Ying-Ming Wang

A group decision method based on prospect theory for emergency situations

Abstract Urgent and critical situations or so-called emergency events, such as terrorist attacks and natural disasters, often require crucial decisions. When an emergency event occurs, emergency decision making plays an important role in dealing with it, and hence, its importance nowadays is increasing. In the real world, it is difficult for only one decision maker to take a comprehensive decision for coping with an emergency event. Consequently, many practical emergency problems are often characterized by a group emergency decision making (GEDM) scheme. Different studies show that human beings are usually bounded rational under risk and uncertainty, and their psychological behavior is very important in the decision-making process. However, such behavior is neglected in current GEDM studies. Therefore, this study proposes a novel GEDM method that considers experts’ psychological behavior in the GEDM process. The method is then applied to a case study and compared with other related approaches. Finally, discussions are presented to illustrate the novelty, feasibility, and validity of the proposed GEDM method, showing the importance of experts’ psychological behavior in GEDM.

Dynamic rule adjustment approach for optimizing belief rule-base expert system

The belief rule-base (BRB) inference methodology, which uses the evidential reasoning (RIMER) approach, has been widely popular in recent years. As an expert-system methodology using the RIMER approach, BRB is used for storing various types of uncertain knowledge in the form of belief structure. Several structure-learning approaches have been proposed in recent years. However, these approaches are deficient in various aspects, do not have repeatability, hold incomplete data, and are constrained by the associated scale-utility value. Moreover, considering the influence of the number of rules for a BRB system, two scenarios are designed to reveal the relationship between structure feature and fewer/excessive rules. Excessive rules may lead to a BRB that is equipped with an over-complete structure, whereas significantly fewer rules may result in a BRB with an incomplete structure. To solve these problems, we initially proposed to develop an adjusted structure that is leading to the establishment of a complete structure instead of incomplete and over-complete structures. By scenario analysis and experimental verification through parameter learning of BRBs, we summarize several features of two scenarios, which can be used to reveal certain number of key BRB properties. Finally, density and error analyses are introduced to dynamically prune or add rules to construct the complete structure, particularly that of the BRB comprising multiple-antecedent attributes. We verify the effectiveness of the proposed approach by testing its use in a practical case study on oil pipeline-leak detection and demonstrate how the approach can be implemented.

Multi-attribute search framework for optimizing extended belief rule-based systems

The advantages and applications of rule-based systems have caused them to be widely recognized as one of the most popular systems in human decision-making, due to their accuracy and efficiency. To improve the performance of rule-based systems, there are several issues proposed to be focused. First, it is unnecessary to take the entire rule base into consideration during each decision-making process. Second, there is no need to visit the entire rule base to search for the key rules. Last, the key rules for each decision-making process should be different. This paper focuses on an advanced extended belief rule base (EBRB) system and proposes a multi-attribute search framework (MaSF) to reconstruct the relationship between rules in the EBRB to form the MaSF-based EBRB. MaSFs can be divided into k-dimensional tree (KDT)-based MaSFs and Burkhard-Keller (BKT)-based MaSFs. The former is targeted at decision-making problems with small-scale attribute datasets, while the latter is for those with large-scale attribute datasets. Based on the MaSF-based EBRB, the k-neighbor search and the best activated rule set algorithms are further proposed to find both the unique and the desired rules for each decision-making process without visiting the entire EBRB, especially when handling classification problems with large attribute datasets. Two sets of experiments based on benchmark datasets with different numbers of attributes are performed to analyze the difference between KDT-based MaSFs and BKT-based MaSFs, and to demonstrate how to use MaSFs to improve the accuracy and efficiency of EBRB systems. MaSFs and their corresponding algorithms are also regarded as a general optimization framework that can be used with other rule-based systems.

