scholarly journals Cognitive Best Worst Method for Multiattribute Decision-Making

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Hongjun Zhang ◽  
Chengxiang Yin ◽  
Xiuli Qi ◽  
Rui Zhang ◽  
Xingdang Kang
Keyword(s):  
Decision Making ◽  
Rating Scale ◽  
Semantic Representation ◽  
Pairwise Comparison ◽  
Pairwise Comparisons ◽  
Ratio Scale ◽  
Interval Scale ◽  
Real World Application ◽  
The Matrix ◽  
Best Worst Method

Pairwise comparison based multiattribute decision-making (MADM) methods are widely used and studied in recent years. However, the perception and cognition towards the semantic representation for the linguistic rating scale and the way in which the pairwise comparisons are executed are still open to discuss. The commonly used ratio scale is likely to produce misapplications and the matrix based comparison style needs too many comparisons and is not able to guarantee the consistency of the matrix when the number of objects involved is large. This research proposes a new MADM method CBWM (Cognitive Best Worst Method) which adopts interval scale to represent the pairwise difference and only compares each object to the best object and the worst object rather than all the other objects. CBWM is a vector based method which only needs 2n-3 pairwise comparisons and is more likely to generate consistent comparisons and reliable results. The theoretical analysis and a real world application demonstrate the effectiveness of CBWM.

scholarly journals SOLUTION OF A MULTI-CRITERIA DECISION- MAKING PROBLEM ON BASE OF PROMETHEE METHOD

2020 ◽  
Author(s):  
Salimov Vagif Hasan Oglu
Keyword(s):  
Decision Making ◽  
Pairwise Comparison ◽  
Preference Function ◽  
Pairwise Comparisons ◽  
Multi Criteria Decision Making ◽  
Job Selection ◽  
Decision Making Problem ◽  
Practice Problem ◽  
Promethee Method ◽  
Large Groups

Multi criteria decision making problem was considered. Review of existing multi criteria decision making methods was presented. Methods of solving this problem can be divided into two large groups: methods using the aggregation of all alternatives according to all criteria and the solution of the obtained one-criterion problem, the second group is associated with the procedure of pairwise comparisons. Promethee method have been considered with details. This method is based on the pairwise comparison of alternatives and specific aggregation procedures. The preference function are considered for minimization and maximization cases. As practice problem the job selection is considered. Three important criteria are used: salary, time, risk. The results of all computations are presented.

scholarly journals Fusion of BWM and AHP MCDM Methods to Choose the Most Suitable Secondary School for an Individual in the Context of Bangladesh

2019 ◽  
Vol 06 (03) ◽  
pp. 311-328
Author(s):  
N. S. M. Rezaur Rahman ◽  
Md. Abdul Ahad Chowdhury ◽  
Adnan Firoze ◽  
Rashedur M. Rahman
Keyword(s):  
Decision Making ◽  
Secondary School ◽  
Pairwise Comparison ◽  
User Preferences ◽  
Multi Criteria Decision Making ◽  
Analytic Hierarchy ◽  
Final Score ◽  
Hierarchy Process ◽  
Best Worst Method

Choosing the best schools from a group of schools is a multi-criteria decision-making (MCDM) problem. In this paper, we have represented a method that uses the fusion of two multi-criteria decision-making methods, Best–Worst Method (BWM) and Analytic Hierarchy Process (AHP), to rank some of the user preferred alternatives. The system considers the choice of the user and the quality of the alternatives to rank them. User preferences on the criteria are taken as inputs in the form of best–worst comparison vectors to measure the choice of the user. These values are applied to calculate the numeric weights of each of the criteria. These weights reflect the preference of the user. A dataset of secondary schools in Bangladesh has been compiled and used for automatic quantitative pairwise comparison on the alternatives to calculate the score of each alternative in every criterion, which reflects its quality in that criterion. These scores are calculated using AHP. The weights of the criteria as well as the scores of these alternatives in those criteria are then used to calculate the final score of the alternatives and to rank them accordingly. An extensive experimental analysis and comparative study is reported at the end of this paper.

