Interval Evidential Reasoning Research Articles

A heterogeneous multi-attribute case retrieval method for generating emergency response alternatives based on interval evidential reasoning and gained and lost dominance score method: An application to the COVID-19 emergency situation

Heterogeneity exists in the case information of an emergency, and case retrieval plays a crucial role in generating an emergency response alternative. Despite advancements, fusing heterogeneous case information and considering decision maker preferences remain challenging issues to be solved. To address this, a novel heterogeneous multi-attribute case retrieval method is proposed and applied to COVID-19 emergency decision-making in this study. To overcome uncertainties and heterogeneities in case information, a new interval evidential reasoning (IER)-based case similarity measurement is developed to better protect data intergrity and improve case retrieval accuracy. Next, the best-worst method and information entropy are used to obtain subjective and objective weights of evaluated attributes, respectively, and subsequently these weights are integrated. Furthermore, a novel interval gained and lost dominance score (GLDS) method based on TODIM (Portuguese acronym for interactive multi-criteria decision-making) is developed to derive the comprehensive utilities of the similar historical case. This method simultaneously considers the fairness of the decision-making process and the psychological behavior of decision makers. Finally, a simulation example with large-scale data and two illustrated examples of generating emergency response altenatives are provided to demonstrate the applicability of the proposed method. Sensitivity and comparative analysis are conducted to verify the validity of the method.

Interval Evidential Reasoning-based Fault Detection of Electromagnetic Relay

The electromagnetic relay is a key switch control component, and its fault detection under uncertainties is a challenging problem. In this paper, a fault detection method based on interval evidential reasoning (IER) is proposed and applied to detect the relay’s fault. The method can handle fuzzy uncertainty and interval uncertainty in relay test data, and iteratively aggregate evidence by using the IER algorithm. Firstly, the relay super-path time data is transformed into the form of an interval belief distribution by using the fuzzy threshold, which is optimized by using training data. Secondly, historical and current information is aggregated to update interval belief distribution. Finally, the fault detection result can be obtained from interval belief distribution by a rule. The experimental results show that the presented method can improve the detection effect significantly.

A New Evidential Reasoning Rule Considering Interval Uncertainty and Perturbation.

The evidential reasoning (ER) rule has been widely applied in the multiple attribute decision making (MADM), which makes the decision-making process transparent and credible by using a belief structure. To improve the ability of the ER rule in dealing with the interval uncertainty, a new interval ER (IER) rule is proposed in this article. The interval uncertainty is described as the interval grade in the new frame of discernment (FoD) to model the local ignorance. It is proved that the IER rule is a generalization of the ER rule. To study the influence of perturbation on the IER rule, the perturbation is first introduced to the belief structure, and the perturbation analysis (PA) is conducted for the IER rule. An optimization model is established to estimate the perturbation threshold, which can measure the effectiveness of the inference result under perturbation. Two numerical examples and a case study are carried out, respectively, to show the implementation process of the proposed IER rule and validate its effectiveness in different decision-making scenarios.

A robust performance evaluation method based on interval evidential reasoning approach under uncertainty

Performance evaluation (PE) is an important part of equipment health management. If the monitoring information of the equipment is interfered, the evaluation results may be erroneous. A robust performance evaluation (RPE) method is proposed to solve this problem. The performance evaluation results are obtained by distinguishing the cases of single evidence with interference and two evidence with interference, and a robustness measurement based on interval similarity is proposed. To improve the accuracy of the evaluation results, the referential values in the IER evaluation model are optimized. The robustness thresholds of the input indexes are obtained under the satisfaction of the robustness constraints. If the interference value of the input index is within the thresholds, the deviation between the evaluation results using monitoring information with interference and those using monitoring information without interference is small. Finally, the proposed method is applied to a type of electric servo mechanism performance evaluation, and the case shows the validity of the RPE method.

Intelligent decision optimization for energy control of direct current power distribution system with multi-port access for intelligent buildings

