In this paper, we aim at generalising the evidential reasoning (ER) rule to establish a new maximum likelihood evidential reasoning (MAKER) framework for probabilistic inference from inputs to outputs in a system space, with their relationships characterised by imperfect data. The MAKER framework consists of three models: system state model (SSM), evidence acquisition model (EAM) and evidential reasoning model (ERM). SSM is introduced to describe system output in the form of ordinary probability distribution on singleton states of the system space to model randomness only, or more generally basic probability distribution on singleton states and their subsets, referred to as states for short, to depict both randomness and ambiguity explicitly. EAM is established to acquire evidence from a data source as system input in the form of basic probability distribution on the evidential elements of the data source, with each evidential element pointing to a state in the system space. ERM is created to combine pieces of acquired evidence, with each represented in the form of basic probability distribution on all the states and the powerset of the system space to facilitate an augmented probabilistic inference process where the trustworthiness of evidence is explicitly modelled alongside its randomness and ambiguity. Within the MAKER framework, the trustworthiness of evidence is defined in terms of its reliability and expected weight to measure the total degree of its support for all states. Interdependence between pairs of evidence is also measured explicitly. A general conjunctive MAKER rule and algorithm are then established to infer system output from multiple inputs by combining multiple pieces of evidence that have weights and reliabilities and are dependent on each other in general. Several special MAKER rules and algorithms are deduced to facilitate inference in special situations where evidence is exclusive or independent of each other. Specific conditions are identified and proven where the MAKER rule reduces to the ER rule, Dempster's rule and Bayes’ rule. A bi-objective nonlinear pre-emptive minimax optimisation model is built to make use of observed data for optimal learning of evidence weights and reliabilities by maximising the predicted likelihood of the true state for each observation. Two numerical examples are analysed to demonstrate the three constituent models of the MAKER framework, the MAKER rules and algorithms, and the optimal learning model. A case study for human well-being analysis is provided where data from a panel survey are used to show the potential applications of the MAKER framework for probabilistic reasoning and decision making under different types of uncertainty.

This article investigates how to make use of imperfect data gathered from different sources for inference and decision making. Based on Bayesian inference and the principle of likelihood, a likelihood analysis method is proposed for acquisition of evidence from imperfect data to enable likelihood inference within the framework of the evidential reasoning (ER). The nature of this inference process is underpinned by the new necessary and sufficient conditions that when a piece of evidence is acquired from a data source it should be represented as a normalized likelihood distribution to capture the essential evidential meanings of data. While the explanation of sufficiency of the conditions is straightforward based on the principle of likelihood, their necessity needs to be established by following the principle of Bayesian inference. It is also revealed that the inference process enabled by the ER rule under the new conditions constitutes a likelihood inference process, which becomes equivalent to Bayesian inference when there is no ambiguity in data and a prior distribution can be obtained as a piece of independent evidence. Two examples in decision analysis under uncertainty and a case study about fault diagnosis for railway track maintenance management are examined to demonstrate the steps of implementation and potential applications of the likelihood inference process.

We propose to employ evidential reasoning (ER) rule to construct a clinical decision support system (CDSS) to aid physicians to predict the probability of intensive care unit (ICU) admission and in-hospital death for trauma patients once they arrive at a hospital. A generalized Bayesian rule is used to mine evidence from historical data. Evidence is profiled using a format of belief distribution, where the belief degrees of different trauma outcomes are assigned with derived probabilities linked to the corresponding outcomes. Inputs to the CDSS are clinical data of a patient, and output from the system is predicted belief degree of severe trauma, including ICU admission and in-hospital death. The inner logic of the CDSS is that pieces of evidence that match the clinical data of a patient are identified from the evidence base first, and then the ER rule-based evidence aggregation mechanism is utilized to combine the matched evidences to arrive at a prediction. The reliability, weight, and interdependence of clinical evidence are taken into account. Moreover, an evidence weight training module is constructed. The ER rule-based prediction model has superior performance compared with logistic regression and artificial neural network models. An innovative and pragmatic ER rule-based CDSS for trauma outcome prediction is contributed by this article. In the era of big data, this CDSS helps predict patient outcomes based on historical data and helps physicians in emergency departments make proper trauma management decisions.

