Decision making under uncertainty with fuzzy targets

This paper discusses the issue of how to use fuzzy targets in the target-based model for decision making under uncertainty. After introducing a target-based interpretation of the expected value on which it is shown that this model implicitly assumes a neutral behavior on attitude about the target, we examine the issue of using fuzzy targets considering different attitudes about the target selection of the decision maker. We also discuss the problem for situations on which the decision maker’s attitude about target may change according to different states of nature. Especially, it is shown that the target-based approach can provide an unified way for solving the problem of fuzzy decision making with uncertainty about the state of nature and imprecision about payoffs. Several numerical examples are given for illustration of the discussed issues.     

An interval-parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty

Planning for water quality management systems is complicated by a variety of uncertainties and nonlinearities, where difficulties in formulating and solving the resulting inexact nonlinear optimization problems exist. With the purpose of tackling such difficulties, this paper presents the development of an interval-fuzzy nonlinear programming (IFNP) model for water quality management under uncertainty. Methods of interval and fuzzy programming were integrated within a general framework to address uncertainties in the left- and right-hand sides of the nonlinear constraints. Uncertainties in water quality, pollutant loading, and the system objective were reflected through the developed IFNP model. The method of piecewise linearization was developed for dealing with the nonlinearity of the objective function. A case study for water quality management planning in the Changsha section of the Xiangjiang River was then conducted for demonstrating applicability of the developed IFNP model. The results demonstrated that the accuracy of solutions through linearized method normally rises positively with the increase of linearization levels. It was also indicated that the proposed linearization method was effective in dealing with IFNP problems; uncertainties can be communicated into optimization process and generate reliable solutions for decision variables and objectives; the decision alternatives can be obtained by adjusting different combinations of the decision variables within their solution intervals. It also suggested that the linearized method should be used under detailed error analysis in tackling IFNP problems.     

Measurement of uncertainty in peptide molecular weight determination using size-exclusion chromatography with multi-angle laser light-scattering detection and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

The molecular weight of biopolymers such as peptides or proteins is vital information for understanding their physical/chemical properties. The matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) and size-exclusion chromotography-multi-angle laser light scattering (SEC-MALLS) techniques each with its advantages and limitations were used for molecular weight determination of the SPf66 peptide. The precision of each method was studied using a two-factor fully-nested design with all the analyses performed by the same operator on a single instrument. The overall precision corresponded to the time-different intermediate precision (i.e. time and repeatability conditions). In the case of SEC-MALLS, all potential uncertainty components were carefully evaluated in an Ishikawa diagram, then included and mathematically combined with the uncertainty arising from the accuracy assessment to provide the overall uncertainty. In this case, the refractive-index increment with solute concentration value (dn/dc) provided the most significant contribution to the combined uncertainty. A method for its quantitation is proposed. The accuracy of method B (SEC-MALLS) against reference method A (MALDI-TOF-MS) was assessed using the interval testing hypothesis to limit the risk of unacceptable bias. The results indicate that the bias of B is higher than the limit established at 5%, and is therefore not traceable to A under the studied conditions.     

Preliminary study to prepare a reference material of styrene metabolites – mandelic acid and phenylglyoxylic acid – in human urine

 A preliminary batch of the reference material was prepared by freeze-drying pooled urine samples obtained from healthy persons occupationally exposed to styrene. Tests for homogeneity and stability were performed by determining urine concentrations of mandelic (MA) and phenylglyoxylic acids (PGA). The urinary MA and PGA concentrations were followed over an 8-month period using high performance liquid chromatography (HPLC). No changes of the concentration values were found. Pure PA and PGA from Merck and Fluka, respectively, were used for traceability purposes, because certified or standard reference materials for MA and PGA do not exist. Control material ClinChek-Urine Control (Recipe) was analysed simultaneously. The mean values of MA and PGA compared well with the means of control samples and fell within the control range. The certified values and their uncertainties were evaluated from the results of interlaboratory comparisons, homogeneity (277.0 ± 7.4 mg L⁻¹ for MA and 148.0 ± 4.7 mg L⁻¹ for FGA) and stability tests. The values are unweighted arithmetical averages of accepted results and their uncertainties are combined uncertainties enlarged by coefficient k=1, evaluated from the standard uncertainties of the interlaboratory comparison, homogeneity and stability tests. Received: 17 September 2002 Accepted: 1 November 2002 Acknowledgement This work was supported by the Internal Grant Agency of Ministry of Health of the Czech Republic (Grant NJ/6784–3). Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to I. Šperlingová     

The use of uncertainty estimates of test results in comparisons with acceptance limits

