Predefined Consensus Level Research Articles

Outline and validation of a new dispatcher-assisted cardiopulmonary resuscitation educational bundle using the Delphi method

AimDispatcher-assisted cardiopulmonary resuscitation (DA-CPR) is time-dependent. To date, evidence-based training programmes for dispatchers are lacking. This study aimed to reach expert consensus on an educational bundle content for dispatchers to provide DA-CPR using the Delphi method. MethodAn educational bundle was created by the Swedish Resuscitation Council consisting of three parts: e-learning on DA-CPR, basic life support training and audit of emergency out-of-hospital cardiac arrest calls. Thereafter, a two-round modified Delphi study was conducted between November 2022 and March 2023; 37 experts with broad clinical and/or scientific knowledge of DA-CPR were invited. In the first round, the experts participated in the e-learning module and answered a questionnaire with 13 closed and open questions, whereafter the e-learning part of the bundle was revised. In the second round, the revised e-learning part was evaluated using Likert scores (20 items). The predefined consensus level was set at 80%. ResultsDelphi rounds one and two were assessed by 20 and 18 of the invited experts, respectively. In round one, 18 experts (18 of 20, 90%) stated that they did not miss any content in the programme. In round two, the scale-level content validity index based on the average method (S-CVI/AVE, 0.99) and scale-level content validity index based on universal agreement (S-CVI/UA, 0.85) exceeded the threshold level of 80%. ConclusionExpert consensus on the educational bundle content was reached using the Delphi method. Further work is required to evaluate its effect in real-world out-of-hospital cardiac arrest calls.

Managing non-cooperative behaviors and ordinal consensus through a self-organized mechanism in multi-attribute group decision making

In consensus-based multi-attribute group decision making (MAGDM) problems, decision makers (DMs) may exhibit non-cooperative behaviors since they usually have different individual interests (sometimes conflicting) or limited knowledge, which strongly affects the efficiency of consensus and the quality of decision outcomes. Additionally, the existing MAGDM studies mainly focus on the cardinal consensus, and the ordinal consensus is ignored. Thus, this paper proposes a self-organized mechanism based framework to manage non-cooperative behaviors and ordinal consensus in MAGDM. First, a dual-membership function based on the basic idea of synergy theory is designed to detect non-cooperative behaviors at the element level of the multiple attribute evaluation matrix (MAEM), and then the weights of elements with non-cooperative behaviors are penalized automatically. In this way, the negative effects of non-cooperative behaviors can be eliminated. Next, a novel preference ranking-based ordinal consensus approach is proposed, which calculates an ordinal consensus based on the preference rankings of alternatives between individuals and the group. If the pre-defined consensus level is not reached, the feedback adjustment is used to help DMs modify their MAEMs to improve the consensus level; otherwise, the selection process is utilized to choose the optimal alternative(s). Finally, detailed simulation experiments and comparative analysis are designed to show the properties and effectiveness of the proposed framework, and an illustrative angel investment case is presented to demonstrate the calculation process and usability.

Analysis of Delphi study 7-point linear scale data by parametric methods: Use of the mean and standard deviation

The Delphi technique is a unique survey method that involves an iterative process to gain consensus when consensus is challenging to establish. Survey participants typically rate a variety of statements using a specified rating scale. The survey is repeated for several rounds, and at each round statements that do not reach a predefined level of consensus are advanced to the next round while giving the participants information about the responses of other participants for their comparison. The final statements are then ranked in order of the average rating. The statistical methods to analyze Delphi studies are not well described. This study investigates the use of a 1–7 linear rating scale along with parametric summary statistics for assessment of consensus and ranking of statements. A study set of 9297 individual ratings on the 1–7 scale were obtained from previously performed Delphi studies and used to create 490,000 simulated Delphi ratings with various numbers of participants. While the overall distribution of ratings was strongly left skewed the sampling distribution was near normally distributed for studies with five or more participants. The average difference between the standard deviation and interquartile range was −0.26/7. The overall risk of falsely concluding consensus using the standard deviation as a summary statistic was 7.3% when compared to using the interquartile range. The average difference between mean and median was −0.20/7. The risk of falsely ranking the statements by a value of 0.5 or more was near zero for all sample sizes when the mean was compared to the median. This study suggests that the use of the 1–7 linear rating scale in combination with the parametric summary statistics of standard deviation and mean is a valid method to analyze ratings from Delphi studies.