FAIR CONSISTENCY EVALUATION FOR RECIPROCAL RELATIONS AND IN GROUP DECISION MAKING

2009 ◽  
Vol 05 (02) ◽  
pp. 407-420 ◽  
Author(s):  
MICHELE FEDRIZZI ◽  
MATTEO BRUNELLI
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Group Decision Making ◽  
Evaluation Method ◽  
Group Decision ◽  
Pairwise Comparison ◽  
Pairwise Comparisons ◽  
Reciprocal Relations ◽  
Decision Making Processes ◽  
Consistency Evaluation

In decision-making processes, it often occurs that the decision maker is asked to pairwise compare alternatives. His/her judgements over a set of pairs of alternatives can be collected into a matrix and some relevant properties, for instance, consistency, can be estimated. Consistency is a desirable property which implies that all the pairwise comparisons respect a principle of transitivity. So far, many indices have been proposed to estimate consistency. Nevertheless, in this paper we argue that most of these indices do not fairly evaluate this property. Then, we introduce a new consistency evaluation method and we propose to use it in group decision making problems in order to fairly weigh the decision maker's preferences according to their consistency. In our analysis, we consider two families of pairwise comparison matrices: additively reciprocal pairwise comparison matrices and multiplicatively reciprocal pairwise comparison matrices.

scholarly journals IMPROVING CONSISTENCY EVALUATION IN FUZZY MULTI-ATTRIBUTE PAIRWISE COMPARISON-BASED DECISION-MAKING METHODS

2014 ◽  
Vol 31 (04) ◽  
pp. 1450024 ◽  
Author(s):  
FARHAD SHAMS ◽  
SHERIF MOHAMED ◽  
AMINAH ROBINSON FAYEK
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Decision Model ◽  
Pairwise Comparison ◽  
Pairwise Comparisons ◽  
Linguistic Data ◽  
Multi Attribute Decision Making ◽  
Numeric Scale ◽  
Consistency Evaluation

A typical approach to handle the complexity of multi-faceted decision-making problems is to use multi-attribute decision-making (MADM) methods based on pairwise comparisons. Fuzzy set theory has also been employed to cope with the uncertainty and vagueness involved in conducting the comparisons between components of a decision model. An important issue regarding the reliability of the output is the consistency of pairwise comparisons provided by the decision maker(s). Using the MADM method developed by Lu et al. (2007) as a foundation, this paper proposes an algorithm for evaluating the consistency level of pairwise comparison matrices, where linguistic data are used. A crisp numeric scale has been introduced to consider the priority of linguistic data and to avoid the complexity of handling fuzzy calculations in consistency evaluation of pairwise comparison matrices. As an advantage, the proposed method of consistency evaluation is capable of assessing the degree of inconsistency among the pairwise comparisons. Therefore, the acceptance or rejection of the pairwise comparisons can be determined based on the desired degree of tolerance in accepting inconsistent judgments. An application of a revised MADM method is then demonstrated in a case study involving flood mitigation project selection in Australia.

scholarly journals Comparing best-worst method and full consistency method in a fuzzy environment

2022 ◽  
Vol 11 (2) ◽  
pp. 181-192
Author(s):  
Arash Haqbin
Keyword(s):  
Decision Making ◽  
Real World ◽  
Pairwise Comparison ◽  
Multicriteria Decision Making ◽  
Fuzzy Environment ◽  
Study Results ◽  
Mcdm Method ◽  
Consistency Method ◽  
Best Worst Method

Multicriteria Decision Making (MCDM) is one the most important branches of decision theory. Due to the fact that MCDM methods have the utmost significance in management, scholars try to develop more MCDM methods. Since calculating the weights of criteria is an important step in any MCDM method, increasing the accuracy of weight calculating methods can highly affect these methods. This accuracy can be improved by less pairwise comparison between criteria. To this end, the present study seeks to make a comparison between two new weight calculating techniques, namely BWM and FUCOM in a fuzzy environment using a real-world case study Results of this study shows that FUCOM-F provides more reliable results compared to FBWM since its consistency is less than FBWM by a great amount.

