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 A Model for Determining Weight Coefficients by Forming a Non-Decreasing Series at Criteria Significance Levels (NDSL)

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 745
Author(s):  
Mališa Žižović ◽  
Dragan Pamučar ◽  
Goran Ćirović ◽  
Miodrag M. Žižović ◽  
Boža D. Miljković
Keyword(s):  
Decision Makers ◽  
Pairwise Comparisons ◽  
Small Range ◽  
Analytic Hierarchy ◽  
Original Algorithm ◽  
Real World Problem ◽  
Significance Levels ◽  
Hierarchy Process ◽  
Weight Coefficients ◽  
Best Worst Method

In this paper, a new method for determining weight coefficients by forming a non-decreasing series at criteria significance levels (the NDSL method) is presented. The NDLS method includes the identification of the best criterion (i.e., the most significant and most influential criterion) and the ranking of criteria in a decreasing series from the most significant to the least significant criterion. Criteria are then grouped as per the levels of significance within the framework of which experts express their preferences in compliance with the significance of such criteria. By employing this procedure, fully consistent results are obtained. In this paper, the advantages of the NDSL model are singled out through a comparison with the Best Worst Method (BWM) and Analytic Hierarchy Process (AHP) models. The advantages include the following: (1) the NDSL model requires a significantly smaller number of pairwise comparisons of criteria, only involving an n − 1 comparison, whereas the AHP requires an n(n − 1)/2 comparison and the BWM a 2n − 3 comparison; (2) it enables us to obtain reliable (consistent) results, even in the case of a larger number of criteria (more than nine criteria); (3) the NDSL model applies an original algorithm for grouping criteria according to the levels of significance, through which the deficiencies of the 9-degree scale applied in the BWM and AHP models are eliminated. By doing so, the small range and inconsistency of the 9-degree scale are eliminated; (4) while the BWM includes the defining of one unique best/worst criterion, the NDSL model eliminates this limitation and gives decision-makers the freedom to express the relationships between criteria in accordance with their preferences. In order to demonstrate the performance of the developed model, it was tested on a real-world problem and the results were validated through a comparison with the BWM and AHP models.

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 Approach for Generating Weights Using the Pairwise Comparison Matrix

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Zaher Sepehrian ◽  
Sahar Khoshfetrat ◽  
Said Ebadi
Keyword(s):  
Pairwise Comparison ◽  
Decision Criterion ◽  
Data Envelopment ◽  
Decision Criteria ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Proposed Model ◽  
Assurance Region ◽  
Potential Applications ◽  
Hierarchy Process

Data envelopment analysis (DEA) has been used for obtaining weights for the analytic hierarchy process (AHP), an approach known as DEAHP. This method sometimes identifies more than one decision criterion or alternative as DEAHP-efficient. To overcome this problem, this paper proposes a new approach that not only generates appropriate weights for the decision criteria or alternatives, but also differentiates between DEAHP-efficient decision criteria or alternatives. To this end, we propose a DEA model with an assurance region and a cross-weight model that prioritizes decision criteria or alternatives by considering their most unfavorable weights. Two numerical examples are also provided to illustrate the advantages and potential applications of the proposed model.

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.

FARSJUM, A FUZZY SYSTEM FOR RANKING SPARSE JUDGMENT MATRICES: A CASE STUDY IN SOCCER TOURNAMENTS

2007 ◽  
Vol 15 (01) ◽  
pp. 115-129 ◽  
Author(s):  
M. R. GHOLAMIAN ◽  
S. M. T. FATEMI GHOMI ◽  
M. GHAZANFARI
Keyword(s):  
Pairwise Comparison ◽  
Major Constituent ◽  
Pairwise Comparisons ◽  
Ahp Method ◽  
World Cup ◽  
Analytic Hierarchy ◽  
Rank Reversal ◽  
Judgment Matrix ◽  
Hierarchy Process

The establishment of the priorities from pairwise comparison matrices is the major constituent of the Analytic Hierarchy Process (AHP). However, the number of pairwise comparisons necessary in real problems often becomes overwhelming. In such cases, generally the experts are not able to answer all questions and consequently sparse judgment matrix is generated which caused "equal ranks" and "rank reversal" based on AHP method. In this paper, a new ranking system (FARSJUM) is developed for such sparse judgment matrix. The system is constructed on fuzzy rules and fuzzy reasoning methods. The numerical example of world cup soccer tournament is brought to clarify the performance of the developed system comparing with AHP method in ranking the sparse judgment matrices.

scholarly journals On the features of the implementation of the interval method for analytic hierarchy process in the problem of assessing the effectiveness of the employment service

2020 ◽  
pp. 41-48
Author(s):  
N. F. Bogachenko ◽  
D. N. Lavrov
Keyword(s):  
Analytic Hierarchy Process ◽  
Interval Arithmetic ◽  
Pairwise Comparisons ◽  
Efficiency Function ◽  
Analytic Hierarchy ◽  
Employment Service ◽  
Interval Method ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process ◽  
Weight Coefficients