Automobile insurance fraud detection has become critically important for reducing the costs of insurance companies. The majority of insurance companies use expert knowledge to detect fraud. Experience-based knowledge are interpretable and re-usable but the simplistic way that this knowledge is used in practice, often leads to some degree of misjudgment. This paper aims to establish a unique Evidential Reasoning (ER) rule that combines independent evidence from both experience based indicators and probabilities of fraud obtained from historical data. Each piece of evidence is weighted and then combined conjunctively with the weights optimised using a maximum likelihood evidential reasoning (MAKER) framework for data-driven inferential modelling. Based on a real-world insurance claim dataset, our experimental results reveal that the proposed approach preserves the interpretability and usability of expert detection system, and anticipates the changes in fraud practices by tracking the trend of the weights of experience-based indicators. Furthermore, the experimental results show that the proposed approach outperforms a number of widely used machine learning models, such as logistic regression and random forests.

Abstract Intuitionistic multiplicative sets use an asymmetric, unbalanced scale to express information from positive, negative, and indeterminate information. They have been found capable of comprehensively and objectively representing a person's intuitive understanding and hence have attracted much attention. Distance techniques are widely used to measure the degree to which arguments deviate from one another. Several fuzzy set extensions have been developed, but little research has been conducted on measures of distance between intuitionistic multiplicative sets. In this paper, we start by presenting a variety of measures of the distance between intuitionistic multiplicative sets, including Hausdorff distance measures, weighted distance measures, ordered weighted distance measures, and continuous weighted distance measures. We then develop a distance‐based intuitionistic multiplicative‐technique for order preference by similarity to ideal solution method and a distance‐based intuitionistic multiplicative‐Vlsekriterijumska Optimizacija I Kompromisno Resenje method for handling multiple criteria decision‐making problems with intuitionistic multiplicative evaluation information. To demonstrate the practical application of these distance measures and the proposed methods, we provide a case study of hospital management of inpatient admission. The paper ends with comparative analyses of the two methods and some concluding remarks.

This paper proposes a new belief rule-based (BRB) expert system for fault diagnosis of marine diesel engines. The expert system is the first of its kind that consists of multiple concurrently activated BRB subsystems, in which each subsystem has its distinctive outputs and uses the evidential reasoning approach for inference. This novel modeling approach can be applied to identify fault modes that may co-exist. In essence, the group of BRB subsystems is used to model the nonlinear relationships between the fault features and the fault modes in marine diesel engines. The initial BRB expert system can be established by using expert experience and then optimized by using the data samples accumulated during the operation of marine diesel engines. Due to limitations in knowledge and data collected, ignorance is also considered in some BRB subsystems. The proposed BRB expert system is applied to abnormal wear detection for a kind of marine diesel engine. The performance of the BRB expert system is investigated in comparison with that of artificial neural network (ANN) models, support vector machine (SVM) models, and binary logistic regression model with fivefold cross-validation. The results show that the BRB expert system can be used for fault diagnosis of marine diesel engines in a probabilistic manner, which outperforms the ANN models, SVM models, and the binary logistic regression model in terms of accuracy and stability, and can effectively identify concurrent faults.

The Evidential Reasoning (ER) approach is an inference method to analyse multi-criteria decision-making problems with uncertainties. However, due to the pressure of time, limit of knowledge and lack of data, such problems need to be assessed using both human judgments and limited data. In this case, it is suitable to provide a belief structure by means of linguistic terms, which we refer to as linguistic belief structure. Considering that different decision-makers may have different perceptions, the semantics of human judgments can also be different. In this paper, we introduce three linguistic scale functions to capture the semantics of linguistic belief degrees for constructing a complete linguistic information fusion method. We then extend the framework of the ER approach to multi-expert multi-criteria decision making. The method proposed in this study can fill the research gap of the ER approach for multi-expert multi-criteria decision-making problems with linguistic belief structures.