Analysis of Delphi Study Seven-Point Linear Scale Data by Parametric Methods–Use of the Mean and Standard Deviation

Introduction:The Delphi technique is a unique survey method that involves an iterative process to gain consensus when consensus is challenging to establish and is widely used in Disaster Medicine research. Participants typically rate a variety of statements using a specified rating scale. The survey is repeated for several rounds, and at each round statements that do not reach a predefined level of consensus are advanced to the next round while giving the participants information about the responses of other participants for their comparison. The final statements are then ranked in order of the average rating. The statistical methods to analyze Delphi studies are not well described. This study investigates the use of a 1 to 7 linear rating scale along with parametric summary statistics for assessment of consensus and ranking of statements.Method:A study set of 9297 individual ratings on the 1 to 7 scale were obtained from previously performed Delphi studies and used to create 490,000 simulated Delphi ratings with various numbers of participants.Results:While the overall distribution of ratings was strongly left skewed the sampling distribution was near normally distributed for studies with five or more participants. The average difference between the standard deviation and interquartile range was -0.26/7. The overall risk of falsely concluding consensus using the standard deviation as a summary statistic was 7.3% when compared to using the interquartile range. The average difference between mean and median was -0.20/7. The risk of falsely ranking the statements by a value of 0.5 or more was near zero for all sample sizes when the mean was compared to the median.Conclusion:This study suggests that the use of the 1 to 7 linear rating scale in combination with the parametric summary statistics of standard deviation and mean is a valid method to analyze ratings from Delphi studies.

Contrast-Enhanced Ultrasound: Development of Syllabus for Core Theoretical and Practical Competencies

Contrast-enhanced ultrasound (CEUS) is dependent on the observer's competencies, and thus, appropriate education and testing of individual competency is essential. The current international curriculum in CEUS is methodologically weak and lacks validated competency assessment tests. In this study, we aimed to develop a syllabus for core competencies in CEUS using the Delphi process and an international panel of experts. A core writing group constructed an initial draft of the syllabus based on the existing literature. Eight international experts in CEUS or medical education were recruited as Delphi panelists. The draft underwent iterative and anonymous Delphi rounds until a pre-defined level of consensus was reached. The final syllabus consisted of 16 items, which were indexed in two main domains and in procedural order. An expert-generated proposal for a syllabus of core CEUS competencies has been constructed via the Delphi process and may serve as framework for future development of a CEUS curriculum, including competency assessment tests.

Controlling the worst consistency index for hesitant fuzzy linguistic preference relations in consensus optimization models

Consistency and consensus using hesitant fuzzy linguistic preference relations (HFLPRs) are two closely related issues for group decision making. However, there are still some gaps that need to be addressed: the normalization methods applied in previous research change the initial information, most approaches modify every element of the original HFLPRs, and the consistency level is uncontrolled in the consensus reaching process. In this paper, two optimization methods are proposed: one that improves the worst consistency index (WCI) and the other that assists groups achieve a predefined consensus level: in which the revised preferences all belong to the original linguistic term set, which makes the revised preferences easier for decision makers (DMs) to interpret and accept. By using the worst consistency level, all possible LPRs in the given HFLPRs are analyzed. After the WCI is controlled, it is then possible to use any part of the preference information from the modified HFLPRs to satisfy the consistency level. Finally, the presented models are validated using numerical examples and extensive comparative analyses.

Direct Iterative Procedures for Consensus Building with Additive Preference Relations Based on the Discrete Assessment Scale

Individual consistency and group consensus are both important when seeking reliable and satisfying solutions for group decision making (GDM) problems using additive preference relations (APRs). In this paper, two new algorithms are proposed to facilitate the consensus reaching process, the first of which is used to improve the individual consistency level, and the second of which is designed to assist the group to achieve a predefined consensus level. Unlike previous GDM studies for consistency and consensus building, the proposed algorithms are essentially heuristic, modify only some of the elements in APRs to reduce the number of preference modifications in the consistency and consensus process, and have modified preferences that belong to the original evaluation scale to make the generated suggestions easier to understand. In particular, the consensus algorithm ensures that the individual consistency level is still acceptable when the predefined consensus level is achieved. Finally, classical examples and simulations are given to demonstrate the effectiveness of the proposed approaches.

