Combining conflicting evidence using the DEMATEL method

Extended DEMATEL method with intuitionistic fuzzy information: A case of electric vehicles

The Decision-Making Trial and Laboratory (DEMATEL) methodology excels in the analysis of interdependent factors within complex systems, with correlation data typically presented in crisp values. Nevertheless, the judgments made by decision-makers often possess a degree of fuzziness and uncertainty, rendering the sole reliance on precise values inadequate for representing real-world scenarios. To address this issue, our study extends the DEMATEL approach to more effectively and efficiently handle intuitionistic fuzzy information, which denotes the factor correlation information from decision-makers in the form of intuitionistic fuzzy terms. The paper aggregates the intuitionistic fuzzy correlation information from each decision-maker, employing operators designed for managing intuitionistic fuzzy numbers. The significance and categorization of factors are determined through intuitionistic fuzzy matrix operations. Additionally, a causal and effect diagram is constructed to elucidate the distinct roles of these factors. Finally, this study illustrates the applicability of our proposed method with a real-world case in the context of electric vehicles (EVs). The study's results identify four cause factors and six effect factors within EV battery technology. The identification and categorization of these factors will assist EV companies in implementing targeted measures to foster the advancement of the battery technology.

Manufacturing system reconfiguration towards sustainable production: a novel hybrid optimization methodology

Developing a sustainable manufacturing system is a progressively challenging issue as governments across the world have been enforcing increasingly severe regulations by promoting the reduction of environmental waste for manufacturing and energy-saving production activities. Thus, there is a need for developing a sustainable manufacturing system that can be fully examined by incorporating ecological aspects (e.g., consumed energy) for related operations of a manufacturing system using computer-based discrete event simulation tools. In this study, a combined framework of a novel hybrid fuzzy multi-objective optimization and discrete event simulation approach is presented. We combine ecological and economic data and optimization techniques that are aimed at minimizing economic and ecological objectives in a manufacturing system at an early design phase. Hence, the fuzzy multi-objective optimization model is formulated by incorporating economic and ecological parameters. Again, the discrete event simulation model is established based on a comprehensive performance evaluation of the production system. This study also supports design decisions in determining optimum machine numbers, lighting, and cooling equipment required for the production processes within the sustainable manufacturing in conjunction with the most effective level of material flows. In addition, an integrated Decision-Making Trial and Evaluation Laboratory (DEMATEL)-epsilon constraint approach is applied to handle the multiple-objective optimization problem towards a set of trade-offs among the optimization objectives. A real-life application is carried out for investigating the applicability of the created hybrid framework. The findings of this study demonstrate that this framework is useful as a decision-making tool since it can develop a sustainable manufacturing system design considering an optimal solution associated with amounts of energy usage and CO2 emissions under economic constraints.

A Novel DEMATEL Approach by Considering Normalization and Invertibility

DEMATEL is a popular approach in multi-criteria decision making (MCDM) to understand the influence relationship between elements. In addition, the result of DEMATEL is used as the input in other approaches to explore further applications. However, DEMATEL may fail to derive the reasonable total influence matrix, i.e., all positive elements. Hence, DEMATEL uses a special normalization method to avoid that situation. It has been reported that selecting the normalization method plays a critical role after we determine the research method. This paper compares different normalization methods in DEMATEL and proposes a novel formula to derive the total influence matrix when the conventional DEMATEL cannot obtain a correct result. The numerical examples demonstrate how different normalization methods generate contradicted results of DEMATEL and the proposed approach ensures a reasonable result. In addition, we also shed light on further applications based on this paper.

Maximum Entropy (MaxEnt) Based DEMATEL and Its Application in Emergency Management

Since DEMATEL can visualize the structure of complex causal relationships, it is widely used in decision making. One of the important steps in DEMATEL is normalization, and it has received a lot of attention in recent years. Maximum entropy is a universal principle, and it is an effective tool for determining the amount of information existed in evidence. In this paper, maximum entropy based DEMATEL, named as MaxEnt-DEMETEL is proposed, the greatest contribution in this paper is the use of maximum entropy principle to determine the normalized direct influence matrix, which makes it possible to obtain the normalized matrix with minimal information loss. Emergency management is illustrated to show the superiority of the proposed method.