A study was carried out to compare an integrated HTML5-based real-time video conferencing solution against a separately installed video conferencing solution in the same web-based meeting support application. To carry out this comparison, WebRTC and Skype have been integrated into an existing groupware application. Our study shows that comparing to a separately installed, best of breed video conferencing solution; the web browser-based solution would be an adequate and more convenient one. Our work indicates that the cost to implement WebRTC is not large in comparison to the number of benefits that can be gained. The quality of video conferencing has been continuously improving, and the implementation cost is getting lower as better WebRTC libraries emerge and evolve.

Abstract Firm growth and profitability come primarily from new product development. Portfolio management has been emphasized in improving new product development (NPD) performance under multiple project environments. However, few researchers have demonstrated the consequence of different combinations of portfolio management practices on NPD performance. In this study, a decision support methodology based on Bayesian network scenarios is used to simulate the effect of portfolio management on NPD performance in uncertain environments. Firstly, portfolio management factors are identified and performance criteria determined. And then, the causal relationships among the factors are modelled within similar time frames, and a Bayesian network model is developed by parameter learning from data. A case study is carried out for project/portfolio managers in Chinese firms. The most informative factors affecting NPD performance are identified by sensitive analysis, and the best and worst scenarios with different combinations of portfolio management practices are analysed. The study extends the application of Bayesian networks to assess the performance under changing conditions and highlights some managerial suggestions to improve NPD performance.

The demand is a fundamental variable in economic analysis that measures the needs of goods and services of the consumers. This paper presents a new approach for representing the demand by using aggregation systems that consider the attitudinal character of the consumers and their beliefs regarding the degree of importance of the different variables that may affect them. Several developments are introduced by using multiperson systems, different criterion, attributes, and states of nature. These developments are focused on the use of the weighted average, the ordered weighted average, and the ordered weighted averaging weighted average. Further aggregation systems are suggested by using the concept of the demand growth. The paper ends with an application of the new approach in a forecasting process that considers the attitude of the decision maker and its subjective beliefs.

In this paper, we present a generic expert system software tool and its application in expert knowledge modelling and inference. The system is able to model expert rule-based knowledge and provide predictions for unseen data by the application of inductive inference. The theoretical framework for modelling expert knowledge is described independently of its implementation as a generic expert system. The framework is based on a review of the literature on belief rule-based inference methodology using the evidential reasoning approach (RIMER) and its applications. The application of the generic expert system is demonstrated by a case study which uses a guideline model for clinical risk assessment of acute upper gastrointestinal bleeding.

The supply represents the available number of products of a specific variable. This paper presents a new approach for studying the supply through the use of aggregation systems. Its main advantage is that it permits to represent the information in a more complete way. Thus, it is possible to develop forecasting methods that consider optimistic and pessimistic scenarios and those that are more expected to occur. A wide range of aggregation operators are used giving special focus on the ordered weighted average (OWA). Several generalizations that use it with the weighted average and the probability are presented including the OWA weighted average (OWAWA) and the probabilistic OWAWA (POWAWA) operator. A numerical example is also presented.

Increases in usage of websites as communication tools has lead to reductions in costs of product and service delivery for companies. Incorrect design of websites leads to redesigning them to fit customer needs. Redesign costs are particularly relevant for resource constrained SMEs. Modeling highly subjective, uncertain and repetitive decisions requires methods that include the benefits of both expert knowledge as well as machine learning. This paper reports a comparison on the application of two such hybrid approaches: Belief Rule-Base Inference Methodology Using the Evidential Reasoning Approach (RIMER) and Artificial Neural Fuzzy Inference System (ANFIS). A numerical example and a case study are reported in order to analyze the potential of the two methods. The results show that both methods can be used to accurately represent and predict the complicated and nonlinear relationships between website characteristics and overall satisfaction. The RIMER approach is found to outperform ANFIS when considering explanatory power.

In this paper, a Genetic Algorithm (GA) search heuristic is proposed for validating the model-structure of Belief Rule-Based (BRB) methodologies. In order to ensure the balance between the model fit/ accuracy and the model complexity, the Akaike Information Criterion (AIC) is used in conjunction with the mentioned heuristic. The resulting framework is tested, using a model consisting of 3 inputs and one output, each of the 4 variables being allocated up to 5 referential values. The presented results illustrate the time-efficiency of the GA heuristic, as well as the penalty imposed by AIC on the number of parameters. The simplest model structure is indicated by AIC to be the optimal one. However, three additional model structures have been found to have AIC values which are moderately close to this optimum. An analysis of their coefficients of determination indicates a higher fit (than AIC optimum) on both testing sets and overall.