Optimal consistency and consensus models for interval additive preference relations: A discrete distribution perspective

To assist in the consensus reaching process, this article presents optimization models with interval additive preference relations (APRs) drawn from pairwise comparisons. First, consistency models are proposed to obtain additively consistent interval APRs for continuous and discrete scale cases, after which consensus models are established to arrive at a predefined consensus level for the two cases. These models seek to minimize the amount of preference changes and can be solved using linear or integer linear programming techniques. While the obtained solutions may not be unique, a second stage model is introduced to reduce the uncertainty degrees in the suggested preferences. Compared to existing approaches, the proposed models have two major advantages: the derived solution can be limited to the easy to understand original scales, and refined solutions can be determined using multi-stage optimization. Finally, several numerical examples are given to verify the proposed models, and several simulations are conducted to demonstrate the potential behaviour of the presented models in practical applications.

Best Practices in Teaching Endoscopy Based on a Delphi Survey of Gastroenterology Program Directors and Experts in Endoscopy Education

Teaching endoscopy is a key objective of gastroenterology (GI) fellowship programs but the best approach is not known. We sought to characterize which teaching competencies experts considered most critical for endoscopy education. We developed and refined 18 endoscopy teaching competencies based on literature review, personal experience, and interviews with experts. We invited GI fellowship program directors and endoscopy education experts to participate in a Delphi process to rate each proposed competency as essential, important but not essential, or not important using a 70% agreement threshold for consensus. Thirty-four GI fellowship program directors and 2 experts in endoscopy education participated (n= 36). Most survey participants were male (61.8%), associate professors (55.9%), and had performed at least a quarter of procedures with fellows (80.6%). Survey response rates were 94% (34 of 36) for round 1 and 91% (31 of 34) for round 2 (overall 31 of 36; 86.1%). After 2 rounds we achieved the predefined consensus level for most competencies. Fourteen of 18 competencies (77.8%) reached consensus after round 2: 10 (55.6%) were deemed essential and 4 (22.2%) were deemed important but not essential. Essential competencies included the following: discusses patient history and plans for procedure with trainee (100%), assumes control of procedure when trainee is unable to progress or if patient safety concerns arise (100%), maintains attention throughout the case (96.8%), and discusses the next steps in management for the patient (96.8%). In a national Delphi survey of endoscopy education experts, we identified 10 essential endoscopy teaching competencies. These can be used to frame faculty development and standardize GI fellowship programs to promote high-quality endoscopy education.

Consensus Building for Probabilistic Hesitant Fuzzy Preference Relations with Expected Additive Consistency

As an extension of hesitant fuzzy element, probabilistic hesitant fuzzy element (PHFE) has received increasing attention. However, some important issues in PHFE utilization remain to be addressed. This study aims to build a consensus among the decision makers for probabilistic hesitant fuzzy preference relations (PHFPRs) with expected additive consistency. First, several generalized operations that are suitable for PHFPRs are defined. Then, expected additive consistent PHFPRs are introduced, and a theorem is proposed to obtain them. Second, the consistency index is defined based on the Hausdorff distance of PHFEs to measure whether individual PHFPRs exhibit acceptable expected additive consistency. If not, then an automatic iterative algorithm is designed to obtain acceptable ones. Third, group PHFPR is obtained based on the proposed generalized operations, and then the consensus index is determined according to the Hausdorff distance. If at least one of the consensus levels of the decision makers is lower than a given threshold, then an automatic iterative algorithm is used to update the PHFPRs to reach a predefined consensus level. Finally, a numerical example is provided, and comparative analyses with existing methods are performed to demonstrate the validity of the proposed method in addressing group decision-making problems.

A decision support model for group decision making with intuitionistic fuzzy linguistic preferences relations

As a new preference structure, the intuitionistic fuzzy linguistic preference relation (IFLPR) was introduced to efficiently cope with situations in which the membership degree and non-membership degree are represented as linguistic terms. For group decision making (GDM) problems with IFLPRs, two significant and challenging issues are individual consistency and group consensus before deriving the reliable priority weights of alternatives. In this paper, a novel decision support model is investigated to simultaneously deal with the individual consistency and group consensus for GDM with IFLPRs. First, the concepts of multiplicative consistency and weak transitivity for IFLPRs are introduced and followed by a discussion of their desirable properties. Then, a transformation approach is developed to convert the normalized intuitionistic fuzzy priority weights into multiplicative consistent IFLPR. Based on the distance of IFLPRs, the consistency index, individual consensus degree and group consensus degree for IFLPRs are further defined. In addition, two convergent automatic iterative algorithms are proposed in the investigated decision support model. The first algorithm is utilized to convert an unacceptable multiplicative consistent IFLPR to an acceptable one. The second algorithm can assist the group decision makers to achieve a predefined consensus level. The main characteristic of the investigated decision support model is that it guarantees each IFLPR is still acceptable multiplicative consistent when the predefined consensus level is achieved. Finally, several numerical examples are provided, and comparative analyses with existing approaches are performed to demonstrate the effectiveness and practicality of the investigated model.