Conflicting evidence combination based on Belief Mover’s Distance

The Dempster-Shafer evidence theory has been extensively used in various applications of information fusion owing to its capability in dealing with uncertain modeling and reasoning. However, when meeting highly conflicting evidence, the classical Dempster’s combination rule may give counter-intuitive results. To address this issue, we propose a new method in this work to fuse conflicting evidence. Firstly, a new evidence distance metric, named Belief Mover’s Distance, which is inspired by the Earth Mover’s Distance, is defined to measure the difference between two pieces of evidence. Subsequently, the credibility weight and distance weight of each piece of evidence are computed according to the Belief Mover’s Distance. Then, the final weight of each piece of evidence is generated by unifying these two weights. Finally, the classical Dempster’s rule is employed to fuse the weighted average evidence. Several examples and applications are presented to analyze the performance of the proposed method. Experimental results manifest that the proposed method is remarkably effective in comparison with other methods.

Assessing the factors affecting implementation of unmanned aerial vehicles in Indian humanitarian logistics: a g-DANP approach

Purpose

The purpose of this paper is to analyze the factors affecting the implementation of unmanned aerial vehicles (UAVs) in Indian humanitarian logistics. The factors listed are significant as they are hindering the incorporation of this new technology into the humanitarian supply chain, thus creating inefficiencies in the humanitarian logistics sector.

Design/methodology/approach

This research is approached using a two-step process. In the first step, the particular barriers for UAV implementation are determined by a literature review and consultation with experts. Next, the proposed framework, a combination of grey-decision-making trial and evaluation laboratory (grey-DEMATEL) and analytic network process (ANP), i.e. g-DANP, is used to determine a hierarchical structure for the factors and sub-factors. The grey hypothesis provides sufficient analytical data to an otherwise lacking DEMATEL technique. Also, the use of ANP gives weightage to each factor, allowing us to categorize their importance further.

Findings

This study reveals that factors like expensive commercial solutions and high transport energy costs are significant factors of the “cause” group, whereas the uncertain cost for maintenance and repair and deficiency of high-level computing are crucial factors of the “effect” category. The mentioned factors, along with many others, are the main reasons for the delayed incorporation of UAVs in humanitarian logistics.

Practical implications

The results of this study present insights for humanitarian supply chain managers, UAV producers and policymakers. Those in the humanitarian logistics sector can use the findings of this study to plan for various challenges faced as they try and implement UAVs in their supply chain.

Originality/value

This research is unique as it analyses the general factors hindering the implementation of UAVs in Indian humanitarian logistics. The study enriches existing literature by providing an analytic approach to determine the weightage of various interrelations between the identified factors affecting UAV incorporation in the humanitarian supply chain.

A New Total Uncertainty Measure from A Perspective of Maximum Entropy Requirement

The Dempster-Shafer theory (DST) is an information fusion framework and widely used in many fields. However, the uncertainty measure of a basic probability assignment (BPA) is still an open issue in DST. There are many methods to quantify the uncertainty of BPAs. However, the existing methods have some limitations. In this paper, a new total uncertainty measure from a perspective of maximum entropy requirement is proposed. The proposed method can measure both dissonance and non-specificity in BPA, which includes two components. The first component is consistent with Yager's dissonance measure. The second component is the non-specificity measurement with different functions. We also prove the desirable properties of the proposed method. Besides, numerical examples and applications are provided to illustrate the effectiveness of the proposed total uncertainty measure.

Multi-sensor data fusion based on soft likelihood functions and OWA aggregation and its application in target recognition system

Multi-sensor data fusion plays an irreplaceable role in actual production and application. Dempster-Shafer theory (DST) is widely used in numerous fields of information modeling and information fusion due to the flexibility and effectiveness of processing uncertain information and dealing with uncertain information without prior probabilities. However, when highly contradictory evidence is combined, it may produce results that are inconsistent with human intuition. In order to solve this problem, a hybrid method for combining belief functions based on soft likelihood functions (SLFs) and ordered weighted averaging (OWA) operators is proposed. More specifically, a soft likelihood function based on OWA operators is used to provide the possibility to fuse uncertain information compatible with each other. It can characterize the degree to which the probability information of compatible propositions in the collected evidence is affected by unknown uncertain factors. This makes the results of using the Dempster's combination rule to fuse uncertain information from multiple sources more comprehensive and credible. Experimental results manifest that this method is reliable. Example and application show that this method has obvious advantages in solving the problem of conflict evidence fusion in multi-sensor. In particular, in target recognition, when three pieces of evidence are fused, the target recognition rate is 96.92%, etc.