A data envelopment analysis (DEA)-based method for rule reduction in extended belief-rule-based systems

Rule reduction is one of the research objectives in numerous successful rule-based systems. In some analyses, too many useless rules may be a concern in a rule-based system. Although rule reduction has already attracted wide attention to optimise the performance of the rule-based system, the extended belief-rule-based system (EBRBS), which is an advanced rule-based system developed from the belief-rule-based system (BRBS) recently, still lacks methods to reduce rules. This study focuses on the rule reduction of EBRBS and introduces data envelopment analysis (DEA) to evaluate the efficiency of each rule in an extended belief-rule-based (EBRB). However, two challenges must be addressed. First, a measure of the extended belief rules efficiency value must be given because it is the foundation of rule reduction. Second, a novel decision-making-unit (DMU) must be constructed using the efficiency value of the extended belief rules to build a bridge for EBRBS and DEA. Therefore, the concepts of contribution degree and the extended belief rule-based DMU are introduced in the present study for the first time to propose a DEA-based rule reduction method. Moreover, the classic CCR model, which is identification engine of the rule reduction method, is applied to calculate the efficiency value of the extended belief rule and finally achieve the compact structure of an EBRB. Two case studies on regression and classification problems are performed to illustrate how efficiency of the DEA-based rule reduction method in promoting the performance of EBRBS. Comparison results demonstrate that the proposed rule reduction can downsize the EBRB and improve the accuracy of EBRBS.

New evidential reasoning rule with both weight and reliability for evidence combination

Abstract Two aspects of problems such as weight over-bounding and reliability-dependence cannot be well solved in the evidential reasoning (ER) approach with both weight and reliability. In order to solve the above problems, the characteristics of weight and reliability are investigated and summarized, i.e., the reliability of evidence is objective and absolute to reflect information quality, while the weight of evidence is subjective and relative to reflect information importance. Then a new discounting method is defined to generate probability masses for the evidence by assigning residual support of weight to empty set and that of reliability to power set. A new ER rule is established for recursively combining the evidence with both reliability and weight by the orthogonal sum operation and a series of theorems and corollaries are introduced and proved. Finally numerical comparison and illustrative example are provided to demonstrate the performances and the applicabilities of the proposed rule and algorithm.

A disjunctive belief rule-based expert system for bridge risk assessment with dynamic parameter optimization model

Abstract Bridge risk assessment is an important approach to avoiding the safety accidents of bridges and ensuring the safety of the public. This can be done by investigating the relationship between bridge risks and bridge criteria. However, such relationship usually is highly complicated in actual situations. In this regard, many approaches were proposed to model bridge risks in the past decades. Particularly, four alternative approaches including the artificial neural network (ANN), evidential reasoning with learning (ERL), multiple regression analysis (MRA), and adaptive neuro-fuzzy inference system (ANFIS) were deeply analyzed and compared for bridge risk assessment. However, these approaches are restricted by their shortages. Thus, this paper utilizes the disjunctive belief rule-based (DBRB) expert system to model bridge risks, where the DBRB expert system is one type of the belief rule-based (BRB) expert system by considering disjunctive belief rules (DBRs) rather than conjunctive belief rules (CBRs) in a BRB. Furthermore, the dynamic parameter optimization model and improved differential evolution (IDE) algorithm are proposed to train the parameters of the DBRB expert system, where the model is applied to ensure the completeness of a DBRB and the algorithm is used to get the global optimal solution. For justification purpose, two existing parameter optimization models and nine alternative models developed by the ANN, ERL, MRA, and ANFIS are applied to assess bridge structures. Comparison results indicate that the DBRB expert system with the dynamic parameter optimization model is better than those alternative models and existing parameter optimization models.