A group consensus decision support model for hesitant 2-tuple fuzzy linguistic preference relations with additive consistency

Hesitant fuzzy linguistic term sets suit the modelling of qualitative setting so that experts provide several possible linguistic values than a single term for an indicator, alternative, variable, etc. This paper proposes a consistency and consensus based decision support model for group decision m aking with hesitant 2-tuple fuzzy linguistic preference relations (H2TFLPRs). A revised definition of hesitant fuzzy linguistic preference relation (HFLPR) is presented. In order to measure the consensus degrees, two indexes, an individual to group consensus index (ICI) and a group consensus index (GCI) are introduced, respectively. A consistency control process is developed to transform an unacceptable consistency H2TFLPR to an acceptable one. Then, an iterative group consensus reaching process is designed to conduct the decision makers (DMs) to achieve the predefined consensus level. In the consistency and consensus improving process, both the feedback mechanism and no-feedback mechanism are devised to conduct the DMs how to modify their original judgments, and both mechanisms can retain the DMs’ original information as much as possible. Finally, a numerical example is illustrated to demonstrate the effectiveness of the proposed method.

A Framework of Group Decision Making with Hesitant Fuzzy Preference Relations Based on Multiplicative Consistency

The purpose of this paper is to develop a general framework of group decision making with hesitant fuzzy preference relations based on the multiplicative consistency. First, we define a consistency index to measure whether or not a hesitant fuzzy preference relation is of acceptably multiplicative consistency. A consistency improving process is developed to improve the consistency level of a hesitant fuzzy preference relation with unacceptably multiplicative consistency until it is acceptably multiplicative. Then, we present a group consensus index to measure the deviation measure between the individual hesitant fuzzy preference relations and their collective hesitant fuzzy preference relation. A consensus reaching process is developed to help the decision makers improve the consensus level among hesitant fuzzy preference relations until they meet a predefined consensus level. Subsequently, we establish a complete framework of group decision making with hesitant fuzzy preference relations. In this framework, individual multiplicative consistency and group consensus are simultaneously highlighted and the acceptably multiplicative consistency of each hesitant fuzzy preference relation is still maintained in the achievement of the predefined consensus level. Finally, an illustrative numerical example is given to verify the effectiveness and practicality of the developed method.

A decision support model for group decision making with hesitant fuzzy preference relations

In this paper, we develop a decision support model that simultaneously addresses the consistency and consensus for group decision making based on hesitant fuzzy preference relations. The concepts of a consistency index and a consensus index are introduced. Two convergent algorithms are proposed in the developed support model. The first algorithm is used to convert an unacceptable hesitant fuzzy preference relation to an acceptable one. The second algorithm is utilized to help the group reach a predefined consensus level. The main characteristic of the developed model is that it makes each hesitant fuzzy preference relation maintain acceptable consistency when the predefined consensus level is achieved. Several illustrative examples are given to illustrate the effectiveness and practicality of the developed model.

A decision support model for group decision making with hesitant multiplicative preference relations

The hesitant fuzzy preference relation (HFPR) was recently introduced by Zhu and Xu to allow the decision makers (DMs) to offer several possible preference values over two alternatives. In this paper, we use an asymmetrical scale (Saaty’s 1–9 scale) to express the decision makers’ preference information instead of the symmetrical scale that is found in a HFPR, and we introduce a new preference structure that is known as the hesitant multiplicative preference relation (HMPR). Each element of the HMPR is characterized by several possible preference values from the closed interval [1/9, 9]; thus, it can model decision makers’ hesitation more accurately and reflect people’s intuitions more objectively. Furthermore, we develop a consistency- and consensus-based decision support model for group decision making (GDM) with hesitant multiplicative preference relations (HMPRs). In this model, an individual consistency index is defined to measure the degree of deviation between an HMPR and its consistent HMPR, and a consistency improving process is designed to convert an unacceptably consistent HMPR to an acceptably consistent HMPR. Additionally, a group consensus index is introduced to measure the degree of deviation between the individual HMPRs and the group HMPR, and a consensus-reaching process is provided to help the individual HMPRs achieve a predefined consensus level. Finally, a numerical example is provided to demonstrate the practicality and effectiveness of the developed model.