Extended two-dimensional belief function based on divergence measurement

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

An evidence combination approach based on fuzzy discounting

In evidence theory, Dempster’s rule of combination is the most commonly applied method to aggregate bodies of evidence obtained from different sources to make a decision. However, when multiple independent bodies of evidence with conflict are aggregated by Dempster’s rule of combination, the counterintuitive results can be generated. Evidence discounting is proved to be an efficient way to eliminate the counterintuitive combination results. Following the discounting ideas, a new combination approach based on fuzzy discounting is put forward. Both the conflict between bodies of evidence and the uncertainty of a body of evidence itself are taken into account to determine the discounting factors. Jousselme’s evidence distance is used to represent conflict between bodies of evidence, and discriminability measure is defined to represent uncertainty of a body of evidence itself. Consider that both the evidence distance and the discriminability measure are semantically fuzzy. Thus, fuzzy membership functions are defined to describe both of them, and a fuzzy reasoning rule base is constructed to derive the discounting factors. Numerical examples indicate that this new combination approach proposed can achieve fast convergence speed and is robust to disturbing evidences, i.e., it is an effective method to process conflicting evidences combination.

An Extended Base Belief Function in Dempster–Shafer Evidence Theory and Its Application in Conflict Data Fusion

The Dempster–Shafer evidence theory has been widely applied in the field of information fusion. However, when the collected evidence data are highly conflicting, the Dempster combination rule (DCR) fails to produce intuitive results most of the time. In order to solve this problem, the base belief function is proposed to modify the basic probability assignment (BPA) in the exhaustive frame of discernment (FOD). However, in the non-exhaustive FOD, the mass function value of the empty set is nonzero, which makes the base belief function no longer applicable. In this paper, considering the influence of the size of the FOD and the mass function value of the empty set, a new belief function named the extended base belief function (EBBF) is proposed. This method can modify the BPA in the non-exhaustive FOD and obtain intuitive fusion results by taking into account the characteristics of the non-exhaustive FOD. In addition, the EBBF can degenerate into the base belief function in the exhaustive FOD. At the same time, by calculating the belief entropy of the modified BPA, we find that the value of belief entropy is higher than before. Belief entropy is used to measure the uncertainty of information, which can show the conflict more intuitively. The increase of the value of entropy belief is the consequence of conflict. This paper also designs an improved conflict data management method based on the EBBF to verify the rationality and effectiveness of the proposed method.

Improved Base Belief Function-Based Conflict Data Fusion Approach Considering Belief Entropy in the Evidence Theory

Due to the nature of the Dempster combination rule, it may produce results contrary to intuition. Therefore, an improved method for conflict evidence fusion is proposed. In this paper, the belief entropy in D–S theory is used to measure the uncertainty in each evidence. First, the initial belief degree is constructed by using an improved base belief function. Then, the information volume of each evidence group is obtained through calculating the belief entropy which can modify the belief degree to get the final evidence that is more reasonable. Using the Dempster combination rule can get the final result after evidence modification, which is helpful to solve the conflict data fusion problems. The rationality and validity of the proposed method are verified by numerical examples and applications of the proposed method in a classification data set.

An integrated decision-making model for supplier evaluation in public healthcare system: the case study of a Spanish hospital

Purpose

In this study, an integrated decision-making model consisting of decision-making trial and evaluation laboratory (DEMATEL), best worst method (BWM) and a modified version of evaluation based on distance from average solution (EDAS) methods is proposed for supplier selection problem in a public procurement system considering sustainable development goals.

Design/methodology/approach

DEMATEL and BWM methods are used to determine weights of the criteria that are defined for the supplier selection problem. Weight aggregation method is applied to combine the weights obtained from these two methods. A modified version of EDAS method is then used in order to rank the alternative suppliers.