A joint optimization method on parameter and structure for belief-rule-based systems

Abstract The belief-rule-based system (BRBS) is one of the most visible and fastest growing branches of decision support systems. As the knowledge base in the BRBS, the belief-rule-base (BRB) is required to be equipped with the optimal parameters and structure, which means the optimal value and number of parameters, respectively. Several optimization methods were therefore proposed in the past decade. However, these methods presented different limitations, such as the use of the incomplete parameter optimization model, lack of structure optimization, and so on. Moreover, it is impracticable to determine the optimal parameters and structure of a BRB using the training error because of over-fitting. The present work is focused on the joint optimization on parameter and structure for the BRB. Firstly, a simple example is utilized to illustrate and analyze the generalization capability of the BRBS under different numbers of rules, which unveils the underlying information that the BRBS with a small training error may not have superior approximation performances. Furthermore, by using the Hoeffding inequality theorem in probability theory, it is a constructive proof that the generalization error could be a better choice of criterion and measurement to determine the optimal parameters and structure of a BRB. Based on the above results, a heuristic strategy to optimize the structure of the BRB is proposed, which is followed by a parameter optimization method using the differential evolution (DE) algorithm. Finally, a joint optimization method is introduced to optimize the parameters and structure of the BRB simultaneously. In order to verify the generality and effectiveness of the proposed method, two practical case studies, namely oil pipeline leak detection and bridge risk assessment, are examined to demonstrate how the proposed method can be implemented in the BRB under disjunctive and conjunctive assumptions along with their performance comparative analysis.

A consistency analysis-based rule activation method for extended belief-rule-based systems

Abstract Problems with inconsistency and incompleteness are widely found in rule-based decision support systems. These problems often impact the accuracy and usability of rule-based decision support systems. The present work focuses on an advanced rule-based decision support system, namely the extended belief-rule-based (EBRB) system, and proposes the consistency analysis-based rule activation (CABRA) method to overcome the above two problems simultaneously. However, two challenges must be discussed and addressed for the EBRB system. First, rather than using activated weights, suitable activated rules must be redefined to better analyze the problems of inconsistency and incompleteness. Second, suitable activated rules must be selected without having to depend on subjective information. Therefore, the proposed CABRA method uses the set of consistent rules as an activation framework to define suitable activated rules before calculating their activated weights, and utilizes the CCR model as a selection model to select suitable activated rules from the set of consistent rules. As such, by embedding the CABRA method, the EBRB system can overcome the problems of inconsistency and incompleteness. Three case studies demonstrate how the use of the CABRA method improves the accuracy and rule activation rate of the EBRB system, which is further confirmed by comparisons with the results of other existing studies. In addition to the work performed in the EBRB system, the CABRA method is treated as a generic rule activation method that can be available for other rule-based decision support systems.

Gini coefficient-based evidential reasoning approach with unknown evidence weights

Abstract The determination of evidence weights is an important step in evidence combination, which significantly influences final results. Taking into account the assumption of “psychology of economic man”, decision-makers may tend to seek similar pieces of evidence to support their own evidence in the process of negotiation and thereby forming an alliance of benefit. In the process of negotiation, decision-makers are concerned about the fairness of negotiation. To achieve the aim of fairness, in this paper, we extend the concept of evidential reasoning (ER) to evidential reasoning based on Gini coefficient (ERBGC) to obtain the weights of evidence. The main concept of the ERBGC approach is that the decision-maker is willing to engage negotiation with others only when the negotiation process is fair, that means the gap between maximum and minimum distributed interests among all decision-makers is less than that without negotiation. It shows that negotiation can make interests distribution fairer among decision-makers. In this study, the optimization model was developed to generate the relative weights based on Gini coefficient and enable weighted evidence to be combined using the ER rule. The approach is then applied to a case study and compared with other related approaches to demonstrate the effectiveness and applicability.

Ranking DMUs by using the upper and lower bounds of the normalized efficiency in data envelopment analysis

Abstract In data envelopment analysis, the existing methods for measuring the relative efficiencies of decision making units (DMUs) are to compare DMUs relative to the best or the worst of all DMUs. In this paper, we consider both the best DMU and the worst DMU as the reference DMUs and propose the normalized efficiency. Further, from the optimistic and pessimistic viewpoints, we construct two DEA models to obtain the upper and lower bounds of the normalized efficiency and then achieve an interval efficiency evaluation to rank all DMUs completely. Finally, two examples are presented to illustrate the performance of the interval efficiency evaluation.