scholarly journals A Concentration Ratio for Nonlinear Best Worst Method

2020 ◽  
Vol 19 (03) ◽  
pp. 891-907 ◽  
Author(s):  
Jafar Rezaei
Keyword(s):  
Decision Making ◽  
Nonlinear Model ◽  
Concentration Ratio ◽  
Pairwise Comparison ◽  
Multi Criteria Decision Making ◽  
Comparison System ◽  
Consistency Ratio ◽  
Optimal Weights ◽  
The Relationship ◽  
Best Worst Method

Best Worst Method (BWM) is a multi-criteria decision-making method that is based on a structured pairwise comparison system. It uses two pairwise comparison vectors (best-to-others and others-to-worst) as input for an optimization model to get the optimal weights of the criteria (or alternatives). The original BWM involves a nonlinear model that sometimes results in multiple optimal weights meaning that the weight of each criterion is presented as an interval. The aim of this paper is to introduce a ratio, called concentration ratio, to check the concentration of the optimal intervals obtained from the nonlinear BWM. The relationship between the concentration ratio and the consistency ratio is investigated and it is found that the concentration ratio along with the consistency ratio of the model provides enhanced insights into the reliability and flexibility of the results of BWM.

scholarly journals A New Model for Determining Weight Coefficients of Criteria in MCDM Models: Full Consistency Method (FUCOM)

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 393 ◽  
Author(s):  
Dragan Pamučar ◽  
Željko Stević ◽  
Siniša Sremac
Keyword(s):  
Pairwise Comparison ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Proposed Model ◽  
Optimal Values ◽  
Definition Of ◽  
Hierarchy Process ◽  
Consistency Method ◽  
Weight Coefficients ◽  
Best Worst Method

In this paper, a new multi-criteria problem solving method—the Full Consistency Method (FUCOM)—is proposed. The model implies the definition of two groups of constraints that need to satisfy the optimal values of weight coefficients. The first group of constraints is the condition that the relations of the weight coefficients of criteria should be equal to the comparative priorities of the criteria. The second group of constraints is defined on the basis of the conditions of mathematical transitivity. After defining the constraints and solving the model, in addition to optimal weight values, a deviation from full consistency (DFC) is obtained. The degree of DFC is the deviation value of the obtained weight coefficients from the estimated comparative priorities of the criteria. In addition, DFC is also the reliability confirmation of the obtained weights of criteria. In order to illustrate the proposed model and evaluate its performance, FUCOM was tested on several numerical examples from the literature. The model validation was performed by comparing it with the other subjective models (the Best Worst Method (BWM) and Analytic Hierarchy Process (AHP)), based on the pairwise comparisons of the criteria and the validation of the results by using DFC. The results show that FUCOM provides better results than the BWM and AHP methods, when the relation between consistency and the required number of the comparisons of the criteria are taken into consideration. The main advantages of FUCOM in relation to the existing multi-criteria decision-making (MCDM) methods are as follows: (1) a significantly smaller number of pairwise comparisons (only n − 1), (2) a consistent pairwise comparison of criteria, and (3) the calculation of the reliable values of criteria weight coefficients, which contribute to rational judgment.

scholarly journals An Integrated Decision Support Model for Evaluating Public Transport Quality

2020 ◽  
Vol 10 (12) ◽  
pp. 4158 ◽  
Author(s):  
Sarbast Moslem ◽  
Ahmad Alkharabsheh ◽  
Karzan Ismael ◽  
Szabolcs Duleba
Keyword(s):  
Public Transport ◽  
Pairwise Comparison ◽  
Quality Criteria ◽  
Evaluation Process ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Urban Bus ◽  
Hierarchy Process ◽  
Bus Transport ◽  
Best Worst Method