When a test is performed in order to qualify a material or a product for a certain use, the result is generally compared with an acceptance limit. The test result has an uncertainty which should be estimated and stated (e.g. in accordance with GUM). Very often this is not the case. Further, discussions often arise on the issue of how the uncertainty shall be considered in relationship to the acceptance limit. The intention of this note is to describe, in simple terms, the statistical background and to give some recommendations. In short, there are two clean-cut, extreme situations. The first case is when the uncertainty of the testing procedure is the dominating factor. Here it is found that the estimates of single laboratories cannot, generally, be used for comparisons with acceptance limits. One should have standardised, well-verified estimates based on comprehensive investigations of the method. It can also be concluded that comparisons between test results and acceptance limits have to be made with regard to the actual circumstances, as, e.g. how the acceptance limit is related to the risk. In the second case, the variation in the property of the material or product dominates and the uncertainty of the testing procedure is negligible. When the results are non-quantitative (go – no go), statistical methods can be used to estimate the risk taken with a certain sampling and acceptance strategy that a certain proportion of the batch to be delivered does not qualify. This should be considered more often in standardisation of product test methods. When the results are quantitative, a statistical analysis should be performed and the uncertainty should be compared with the acceptance limit as before, from the actual circumstances. When effects of testing uncertainty and product variation are comparable a sound treatment requires extensive experimental work. No short cuts can be made without loss of confidence! Received: 17 August 2001 Accepted: 21 March 2002     

环境监测仪器精密度及总不确定度初探

本文以日立１８０－８０原子吸收分光光度计为例进行了仪器精密度及总不确定度实验的初步探讨，同时作出了该仪器适用性的判断。     

Determination of methylmercury in marine sediment samples: Method validation and occurrence data

The determination of methylmercury (MeHg) in sediment samples is a difficult task due to the extremely low MeHg/THg (total mercury) ratio and species interconversion. Here, we present the method validation of a cost-effective fit-for-purpose analytical procedure for the measurement of MeHg in sediments, which is based on aqueous phase ethylation, followed by purge and trap and hyphenated gas chromatography–pyrolysis–atomic fluorescence spectrometry (GC–Py–AFS) separation and detection. Four different extraction techniques, namely acid and alkaline leaching followed by solvent extraction and evaporation, microwave-assisted extraction with 2-mercaptoethanol, and acid leaching, solvent extraction and back extraction into sodium thiosulfate, were examined regarding their potential to selectively extract MeHg from estuarine sediment IAEA-405 certified reference material (CRM). The procedure based on acid leaching with HNO₃/CuSO₄, solvent extraction and back extraction into Na₂S₂O₃ yielded the highest extraction recovery, i.e., 94 ± 3% and offered the possibility to perform the extraction of a large number of samples in a short time, by eliminating the evaporation step. The artifact formation of MeHg was evaluated by high performance liquid chromatography coupled to inductively coupled plasma mass spectrometry (HPLC–ICP–MS), using isotopically enriched Me²⁰¹Hg and ²⁰²Hg and it was found to be nonexistent. A full validation approach in line with ISO 17025 and Eurachem guidelines was followed. With this in mind, blanks, selectivity, working range (1–800 pg), linearity (0.9995), recovery (94–96%), repeatability (3%), intermediate precision (4%), limit of detection (0.45 pg) and limit of quantification (0.85 pg) were systematically assessed with CRM IAEA-405. The uncertainty budget was calculated and the major contribution to the combined uncertainty (16.24%, k = 2) was found to arise from the uncertainty associated with recovery (74.1%). Demonstration of traceability of measurement results is also presented. The validated measurement procedure was applied to the determination of MeHg incurred in sediments from a highly polluted and scarcely studied area in the Caribbean region.     

智能岩石力学及其内容

本文针对岩石力学研究中目前存在的问题和信息时代的要求, 提出了21世纪的智能岩石力学的新思想和研究内容。它是综合现有各种行之有效的方法, 系统研究岩石工程问题, 提高岩石力学解决复杂问题的准确性。     

Total error and uncertainty: Friends or foes?

Guidelines ISO 17025 and ISO 15189 aim to improve the quality-assurance scheme of laboratories. Reliable analytical results are of central importance due to the critical decisions that are taken with them. ISO 17025 and ISO 15189 therefore require that analytical methods be validated and that laboratories can routinely provide the measurement uncertainty of the results of measurements. To evaluate the fitness of purpose of analytical methods, total error is increasingly applied to assess the reliability of results generated by analytical methods. However, the ISO requirement to estimate measurement uncertainty seems opposed to the concept of total error, leading to delays in laboratories implementing ISO 17025 and ISO 15189 and confusion for the analysts. This article therefore aims to clarify the divergences between total error and measurement uncertainty, but also to discuss their main similarities and emphasize their implementation.     

Large deviation theory for a homogenized and “corrected” elliptic ODE

We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a “pointwise” large deviation principle (LDP) for the full solution and approximate this LDP with a more tractable form. Applications to uncertainty quantification are considered.