Findings

The proposed decision-making model is investigated for a supplier selection problem for a hospital in Spain. The validity of the results is checked using comparison with other decision-making methods and several performance analysis tests.

Practical implications

The proposed multi-criteria decision-making (MCDM) model contributes to the healthcare supply chain management (SCM) and aims to lead the policy makers in selecting the best supplier.

Originality/value

There is no such study that combines DEMATEL and BWM together for weight generation. The application of the modified EDAS method is also new. In real time situations, the decision experts may confront to the difficulty of using BWM while identifying the best and the worst criteria choices. The idea of using DEMATEL is to aid the experts to make them enable in distinguishing between the best/worst criteria and handle BWM easily.

An Improved Total Uncertainty Measure in the Evidence Theory and Its Application in Decision Making

Dempster–Shafer evidence theory (DS theory) has some superiorities in uncertain information processing for a large variety of applications. However, the problem of how to quantify the uncertainty of basic probability assignment (BPA) in DS theory framework remain unresolved. The goal of this paper is to define a new belief entropy for measuring uncertainty of BPA with desirable properties. The new entropy can be helpful for uncertainty management in practical applications such as decision making. The proposed uncertainty measure has two components. The first component is an improved version of Dubois–Prade entropy, which aims to capture the non-specificity portion of uncertainty with a consideration of the element number in frame of discernment (FOD). The second component is adopted from Nguyen entropy, which captures conflict in BPA. We prove that the proposed entropy satisfies some desired properties proposed in the literature. In addition, the proposed entropy can be reduced to Shannon entropy if the BPA is a probability distribution. Numerical examples are presented to show the efficiency and superiority of the proposed measure as well as an application in decision making.

Analysis of Environmental Activities for Developing Public Health Investments and Policies: A Comparative Study with Structure Equation and Interval Type 2 Fuzzy Hybrid Models

The design of elements which exert pivotal effects on leisurely physical activity (LPA) in open space is an important part of urban development. However, little research has been done about the influence and discrepancies of those elements in different types of open space. To research these issues and to guide the design of urban open space, a survey from 8 open spaces (2 curtilage, 2 neighborhood squares (NS), 2 parks, and 2 campus) is conducted and a questionnaire is administered. Simultaneous analysis of several groups (SASG) of Structure equation model (SEM) is used, and the effects and discrepancies are acquired. In addition to this situation, interval type 2 (IT2) fuzzy hybrid decision making model is proposed in the second analysis. In this framework, IT2 fuzzy decision-making trial, evaluation laboratory (DEMATEL), and IT2 fuzzy technique for order preference by similarity to ideal solution (TOPSIS) methods are used. The results show that the influence relationships between elements and LPA did exist in four groups. Another important conclusion is that there were discrepancies of influence among different space groups. Physical environment (PE) has the greatest influence on LPA in the curtilage, whereas facilities exert the most effect in NS group. Additionally, amenities only have significant impact in parks and facilities only exercise remarkable influence on duration on campus. In addition to them, it is also identified that key design elements are presented for different types of space and that design strategy is provided through 4 specific examples.

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.

Combined Conflict Evidence Based on Two-Tuple IOWA Operators

Due to poor natural factors and human interference, the information that was obtained by sensors tends to have high uncertainty and high conflict with others. A combination of highly conflicting evidence with Dempster’s rule often produces results that run counter to intuition. To solve the above problem, a conflict evidence combination methodology is proposed in this article, which contains the distance of evidence, classical conflict coefficient, and two-tuple IOWA operator. Both the classical conflict coefficient and Jousselme distance indicate the degree of evidence conflict, and it is clear that the two parameters are symmetrical. First, the two-tuple IOWA operator is proposed. Second, the orness is determined by aggregated data; then, the weighting vector is calculated by a maximal entropy method. Finally, the weighted average is the evidence in the system by a two-tuple IOWA operator; then, the Dempster combination rule is utilized to fuse information. Compared with other existing methods, the presented methodology has high performance when dealing with conflict evidence and has strong anti-interference ability.