The structure of direct current (DC) appliances is simpler and more energy-efficient than that of alternating current (AC) appliances. With the proliferation of novel DC loads (e.g., e-bikes and electric vehicles), DC loads will dominate the loads in buildings. It is necessary to develop a DC power distribution method that better accommodates renewable energy, effectively improves the working efficiency of loads, and significantly enhances energy utilization efficiency. However, there is not yet a unified design for the multi-port converter of DC microgrids. The experience is severely lacking in the overall energy planning for buildings from the perspectives of economy and environmental friendliness. To solve the problems, this paper explores the intelligent decision optimization for energy control in DC power distribution system with multi-port access for intelligent buildings. Firstly, a feature analysis was carried out on the multi-port converter of the DC power distribution system for intelligent buildings. With economy and environmental friendliness as the goals, the authors designed constraints related to energy output power, power balance, and distribution node voltage, and established an intelligent decision optimization model for the energy control of the DC microgrid for intelligent buildings. The model was combined with the multi-attribute decision-making framework into a decision-making framework for the coordinated operation of distributed energy supply units, which is based on the interval evidential reasoning (IER). Finally, the authors proposed an evaluation method for the decision-making of the energy control of DC power distribution for intelligent buildings, based on the Maclaurin symmetric mean (MSM) operator, and the IER-based decision-making framework. The proposed method was proved effective through experiments.

A Performance Evaluation Method Based on Interval Evidential Reasoning Approach With Function Monotonicity

The performance of complex systems is closely related to their security and reliability. Accurate performance evaluation is critical for timely system maintenance. Since the system monitoring information obtained usually contains noise, using this information to evaluate the performance of the device may result in inaccurate results. Interval values are used to represent the uncertainty of the monitoring information containing noise in the case of small samples. The uncertainty in the evaluation results is divided into two categories: the uncertainty of the evaluation model and the uncertainty of the monitoring information. The effects of the two categories on the evaluation results and the monotonicity of the output results on the monitoring information and model parameters are quantitatively analyzed. To avoid the problem of interval expansion during model optimization, an IER optimization model based on the belief degrees of monitoring information is built, and the whole evaluation process is solved and optimized uniformly. The monotonicity analysis results simplify the solving process of the IER optimization model, which reduces the difficulty and complexity. Validity and normalization tests are performed on the belief structure of the evaluation results, eliminating the invalid and redundant parts, and obtaining the best interval range of the evaluation results. The effectiveness of the proposed method is verified by its application in an electric servo mechanism.

An interval evidential reasoning-based dynamic performance evaluation method for complex systems

The performance of complex systems is closely related to its safety and reliability. Grasping the performance of complex systems accurately and timely can help avoid or reduce losses if performance drops. In engineering practice, the monitoring information in interval form can express uncertainty. The upper and lower bounds of monitoring information are easier to obtain than the probability distribution, which can reduce the requirements for information distribution. In this paper, the interval evidential reasoning approach is used to evaluate performance of complex systems. A Monte Carlo simulation-based method for calculating the reliability and weight of evidence is proposed. The initial performance evaluation results are obtained by constructing a nonlinear optimization model. Then the historical performance evaluation information is fully considered to obtain the optimal evaluation results dynamically using a linear weighted update method. An uncertainty quantification method is proposed to quantify the uncertainty of input information and evaluation results. Finally, a case study is carried out for a kind of diesel generator to validate the applicability of the proposed method, and shows that the proposed method can improve the evaluation accuracy.

A probabilistic interval-valued hesitant fuzzy gained and lost dominance score method based on regret theory

With the increasing complexity of the decision environment, the fuzzy theory has attracted the extensive attention of scholars. Probabilistic interval-valued hesitant fuzzy set, as a complex ambiguous information representation tool, dedicates to depict uncertain information as complete as possible. Thus, this paper proposes a probabilistic interval-valued hesitant fuzzy gained and lost dominance score method based on regret theory and interval evidential reasoning approach. In view of the uncertainties in evaluations, the interval evidential reasoning approach is an effective tool to deal with the fuzziness and ignorance, which is first applied in probabilistic interval-valued hesitant fuzzy information in this paper. Besides, an interval projection measure is proposed to consider both distance and direction simultaneously, so as to avoid the problem of information losses in the decision process. On this basis, a novel regret-rejoice function is developed. Then, an extended gained and lost dominance score method based on regret theory and interval evidential reasoning approach is developed, which considers the regret avoidance behavior of experts. Finally, a case study on supplier selection of epidemic prevention products is applied to elucidate and illustrate the application of the proposed method in this paper.

A Novel Interval Evidential Reasoning Approach to the Physical and Mechanical Property Assessment of Particleboards

In this paper, a new assessment method based on the interval evidential reasoning (IER) rule is proposed to solve the problem of physical and mechanical property assessment (PMPA) for particleboards. Because the detection data of the density and thickness swelling (TS) of particleboards are in an interval form, a model with precise values as input becomes inappropriate, so the PMPA of particleboards is not feasible. In the proposed method, expert knowledge and interval data are integrated to solve the assessment problem. First, the overall reliability of attributes is calculated, and the interval data are transformed into an interval belief structure. Then, the multiple interval belief structures are aggregated by ER nonlinear optimization models. Finally, the assessment results are obtained by utility theory. With the proposed method, the PMPA of particleboards with interval values can be assessed reasonably, and the combination interval belief degree of different grades of particleboard can be obtained, which has a certain guiding significance for the production and subsequent operation of enterprises. A case study for the PMPA of particleboards is conducted to demonstrate the effectiveness of the proposed method.