Big cities suffer from serious complex problems such as air pollution, congestion, and traffic accidents. Developing public transport quality in such cities is considered an efficient remedy to obviate these critical issues. This paper aims to determine the significant supply quality criteria of public transportation. As a methodology, a hybrid Analytic Hierarchy Process (AHP) combined with the Best Worst Method (BWM) is applied. The proposed model is basically a hierarchy structure with at least a 5 × 5 pairwise comparison matrix or larger. A real-world complex problem was examined to validate the created model (public transport quality improvement). An urban bus transport system in the Jordanian capital city, Amman, was used as a case study; three stakeholder groups (passengers, nonpassengers, and representatives of the local government) participated in the evaluation process. The conventional Analytic Hierarchy Process (AHP) leads to weak consistency in the case of existing 5 × 5 pairwise comparison matrices or larger, particularly in estimating complex problems. To avoid this critical issue in AHP, we used Best Worst Method (BWM) comparisons, which make the evaluation process easier for decision makers; moreover, it saves survey time and provides more consistency when compared to AHP pairwise comparisons. The model adopted highlighted the most significant service quality criteria that influence urban bus transport systems. Furthermore, the sensitivity analysis conducted detected the stability of the criteria ranking in the three levels of the hierarchical structure. Since the proposed AHP–BWM model (which is the sole example of this sort of combination) is independent from the decision attributes, it can be applied to arbitrary hierarchically structured decision problems with a relatively large number of pairwise comparisons.

scholarly journals An Extension of Cross Redundancy of Interval Scale Outputs and Inputs in DEA

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Farhad Hosseinzadeh-Lotfi ◽  
Gholam-Reza Jahanshahloo ◽  
Mansour Mohammadpour
Keyword(s):  
Decision Making ◽  
Linear Combination ◽  
Data Envelopment ◽  
Ratio Scale ◽  
Interval Scale ◽  
Output Variable ◽  
Input And Output ◽  
Dea Models ◽  
Decision Making Units ◽  
Selection Of

It is well known that data envelopment analysis (DEA) models are sensitive to selection of input and output variables. As the number of variables increases, the ability to discriminate between the decision making units (DMUs) decreases. Thus, to preserve the discriminatory power of a DEA model, the number of inputs and outputs should be kept at a reasonable level. There are many cases in which an interval scale output in the sample is derived from the subtraction of nonnegative linear combination of ratio scale outputs and nonnegative linear combination of ratio scale inputs. There are also cases in which an interval scale input is derived from the subtraction of nonnegative linear combination of ratio scale inputs and nonnegative linear combination of ratio scale outputs. Lee and Choi (2010) called such interval scale output and input a cross redundancy. They proved that the addition or deletion of a cross-redundant output variable does not affect the efficiency estimates yielded by the CCR or BCC models. In this paper, we present an extension of cross redundancy of interval scale outputs and inputs in DEA models. We prove that the addition or deletion of a cross-redundant output and input variable does not affect the efficiency estimates yielded by the CCR or BCC models.

An Evaluation Method for Inconsistency of the AHP Judgment Matrix

2002 ◽  
Author(s):  
Yuan Mao Huang ◽  
Hsin-Ni Ho
Keyword(s):  
Decision Making ◽  
Evaluation Method ◽  
Decision Makers ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Principal Eigenvector ◽  
The Matrix ◽  
Judgment Matrix ◽  
Index Value ◽  
Hierarchy Process

Applications of the analytic hierarchy process have been widespread in the field of decision-making for decades. In this process, decision-makers perform pairwise comparisons to form a judgment matrix, and its principal eigenvector is used to represent the priorities. Thus it is important to evaluate the degree of inconsistency in a judgment matrix to ensure the principal eigenvector reflects the true priorities among the alternatives. This study proposes the I3 circuit method, which is based on the graph theory, with a critical inconsistent index value of 3.75 to judge and evaluate consistency or the degree of inconsistency for judgment matrices. In addition, it can also spot the matrix entries that create the most inconsistency. With these advantages of the proposed method, decision-makers can easily evaluate the pairwise comparisons of a matrix and revise some entries of the matrix toward consistency if needed.

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