Peida Xu

Dependence Assessment in Human Reliability Analysis Using Evidence Theory and AHP

Dependence assessment among human errors in human reliability analysis (HRA) is an important issue. Many of the dependence assessment methods in HRA rely heavily on the experts opinion, thus are subjective and may sometimes cause inconsistency. In this article, we propose a computational model based on the Dempster-Shafer evidence theory (DSET) and the analytic hierarchy process (AHP) method to handle dependence in HRA. First, dependence influencing factors among human tasks are identified and the weights of the factors are determined by experts using the AHP method. Second, judgment on each factor is given by the analyst referring to anchors and linguistic labels. Third, the judgments are represented as basic belief assignments (BBAs) and are integrated into a fused BBA by weighted average combination in DSET. Finally, the CHEP is calculated based on the fused BBA. The proposed model can deal with ambiguity and the degree of confidence in the judgments, and is able to reduce the subjectivity and improve the consistency in the evaluation process.

IFSJSP: A novel methodology for the Job-Shop Scheduling Problem based on intuitionistic fuzzy sets

The Job-Shop Scheduling Problem (JSP) is an important concern in advanced manufacturing systems. In real applications, uncertainties exist practically everywhere in the JSP, ranging from engineering design to product manufacturing, product operating conditions and maintenance. A variety of approaches have been proposed to handle the uncertain information. Among them, the Intuitionistic Fuzzy Sets (IFS) is a novel tool with the ability to handle vague information and is widely used in many fields. This paper develops a method to address the JSP under an uncertain environment based on IFSs. Another contribution of this paper is to put forward a generalised (or extended) IFS to process the additive operation and to compare the operation between two IFSs. The methodology is illustrated using a three-step procedure. First, a transformation is constructed to convert the uncertain information in the JSP into the corresponding IFS. Secondly, a novel addition operation between two IFSs is proposed that is suitable for the JSP. Then a novel comparison operation on two IFSs is presented. Finally, a procedure is constructed using the chromosome of an operation-based representation and a genetic algorithm. Two examples are used to demonstrate the efficiency of the proposed method. In addition, a comparison between the results of the proposed IFSJSP and other existing approaches demonstrates that IFSJSP significantly outperforms other existing methods.

A new method to determine basic probability assignment from training data

The Dempster-Shafer evidence theory (D-S theory) is one of the primary tools for knowledge representation and uncertain reasoning, and has been widely used in many information fusion systems. However, how to determine the basic probability assignment (BPA), which is the main and first step in D-S theory, is still an open issue. In this paper, based on the normal distribution, a method to obtain BPA is proposed. The training data are used to build a normal distribution-based model for each attribute of the data. Then, a nested structure BPA function can be constructed, using the relationship between the test data and the normal distribution model. A normality test and normality transformation are integrated into the proposed method to handle non-normal data. The missing attribute values in datasets are addressed as ignorance in the framework of the evidence theory. Several benchmark pattern classification problems are used to demonstrate the proposed method and to compare against existing methods. Experiments provide encouraging results in terms of classification accuracy, and the proposed method is seen to perform well without a large amount of training data.

Handling of Dependence in Dempster-Shafer Theory

Dempsters rule of combination can only be used when the bodies of evidence are assumed to be independent. However, such an assumption is often unrealistic. This paper proposes a systematic approach to handle dependence in evidence theory. It includes both the representation of dependence among information sources and the aggregation of the dependent evidence. For the representation of the dependence, the proposed methodology is able to capture both inner dependence (i.e., dependence among features of a system) and outer dependence (i.e., dependence among the evidence sources during the information propagating and evaluating process). We suggest dealing with the inner dependence by applying the analytic network process model, and modeling the outer dependence based on the intersection situations of the identified influencing factors. Then for the combination of dependent evidence, the strategy is to use discounting aggregation where the discounting coefficients are related to the degree of both outer and inner dependence. The discounting operator helps reduce the duplicate calculations in the fusion of dependent evidence and relax the assumption of independence when using Dempsters rule. A case study of transportation project evaluation is used to illustrate the proposed methodology.

A non-parametric method to determine basic probability assignment for classification problems

As an important tool for knowledge representation and decision-making under uncertainty, Dempster-Shafer evidence theory (D-S theory) has been used in many fields. The application of D-S theory is critically dependent on the availability of the basic probability assignment (BPA). The determination of BPA is still an open issue. A non-parametric method to obtain BPA is proposed in this paper. This method can handle multi-attribute datasets in classification problems. Each attribute value of the dataset sample is treated as a stochastic quantity. Its non-parametric probability density function (PDF) is calculated using the training data, which can be regarded as the probability model for the corresponding attribute. The BPA function is then constructed based on the relationship between the test sample and the probability models. The missing attribute values in datasets are treated as ignorance in the framework of the evidence theory. This method does not have the assumption of any particular distribution. As a result, it can be flexibly used in many engineering applications. The obtained BPA can avoid high conflict between evidence, which is desired in data fusion. Several benchmark classification problems are used to demonstrate the proposed method and to compare against existing methods. The constructed classifier based on the proposed method compares well to the state-of-the-art algorithms.

A note on ranking generalized fuzzy numbers

Ranking fuzzy numbers plays an important role in decision making under uncertain environment. Recently, Chen and Sanguansat (2011) [Chen, S. M. & Sanguansat, K. (2011). Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers. Expert Systems with Applications, 38(3), (pp. 2163-2171)] proposed a method for ranking generalized fuzzy numbers. It considers the areas on the positive side, the areas on the negative side and the heights of the generalized fuzzy numbers to evaluate ranking scores of the generalized fuzzy numbers. Chen and Sanguansats method (2011) can overcome the drawbacks of some existing methods for ranking generalized fuzzy numbers. However, in the situation when the score is zero, the results of the Chen and Sanguansats ranking method (2011) ranking method are unreasonable. The aim of this short note is to give a modification on Chen and Sanguansats method (2011) to make the method more reasonable.

Inclusion of task dependence in human reliability analysis

Abstract Dependence assessment among human errors in human reliability analysis (HRA) is an important issue, which includes the evaluation of the dependence among human tasks and the effect of the dependence on the final human error probability (HEP). This paper represents a computational model to handle dependence in human reliability analysis. The aim of the study is to automatically provide conclusions on the overall degree of dependence and calculate the conditional human error probability (CHEP) once the judgments of the input factors are given. The dependence influencing factors are first identified by the experts and the priorities of these factors are also taken into consideration. Anchors and qualitative labels are provided as guidance for the HRA analyst׳s judgment of the input factors. The overall degree of dependence between human failure events is calculated based on the input values and the weights of the input factors. Finally, the CHEP is obtained according to a computing formula derived from the technique for human error rate prediction (THERP) method. The proposed method is able to quantify the subjective judgment from the experts and improve the transparency in the HEP evaluation process. Two examples are illustrated to show the effectiveness and the flexibility of the proposed method.

Risk analysis of system security based on evidence theory

Risk evaluation is very important to the design and improvement of physical protection systems. In this paper, an evaluation method of multi-source information fusion is proposed based on the D-S evidence theory. In the proposed method, each individual component of the protection system in the simulated plane is modeled. Then, the threat report of each component according to the specific tactics is determined based on its real environment. Finally, the comprehensive threat distribution is obtained based on through the D-S evidence theory to combine multi-sources information. The proposed method can easily applied to the evaluation of the effectiveness of the protection system. We make the total threat of the protection system lowest through changes of the protection resources allocation. A numerical example is used to illustrate the efficiency of the proposed method.