Interval-valued hesitant fuzzy TODIM method for dynamic emergency responses.

Emergency responses bear the characteristics of uncertainty and possess multi-attributes in decision making. This paper applies the interval evidential reasoning approach and the interval-valued hesitant fuzzy TODIM (IVHF-TODIM) method to tackle the dynamic emergency decision-making problem. We introduce a function to obtain the gain and loss degrees through the geometric area method. The gain and loss matrices of the interval belief degrees are found probabilistically. A new approach to obtaining the dominance degree matrix is proposed. From the IVHF-TODIM method, the overall dominance degree is established to provide the ranking of the decision alternatives. A recent case of selecting an emergency decision alternative for a large bushfire is used to validate the proposed method, followed by a comparative analysis.

A location-allocation model for quality-based blood supply chain under IER uncertainty

Providing blood with high quality at the lowest cost and the shortest time is main challenge of blood supply chain management. This paper presents a new model for designing a dynamic and three level blood supply chain incorporating the quality issues. The proposed model intends to locate facilities, and to determine the best strategy for blood allocation by minimizing both cost and time and maximizing the customer satisfaction based on quality of blood delivery. In order to deal with consideration of real world, intricacies such as blood freshness, both separation and apheresis extraction methods, Cross match to Transfusion ratio (C/T) and equipment failure have been involved. Also, Interval Evidential Reasoning (IER) approach is applied to handle the uncertainty of blood product demand. Since the proposed model is NP-hard, MOPSO and NSGAII algorithms are utilized to solve it. Finally, to demonstrate the applicability of the problem some numerical examples are designed in different sizes and the most favorable algorithm is determined using TOPSIS method.

Dependence Assessment in Human Reliability Analysis Based on the Interval Evidential Reasoning Algorithm Under Interval Uncertainty

Dependence assessment, which is to assess the influence of the operator’s failure of a task on the failure probability of subsequent tasks, is an important part in Human reliability analysis (HRA). The technique for human error rate prediction (THERP) has been widely applied to assess the dependence in HRA. However, due to the complexity of the real world, various kinds of uncertainty could occur in dependence assessment problem, and how to properly express and deal with uncertainty especially interval uncertainty remains a pressing issue. In this article, a novel method based on the interval evidential reasoning (IER) algorithm is proposed to assess dependence in HRA under interval uncertainty. First, dependence influential factors are identified and their functional relationship is determined. Then, judgments on these factors provided by the analysts are represented using interval belief distributions. Next, the interval evidential reasoning algorithm is employed to aggregate interval belief distributions of different factors according to their functional relationship while considering the credibility of the interval belief distribution. Finally, the conditional human error probability (CHEP) is calculated based on the fused interval belief distribution, where the upper and lower values are determined by assigning belief degree to the highest and lowest grade of the corresponding grade interval, respectively. Two numerical examples demonstrate that the proposed method not only properly deals with interval uncertainty using interval belief distribution and IER algorithm, but also provides a novel and effective way for dependence assessment in HRA.

An interval efficiency evaluation model for air pollution management based on indicators integration and different perspectives

Abstract Efficiency evaluation of air pollution management is one of China’s most popular political concerns. Many studies have been devoted to developing an effective efficiency evaluation model for air pollution management. However, three challenges must be addressed and solved. First, previous studies treated air pollution data as real numbers in efficiency evaluation. This ignored the fluidity and variability of air pollutants. Second, the indicators used in previous studies were selected based on experts’ knowledge. Accordingly, there was information loss in efficiency evaluation. Last, many factors can affect the efficiency evaluation of air pollution management. Yet, previous studies neglected to evaluate efficiencies from different perspectives. To address the challenges above, the interval data was first used as basic data to meet the flow characteristics of air pollution management. Next, the interval evidential reasoning (IER) model and the interval data envelopment analysis (IDEA) model were employed. Both models are suitable for interval data. They were introduced to propose a new efficiency evaluation model: the IER-IDEA model. The main aims of the proposed model are twofold: 1) include interval indicator integration with a new weight calculation method; and 2) evaluate interval efficiency from three different perspectives. To demonstrate the effectiveness of the proposed IER-IDEA model, a case study was performed in 29 Chinese provinces. Its purpose was to assess efficiency evaluation of air pollution management. Experimental results demonstrated that the IER-IDEA model obtains desired efficiencies of air pollution management under the consideration of indicator integrity, interval uncertainty, and different perspectives. Moreover, it can effectively distinguish regional differences in the efficiency of air pollution management compared to some existing efficiency evaluation models.