Essential key indicators for disaster medical response suggested to be included in a national uniform protocol for documentation of major incidents: a Delphi study

BackgroundRegistration of data from a major incident or disaster serves several purposes such as to record data for evaluation of response as well as for research. Data needed can often be retrieved after an incident while other must be recorded during the incident. There is a need for a consensus on what is essential to record from a disaster response. The aim of this study was to identify key indicators essential for initial disaster medical response registration. By this is meant nationally accepted processes involved, from the time of the emergency call to the emergency medical communication centre until medical care is provided at the emergency department.MethodsA three round Delphi study was conducted. Thirty experts with a broad knowledge in disaster and emergency response and medical management were invited. In this study we estimated 30 experts to be approximately one third of the number in Sweden eligible for recruitment. Process, structure and outcome indicators for the initial disaster medical response were identified. These were based on previous research and expressed as statements and were grouped into eight categories, and presented to the panel of experts. The experts were instructed to score each statement, using a five point Likert scale, and were also invited to include additional statements. Statements reaching a predefined consensus level of 80% were considered as essential to register.ResultsIn total 97 statements were generated, 77 statements reached consensus. The 77 statements covered parts of all relevant aspects involved in the initial disaster medical response. The 20 indicators that did not reach consensus mostly concerned patient related times in hospital, types of support systems and security for health care staff.ConclusionsThe Delphi technique can be used for reaching consensus of data, comprising process, structure and outcome indicators, identified as essential for recording from major incidents and disasters.

A concise consensus support model for group decision making with reciprocal preference relations based on deviation measures

Supporting the process of consensus building has become a major research field in group decision making (GDM). The purpose of this paper is to present a consistency consensus based decision support model for GDM based on reciprocal preference relations. Inspired by the concept of a deviation measure between two matrices, an individual consistency index and a group consensus index are presented. In the support model, a consistency control process is designed to make an inconsistent reciprocal preference relation one of acceptable consistency. To achieve a predefined consensus level, an interactive consensus reaching process is provided where the group reciprocal preference relation is seen as a reference when experts change their preferences. Theoretical foundations are then established for the proposed model. The proposed model revises the original information in a simple and straightforward gradual way. In the consensus process, the individual rationality level in terms of consistency is maintained. Two examples are examined to demonstrate the model in practical problems.

A consistency and consensus based decision support model for group decision making with multiplicative preference relations

In group decision making (GDM) with multiplicative preference relations (also known as pairwise comparison matrices in the Analytical Hierarchy Process), to come to a meaningful and reliable solution, it is preferable to consider individual consistency and group consensus in the decision process. This paper provides a decision support model to aid the group consensus process while keeping an acceptable individual consistency for each decision maker. The concept of an individual consistency index and a group consensus index is introduced based on the Hadamard product of two matrices. Two algorithms are presented in the designed support model. The first algorithm is utilized to convert an unacceptable preference relation to an acceptable one. The second algorithm is designed to assist the group in achieving a predefined consensus level. The main characteristics of our model are that: (1) it is independent of the prioritization method used in the consensus process; (2) it ensures that each individual multiplicative preference relation is of acceptable consistency when the predefined consensus level is achieved. Finally, some numerical examples are given to verify the effectiveness of our model.

Consensus reaching models of linguistic preference relations based on distance functions

In group decision making (GDM) using linguistic preference relations to obtain the maximum degree of agreement, it is desirable to develop a consensus process prior to the selection process. This paper proposes two consensus models with linguistic information to support the GDM consensus reaching process. Two different distance functions between linguistic preference relations are introduced to measure both individual consistency and group consensus. Based on these measures, the consensus reaching models are developed. The two models presented have the same concept that the expert whose preference is farthest from the group preference needs to update their opinion according to the group preference relation. In addition, the convergence of the models is proved. After achieving the predefined consensus level, each expert’s consistency indexes are still acceptable under the condition that the initial preference relations are of satisfactory consistency. Finally, an example is given to show the effectiveness of the models and to verify the theoretical results.

A discrete consensus support model for multiple attribute group decision making

In multiple attribute group decision making (MAGDM), it is preferable that the set of experts reach a high degree of consensus amongst their opinions before applying a selection process. In this paper, we present a discrete model to support the consensus reaching process for MAGDM problems. Firstly, a consensus scheme for a set of arguments is provided, where the basic idea is to tighten the range of opinions amongst experts. Based on the well-defined scheme, a convergent algorithm is presented to autocratically guide experts to reach a predefined consensus level. In the selection process, the maximizing deviation method is applied to determine the attribute weights. Then, the choice of the best alternative(s) from the group decision matrix is obtained by the simple additive weighting method. Finally, one example is presented to show the application and effectiveness of the proposed model.