It is important to predict both observable and hidden behaviors in complex engineering systems. However, compared with observable behavior, it is often difficult to establish a forecasting model for hidden behavior. The existing methods for predicting the hidden behavior cannot effectively and simultaneously use the hybrid information with uncertainties that include qualitative knowledge and quantitative data. Although belief rule base (BRB) has been employed to predict the observable behavior using the hybrid information with uncertainties, it is still not applicable to predict the hidden behavior directly. As such, in this paper, a new BRB-based model is proposed to predict the hidden behavior. In the proposed BRB-based model, the initial values of parameters are usually given by experts, thus some of them may not be accurate, which can lead to inaccurate prediction results. In order to solve the problem, a parameter estimation algorithm for training the parameters of the forecasting model is further proposed on the basis of maximum likelihood algorithm. Using the hybrid information with uncertainties, the proposed model can combine together with the parameter estimation algorithm and improve the forecasting precision in an integrated and effective manner. A case study is conducted to demonstrate the capability and potential applications of the proposed forecasting model with the parameter estimation algorithm.

The evidential reasoning (ER) approach was developed to support multiple criteria decision analysis (MCDA). It is based on the Dampster's combination rule for criteria aggregation and belief function for treating ignorance. In the original ER approach, however, alternative ranking depends on the accurate estimation of a value function, which may be difficult in certain decision environments. In this paper, the link and difference between the ER algorithm and Dampster's combination rule are analysed first. A new alternative ranking method is then investigated as an integrated part of the enhanced ER approach.

Research in recommender systems is now starting to recognise the importance of multiple selection criteria to improve the recommendation output. In this paper, we present a novel approach to multi-criteria recommendation, based on the idea of clustering users in "preference lattices" (partial orders) according to their criteria preferences. We assume that some selection criteria for an item (product or a service) will dominate the overall ranking, and that these dominant criteria will be different for different users. Following this assumption, we cluster users based on their criteria preferences, creating a "preference lattice". The recommendation output for a user is then based on ratings by other users from the same or close clusters. Having introduced the general approach of clustering, we proceed to formulate three alternative recommendation methods instantiating the approach: (a) using the aggregation function of the criteria, (b) using the overall item ratings, and (c) combining clustering with collaborative filtering. We then evaluate the accuracy of the three methods using a set of experiments on a service ranking dataset, and compare them with a conventional collaborative filtering approach extended to cover multiple criteria. The results indicate that our third method, which combines clustering and extended collaborative filtering, produces the highest accuracy.

In order to determine the parameters of belief-rule-base (BRB) accurately, several optimization methods have been proposed for training BRB, on the basis of a generic rule-base inference methodology using the evidential reasoning (RIMER) approach. These optimization methods are implemented offline, and such are not suitable for training BRB in a dynamic fashion. In this paper, two recursive algorithms are proposed to update BRB online that can simulate dynamic systems. The main feature of the proposed algorithms is that only partial input and output information is required, which can be incomplete or vague, numerical or judgmental, or mixed. If the internal structure of a BRB is initially decided using expert judgments, domain-specific knowledge and/or commonsense rules, the proposed algorithms can be used to fine-tune the initial BRB online, once input and output datasets become available. Using the proposed algorithms, there is no need to collect a complete set of data before a BRB can be trained, which is necessary if the BRB is used to simulate a dynamic system. A numerical example and a case study are reported to demonstrate the potential of the algorithms for online fault diagnosis.

