.3% to 1.5%). CVS entails a greater risk of fetal loss than amniocentesis (odds ratio 1.32, 95% confidence interval 1.11 to 1.57). There is little evidence from controlled trials of significant associations between amniocentesis or CVS and neonatal morbidity or malformations; however, samples have been too small to show differences in rare outcomes. Results from some case-control studies suggest that CVS increases the risk of transverse limb deficiency. Costs were not considered because they are beyond the scope of this review. RECOMMENDATIONS: There is fair evidence to offer triple-marker screening through a comprehensive program to pregnant women under 35 years of age (grade B recommendation). Women given detailed information about serum-marker screening show more satisfaction with the screening than those not given this information. There is fair evidence to offer amniocentesis or CVS to pregnant women 35 years of age and older and to women with a history of a fetus with DS or of a chromosome 21 anomaly (grade B recommendation). Information on the limitations and advantages of each procedure should be offered. Triple-marker screening may be offered as an alternative to CVS or amniocentesis to pregnant women over 35. VALIDATION: Recommendations concerning prenatal diagnosis are similar to those of the US Preventive Services Task Force, the Society of Obstetricians and Gynaecologists of Canada, the Canadian College of Medical Geneticists and the Cochrane Pregnancy and Childbirth Group. No previous specific recommendations concerning triple-maker screening exist. SPONSORS: These guidelines were developed and endorsed by the Canadian Task Force on the Periodic Health Examination, which is funded by Health Canada and the National Health Research and Development Program.     

A Recipe for Unconventional Evenness Measures

The degree to which abundances are evenly divided among the species of a given community is a basic property of any biological community. Several evenness indices have thus far been proposed in ecological literature. However, despite their vast potential applicability in ecological research, none seems to be generally preferred. In this paper, I first summarize the basic requirements that evenness measures should meet to adequately behave in ecological studies. Then, I discuss the major drawbacks of these requirements and propose an alternative family of measures that are based on the notion of specificity used in fuzzy set theory for measuring the uncertainty associated with a fuzzy set.     

Flagellar hydrodynamics. A comparison between resistive-force theory and slender-body theory.

This paper investigates the accuracy of the resistive-force theory (Gray and Hancock method) which is commonly used for hydrodynamic analysis of swimming flagella. We made a comparison between the forces, bending moments, and shear moments calculated by resistive-force theory and by the more accurate slender-body theory for large-amplitude, planar wave forms computed for a flagellar model. By making an upward empirical adjustment, by about 35%, of the classical drag coefficient values used in the resistive-force theory calculations, we obtained good agreement between the distributions of the forces and moments along the length of the flagellum predicted by the two methods when the flagellum has no cell body attached. After this adjustment, we found the rate of energy expenditure calculated by the two methods for the few typical test cases to be almost identical. The resistive-force theory is thus completely satisfactory for use in analysis of mechanisms for the control of flagellar bending, at the current level of sophistication of this analysis. We also examined the effects of the presence of a cell body attached to one end of the flagellum, which modifies the flow field experienced by the flagellum. This interaction, which is not considered in resistive-force theory, is probably insignificant for small cell bodies, such as the heads of simple spermatozoa, but for larger cell bodies, or cell bodies that have large-amplitude motions transverse to the swimming direction, use of slender-body theory is required for accurate analysis.     

基于模糊理论预测CpG岛新方法

启动子区域的CpG岛的异常甲基化是识别癌症的重要标志之一。目前已经建立的一些CpG岛的预测思想和方法都有自身的缺点,基于模糊理论的预测思想从贴进度的角度来判定CpG岛,能更容易地找到被以往方法所忽略的具有更多生物学意义的CpG岛。本研究通过构建属于CpG岛集合的隶属函数,计算候选序列的隶属度,找出所有的可接受隶属程度的CpG岛。将该方法应用于UCSC数据库中的一段序列（hg18．chr1．31618510.31623510.-1000）进行预测,发现提高了预测的精确度。可见应用模糊理论预测CpG岛具有一定的可行性,利用选取不同的截集,可以得到更为精确的CpG岛。     

Quantification of formaldehyde-mediated covalent adducts of adriamycin with DNA.

Duplex DNA incubated with adriamycin, dithiothreitol (DTT), and Fe3+ under aerobic, aqueous conditions yields double-stranded (DS) DNA bands by denaturing polyacrylamide gel electrophoresis (DPAGE) analysis, characteristic of DNAs which are interstrand cross-linked. Another laboratory has provided evidence that formaldehyde produced under these conditions promotes the covalent linkage of adriamycin to one strand of DNA and suggested that this complex results in the anomalous DPAGE behavior. We provide herein strong support for this interpretation. We show: (a) that mixtures of DNA and adriamycin incubated with DTT/Fe3+, H2O2, or formaldehyde all show DS DNA bands on DPAGE, (b) that the DS DNA bands and the formaldehyde-mediated lesion (detected by an indirect, GC-MS analysis) form with similar time courses, and in similar amounts, and (c) that the DNA in the DS DNA bands contains approximately one such lesion per DNA, whereas the single-stranded DNA is devoid of it. These results further support the interpretation that adriamycin does not create interstrand cross-links in DNA, and that the DS DNA observed in DPAGE experiments derives from the formaldehyde-mediated monoadduct.     

Applying Fuzzy and Probabilistic Uncertainty Concepts to the Material Flow Analysis of Palladium in Austria

Material flow analysis (MFA) is a widely applied tool to investigate resource and recycling systems of metals and minerals. Owing to data limitations and restricted system understanding, MFA results are inherently uncertain. To demonstrate the systematic implementation of uncertainty analysis in MFA, two mathematical concepts for the quantification of uncertainties were applied to Austrian palladium (Pd) resource flows and evaluated: (1) uncertainty ranges expressed by fuzzy sets and (2) uncertainty ranges defined by normal distributions given as mean values and standard deviations. Whereas normal distributions represent the traditional approach for quantifying uncertainties in MFA, fuzzy sets may offer additional benefits in relation to uncertainty quantification in cases of scarce information. With respect to the Pd case study, the fuzzy representation of uncertain quantities is more consistent with the actual data availability in cases of incomplete databases, and fuzzy sets serve to highlight the effect of uncertainty on resource efficiency indicators derived from the MFA results. For both approaches, data reconciliation procedures offer the potential to reduce uncertainty and evaluate the plausibility of the model results. With respect to Pd resource management, improved formal collection of end‐of‐life (EOL) consumer products is identified as a key factor in increasing the recycling efficiency. In particular, the partial export of EOL vehicles represents a substantial loss of Pd from the Austrian resource system, whereas approximately 70% of the Pd in the EOL consumer products is recovered in waste management. In conclusion, systematic uncertainty analysis is an integral part of MFA required to provide robust decision support in resource management.