To determine the weight coefficients of the efficiency function of the employment service, the analytic hierarchy process and interval arithmetic were used. This made it possible to take into account the opinions of various experts without losing the consistency of the matrices of pairwise comparisons.

scholarly journals The Triads Geometric Consistency Index in AHP-Pairwise Comparison Matrices

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 926 ◽  
Author(s):  
Juan Aguarón ◽  
María Teresa Escobar ◽  
José María Moreno-Jiménez ◽  
Alberto Turón
Keyword(s):  
Pairwise Comparison ◽  
Consistency Index ◽  
Analytic Hierarchy ◽  
Priority Vector ◽  
Decision Tools ◽  
Geometric Consistency ◽  
The Matrix ◽  
Stability Intervals ◽  
Definition Of ◽  
Hierarchy Process

The paper presents the Triads Geometric Consistency Index ( T - G C I ), a measure for evaluating the inconsistency of the pairwise comparison matrices employed in the Analytic Hierarchy Process (AHP). Based on the Saaty’s definition of consistency for AHP, the new measure works directly with triads of the initial judgements, without having to previously calculate the priority vector, and therefore is valid for any prioritisation procedure used in AHP. The T - G C I is an intuitive indicator defined as the average of the log quadratic deviations from the unit of the intensities of all the cycles of length three. Its value coincides with that of the Geometric Consistency Index ( G C I ) and this allows the utilisation of the inconsistency thresholds as well as the properties of the G C I when using the T - G C I . In addition, the decision tools developed for the G C I can be used when working with triads ( T - G C I ), especially the procedure for improving the inconsistency and the consistency stability intervals of the judgements used in group decision making. The paper further includes a study of the computational complexity of both measures ( T - G C I and G C I ) which allows selecting the most appropriate expression, depending on the size of the matrix. Finally, it is proved that the generalisation of the proposed measure to cycles of any length coincides with the T - G C I . It is not therefore necessary to consider cycles of length greater than three, as they are more complex to obtain and the calculation of their associated measure is more difficult.

scholarly journals A Study of using AHP Method to Evaluate the Criteria and Attribute of Defects in Heritage Building

2018 ◽  
Vol 65 ◽  
pp. 01002
Author(s):  
Siti Nor Fatimah Zuraidi ◽  
Mohammad Ashraf Abdul Rahman ◽  
Zainal Abidin Akasah
Keyword(s):  
Pairwise Comparison ◽  
Pairwise Comparisons ◽  
Building Performance ◽  
Survey Questionnaire ◽  
Ahp Method ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Heritage Building ◽  
Element Type ◽  
Hierarchy Process

This paper examines the criteria and attributes for assessing defects in a heritage building. The goal of this paper is to solve element type for building defects by using the Analytic Hierarchy Process (AHP). A survey questionnaire was develop based on the identified criteria and attributes of defect for a heritage building in Malaysia. The survey questionnaire was administered to consultants, academics, and contractors. A total of 20 expert panels was selected to determine the element of the defect in building performance. The sensitivity analysis of alternative ratings in respect to difference pairwise comparisons of the criteria and attribute was carried out. By changing one element in the pairwise comparison matrix, the process of defect element is monitored thus enabling possible improvements. An overall ranking of the Hierarchy priorities of criteria and attribute was a result of the AHP analysis. The result of the research is weightage for each criterion and its respective attributes. The criteria and attributes will be used as elements to develop a strategic heritage building performance procedure in Malaysia.

DETERMINING THE DESALINATION UNIT COMPOSITION FOR COSTAL AREAS AND SMALL ISLANDS USE ANALYTIC HIERARCHY PROCESS

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Imam Setiadi ◽  
Dinda Rita K. Hartaja
Keyword(s):  
Analytic Hierarchy Process ◽  
Energy Demand ◽  
Pairwise Comparison ◽  
Small Islands ◽  
Ahp Method ◽  
Analytic Hierarchy ◽  
Comparison Research ◽  
Hierarchy Process ◽  
Selection Of

Selection of the appropriate composition desalination units can be done with a variety of method approaches, one of the method is the Analytic Hierarchy Process. In determining the desalination unit with AHP method to consider is setting a goal, an alternative criteria and pairwise comparison. Research for the determination of the exact composition of the desalination unit in order to achieve sustainable drinking water suppy in coastal areas and small islands has been conducted. The results of the study are as follows, the energy demand of 50.83%, operator costs of 26.64%, maintenance costs of 14.13% and chemical requirement 8.4%. For an alternative composition desalination unit of RO 10 m3 / day is the best alternative composition with value of 59.61%, the composition of the next alternative is RO 20 m3/ day of 30.40% and the last alternative of the desalination unit composition is RO 120 m3/ day of 09.99%.Key words : Desalination, Mukti Stage Flash Composition, AHP

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