An Improved Multi-Source Data Fusion Method Based on the Belief Entropy and Divergence Measure

Dempster–Shafer (DS) evidence theory is widely applied in multi-source data fusion technology. However, classical DS combination rule fails to deal with the situation when evidence is highly in conflict. To address this problem, a novel multi-source data fusion method is proposed in this paper. The main steps of the proposed method are presented as follows. Firstly, the credibility weight of each piece of evidence is obtained after transforming the belief Jenson–Shannon divergence into belief similarities. Next, the belief entropy of each piece of evidence is calculated and the information volume weights of evidence are generated. Then, both credibility weights and information volume weights of evidence are unified to generate the final weight of each piece of evidence before the weighted average evidence is calculated. Then, the classical DS combination rule is used multiple times on the modified evidence to generate the fusing results. A numerical example compares the fusing result of the proposed method with that of other existing combination rules. Further, a practical application of fault diagnosis is presented to illustrate the plausibility and efficiency of the proposed method. The experimental result shows that the targeted type of fault is recognized most accurately by the proposed method in comparing with other combination rules.

Fire Control System Operation Status Assessment Based on Information Fusion: Case Study

In traditional fault diagnosis strategies, massive and disordered data cannot be utilized effectively. Furthermore, just a single parameter is used for fault diagnosis of a weapons fire control system, which might lead to uncertainty in the results. This paper proposes an information fusion method in which rough set theory (RST) is combined with an improved Dempster–Shafer (DS) evidence theory to identify various system operation states. First, the feature information of different faults is extracted from the original data, then this information is used as the evidence of the state for a diagnosis object. By introducing RST, the extracted fault information is reduced in terms of the number of attributes, and the basic probability value of the reduced fault information is obtained. Based on an analysis of conflicts in the existing DS evidence theory, an improved conflict evidence synthesis method is proposed, which combines the improved synthesis rule and the conflict evidence weight allocation methods. Then, an intelligent evaluation model for the fire control system operation state is established, which is based on the improved evidence theory and RST. The case of a power supply module in a fire control computer is analyzed. In this case, the state grade of the power supply module is evaluated by the proposed method, and the conclusion verifies the effectiveness of the proposed method in evaluating the operation state of a fire control system.

Time Series Data Fusion Based on Evidence Theory and OWA Operator

Time series data fusion is important in real applications such as target recognition based on sensors' information. The existing credibility decay model (CDM) is not efficient in the situation when the time interval between data from sensors is too long. To address this issue, a new method based on the ordered weighted aggregation operator (OWA) is presented in this paper. With the improvement to use the Q function in the OWA, the effect of time interval on the final fusion result is decreased. The application in target recognition based on time series data fusion illustrates the efficiency of the new method. The proposed method has promising aspects in time series data fusion.

An Intuitionistic Evidential Method for Weight Determination in FMEA Based on Belief Entropy

Failure Mode and Effects Analysis (FMEA) has been regarded as an effective analysis approach to identify and rank the potential failure modes in many applications. However, how to determine the weights of team members appropriately, with the impact factor of domain experts’ uncertainty in decision-making of FMEA, is still an open issue. In this paper, a new method to determine the weights of team members, which combines evidence theory, intuitionistic fuzzy sets (IFSs) and belief entropy, is proposed to analyze the failure modes. One of the advantages of the presented model is that the uncertainty of experts in the decision-making process is taken into consideration. The proposed method is data driven with objective and reasonable properties, which considers the risk of weights more completely. A numerical example is shown to illustrate the feasibility and availability of the proposed method.

Negation of Belief Function Based on the Total Uncertainty Measure

The negation of probability provides a new way of looking at information representation. However, the negation of basic probability assignment (BPA) is still an open issue. To address this issue, a novel negation method of basic probability assignment based on total uncertainty measure is proposed in this paper. The uncertainty of non-singleton elements in the power set is taken into account. Compared with the negation method of a probability distribution, the proposed negation method of BPA differs becausethe BPA of a certain element is reassigned to the other elements in the power set where the weight of reassignment is proportional to the cardinality of intersection of the element and each remaining element in the power set. Notably, the proposed negation method of BPA reduces to the negation of probability distribution as BPA reduces to classical probability. Furthermore, it is proved mathematically that our proposed negation method of BPA is indeed based on the maximum uncertainty.