Abstract: A critical issue in the clinical decision support system (CDSS) research area is how to represent and reason with both uncertain medical domain knowledge and clinical symptoms to arrive at accurate conclusions. Although a number of methods and tools have been developed in the past two decades for modelling clinical guidelines, few of those modelling methods have capabilities of handling the uncertainties that exist in almost every stage of a clinical decision‐making process. This paper describes how to apply a recently developed generic rule‐base inference methodology using the evidential reasoning approach (RIMER) to model clinical guidelines and the clinical inference process in a CDSS. In RIMER, a rule base is designed with belief degrees embedded in all possible consequents of a rule. Such a rule base is capable of capturing vagueness, incompleteness and non‐linear causal relationships, while traditional IF–THEN rules can be represented as a special case. Inference in such a rule base is implemented using the evidential reasoning approach which has the capability of handling different types and degrees of uncertainty in both medical domain knowledge and clinical symptoms. A case study demonstrates that employing RIMER in developing a guideline‐based CDSS is a valid novel approach.

A belief rule-base inference methodology using the evidential reasoning approach (RIMER) has been developed recently, where a new belief rule representation scheme is proposed to extend traditional IF-THEN rules. The belief rule expression matrix in RIMER provides a compact framework for representing expert knowledge. However, it is difficult to accurately determine the parameters of a belief rule base (BRB) entirely subjectively, particularly, for a large-scale BRB with hundreds or even thousands of rules. In addition, a change in rule weight or attribute weight may lead to changes in the performance of a BRB. As such, there is a need to develop a supporting mechanism that can be used to train, in a locally optimal way, a BRB that is initially built using expert knowledge. In this paper, several new optimization models for locally training a BRB are developed. The new models are either single- or multiple-objective nonlinear optimization problems. The main feature of these new models is that only partial input and output information is required, which can be either incomplete or vague, either numerical or judgmental, or mixed. The models can be used to fine tune a BRB whose internal structure is initially decided by experts' domain-specific knowledge or common sense judgments. As such, a wide range of knowledge representation schemes can be handled, thereby facilitating the construction of various types of BRB systems. Conclusions drawn from such a trained BRB with partially built-in expert knowledge can simulate real situations in a meaningful, consistent, and locally optimal way. A numerical study for a hierarchical rule base is examined to demonstrate how the new models can be implemented as well as their potential applications.

In multiple attribute decision analysis (MADA), one often needs to deal with both numerical data and qualitative information with uncertainty. It is essential to properly represent and use uncertain information to conduct rational decision analysis. Based on a multilevel evaluation framework, an evidential reasoning (ER) approach has been developed for supporting such decision analysis, the kernel of which is an ER algorithm developed on the basis of the framework and the evidence combination rule of the Dempster-Shafer (D-S) theory. The approach has been applied to engineering design selection, organizational self-assessment, safety and risk assessment, and supplier assessment. In this paper, the fundamental features of the ER approach are investigated. New schemes for weight normalization and basic probability assignments are proposed. The original ER approach is further developed to enhance the process of aggregating attributes with uncertainty. Utility intervals are proposed to describe the impact of ignorance on decision analysis. Several properties of the new ER approach are explored, which lay the theoretical foundation of the ER approach. A numerical example of a motorcycle evaluation problem is examined using the ER approach. Computation steps and analysis results are provided in order to demonstrate its implementation process.

In many decision situations, it is inevitable to deal with both quantitative and qualitative information under uncertainty. Evidence-based reasoning within a multiple criteria decision analysis framework provides an alternative way of handling such information systematically and consistently. In this paper, the evidential reasoning (ER) approach is introduced, which is based on a recursive ER algorithm that, in essence, constitutes a nonlinear information aggregation process. To facilitate the application of the ER approach and as an indispensable part of its development, the nonlinear features of the ER information aggregation process need to be thoroughly investigated and properly understood. This forms the theme of this paper where the nonlinear features are explored by examining typical reasoning patterns in aggregating harmonic, quasi-harmonic, and contradictory decision information. This analytical investigation provides insights into the recursive nature of the ER approach as well as valuable experience that could be useful to other researchers and practitioners interested in developing and applying operation research/artificial intelligence (OR/AI)-based approaches for decision analysis under uncertainty. The analytical study is complemented by the numerical studies of two application examples. The analysis of a quality assessment problem for motor engines is aimed to show the step-by-step process of implementing the ER approach and to illustrate its nonlinear features in a real-life decision situation. The study of a more complex assessment problem in ship design is intended to demonstrate the potential of the ER approach and its supporting software for dealing with general decision problems.