Performance evaluation of four-stage blood supply chain with feedback variables using NDEA cross-efficiency and entropy measures under IER uncertainty

Blood supply chain management has been considered by many managers in recent years, as one of the major challenges in health systems. In order to ensure the optimal performance of the supply chain, enable continuous improvement and create competitive advantage, establishment of a performance evaluation system is essential. For this purpose, the current study proposes a Network Data Envelopment Analysis (NDEA) model for measuring efficiency of four-stage serial network of blood supply chain in presence of feedback variables by identifying comprehensive and balanced criteria as evaluation variables. Since criteria values are obtained from subjective judgment of individuals, are uncertain. Interval Evidential Reasoning (IER) approach that deals with a variety of uncertainties such as ignorance and vagueness, has been used to control the uncertainty and provide reliable evaluation. In order to rank the units a new cross-efficiency based model is presented as a remedy for the issue of non-uniqueness of optimal weights in cross efficiency. Then, Gibbs entropy is utilized to measure the uncertainty of obtained interval cross efficiency. Finally, a numerical example is provided to illustrate the proposed model.

Study of aggregation algorithms for aggregating imprecise software requirements’ priorities

Extensive Numerical Assignment (ENA) is a novel Requirements Prioritization Technique introduced by the authors that acknowledges the uncertain and imprecise nature of human judgment. A controlled experiment is conducted during which data are collected using ENA for the requirements assessment of university website system. The objective of this paper is to study how the imprecise data obtained from ENA can be aggregated using aggregation algorithms: Multiple Attribute Utility Theory (MAUT) and Interval Evidential Reasoning (IER) to generate requirements’ priorities in the presence of conflicting personal preferences among assessors. A simplified version of IER called Laplace Evidential Reasoning (LER) is introduced and the results are discussed. LER has the potential to emerge as a competent aggregation algorithm when compared to MAUT and IER, because of its reasonable processing requirements when compared to IER and its ability to produce rich set of outputs when compared to MAUT.

Coordinated scheduling strategy to optimize conflicting benefits for daily operation of integrated electricity and gas networks

The increasing share of variable renewable energy sources and the improving requirements on system security and reliability are calling for important changes in our energy systems. The synergies between energy supply networks are of great importance to satisfy the development of the integrated energy system (IES). Hence this paper presents the study of the coordinated scheduling strategy (CSS), in which, the models of the electricity network and gas network are developed in detail, and the operation constraints of the networks are fully considered. The purpose of the CSS is to optimize the conflicting benefits of the electricity network and gas network for daily operation of the IES, while satisfying the operation constraints. In the CSS, a multi-objective optimization algorithm is applied to obtain a Pareto-optimal solution set, and a multiple attribute decision analysis (MADA) using interval evidential reasoning (IER) is developed to determine a final optimal daily operation solution for the IES. Simulation studies are conducted on an IES consisting of a modified IEEE 30-bus electricity network and a 15-node gas network to verify the effectiveness of the CSS, and to evaluate the interdependency between the electricity network and gas network.

A general evidential reasoning algorithm for multi-attribute decision analysis under interval uncertainty

Evidential reasoning (ER) is one of the important approaches used to solve multi-attribute decision analysis (MADA) problems under uncertainty, involving both quantitative and qualitative attributes. The ER approach provides a distributed modeling framework fusing several types of uncertain and incomplete information, including ignorance and vagueness, to work out the optimum alternative rationally. In this paper, we review the original ER algorithm and recursive interval evidential reasoning (IER) algorithm and derive a general analytical algorithm for IER, thus enabling an aggregation of attributes’ assessments in an explicit manner. Then, a more complicated uncertain occasion is investigated, where it is possible to conduct evaluation assessments, including quantitative data, belief degrees, grades, and weights, in the form of an interval. A pair of nonlinear optimization models based on the new algorithm is established to solve this problem under interval uncertainty, and the maximum and minimum expected utilities of each alternative are calculated and ranked accordingly. Additionally, we prove that the original ER and recursive IER algorithms are special cases of the new algorithm. Finally, a numerical example is used to demonstrate the steps involved in the proposed approach.