A Condorcet Voting Theory Based AHP Approach for MCDM Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 276
Author(s):  
Sweta Bhattacharya ◽  
V Raju
Keyword(s):  
Decision Making ◽  
Pairwise Comparison ◽  
Ratio Method ◽  
Multi Criteria Decision Making ◽  
Voting Theory ◽  
Ahp Method ◽  
Pairwise Comparison Matrix ◽  
Consistency Ratio ◽  
Comparison Matrix ◽  
Subjective Judgement

<p>Analytical Hierarchical Process has been used as a useful methodology for multi-criteria decision making environments with substantial applications in recent years. But the weakness of the traditional AHP method lies in the use of subjective judgement based assessment and standardized scale for pairwise comparison matrix creation. The paper proposes a Condorcet Voting Theory based AHP method to solve multi criteria decision making problems where Analytical Hierarchy Process (AHP) is combined with Condorcet theory based preferential voting technique followed by a quantitative ratio method for framing the comparison matrix instead of the standard importance scale in traditional AHP approach. The consistency ratio (CR) is calculated for both the approaches to determine and compare the consistency of both the methods. The results reveal Condorcet – AHP method to be superior generating lower consistency ratio and more accurate ranking of the criterion for solving MCDM problems.</p>

scholarly journals Utilization of AHP-MAUT Method to Determine the Country of Exhibition Abroad in Batik Hatta Boutique

2021 ◽  
Vol 5 (02) ◽  
pp. 52-56
Author(s):  
Saifur Rohman Cholil ◽  
Tria Ardianita
Keyword(s):  
Decision Making ◽  
Rank Correlation ◽  
Pairwise Comparison ◽  
Hierarchical Level ◽  
Spearman Rank Correlation ◽  
Ahp Method ◽  
Pairwise Comparison Matrix ◽  
Spearman Rank ◽  
Comparison Matrix ◽  
A Value

This research was conducted with the aim of helping decide the destination country for overseas exhibitions at the Batik Hatta Boutique. By knowing all the data and information of a country, boutique owners can decide which country to visit in the batik exhibition. Because if you attend the cast in all countries, there will be overruns in costs. The methods used are AHP and MAUT. The AHP method is used as a weighting using a linguistic value scale. Weights are obtained from the pairwise comparison matrix between two elements of all elements that occur at the same hierarchical level. The MAUT method is used to determine the importance of each alternative for the ranking process. The results of this study indicate that Cambodia was chosen as the location to be visited for the batik exhibition. The results of the validation using the Spearman Rank correlation comparison obtained a value of 0.951 meaning that this method can be used as a decision making.

scholarly journals A Discussion on “Pythagorean fuzzy AHP based risk assessment methodology for hazardous material transportation: an application in Istanbul”

2022 ◽  
Author(s):  
Shahid Bhat ◽  
Akanksha Singh
Keyword(s):  
Decision Making ◽  
Fuzzy Ahp ◽  
Value Added ◽  
Pairwise Comparison ◽  
Ahp Method ◽  
Hazardous Material ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
Hazardous Material Transportation ◽  
Material Transportation

Abstract Ayyildiz et al. (Environmental Science and Pollution Research (2021), 1-13) pointed out that it is important to identify and minimize the critical risks in the transportation of hazardous material. For the same, Ayyildiz et al. proposed an effective integrated decision-making methodology by combining the Modified Delphi Method (MDM) and Pythagorean fuzzy analytic hierarchy process (PF-AHP). In this integrated methodology, PF-AHP method is utilized to obtain weights of main and sub-risk factors in order to rank these factors. In Step 5 of PF-AHP method an interval valued Pythagorean fuzzy pairwise comparison matrix is transformed into a crisp matrix and then crisp AHP is applied to obtain the normalized weights from the transformed crisp matrix. It is quite evident that the crisp AHP is used only for crisp pairwise comparison matrix. However, after a deep study, it is observed that the transformed crisp matrix, obtained on applying the steps of Ayyildiz et al. methodology, violates the reciprocal propriety of pairwise comparison matrix. Therefore, to apply crisp AHP on the transformed crisp matrix is mathematically incorrect and will lead to problematic decision-making approach. Hence, may result in a heavy loss in any value-added model such as hazardous material transportation problems. Therefore, the Ayyildiz et al. methodology is not valid in its present form and cannot be used to find the solution of such type of real-life problem. Keeping the same in mind, the focus of this discussion is to make the researchers aware about these mathematical incorrect assumptions and the necessary modification is suggested.

scholarly journals Proposed Method for Supplier Selection

2020 ◽  
Vol 13 ◽  
pp. 376-394
Author(s):  
Agus Ristono ◽  
Tri Wahyuningsih ◽  
Eko Junianto
Keyword(s):  
Network Model ◽  
Analytical Hierarchy Process ◽  
Supplier Selection ◽  
Pairwise Comparison ◽  
Pairwise Comparisons ◽  
Chain Process ◽  
Ahp Method ◽  
Pairwise Comparison Matrix ◽  
Consistency Ratio ◽  
Hierarchy Process

The use of the Analytical Hierarchy Process (AHP) is frequent in supplier selection. First, AHP is a pairwise comparison between criteria. If the pairwise comparisons are inconsistent, the result is invalid. Thus, the process of comparing criteria must be repeated continuously until valid results are obtained. This process takes time and costs so it is considered inefficient. This research proposes the application of the Hamilton chain process into the pairwise comparison matrix. One criterion is symbolized as a knot, while the arc is symbolized as the pairwise comparison value between the two nodes or the connected criterion. In the network model of the AHP method, each node is connected to all other nodes without exception. Whereas in the proposed method, each criterion or node is compared only once. That said, avoiding inconsistencies can be made. The consistency ratio result of the proposed method is found to be consistent

scholarly journals PAIRWISE COMPARISON MATRIX IN MULTIPLE CRITERIA DECISION MAKING

2016 ◽  
Vol 22 (5) ◽  
pp. 738-765 ◽  
Author(s):  
Gang KOU ◽  
Daji ERGU ◽  
Yang CHEN ◽  
Changsheng LIN
Keyword(s):  
Decision Making ◽  
Web Of Science ◽  
Multiple Criteria Decision Making ◽  
Pairwise Comparison ◽  
Future Research ◽  
Measurement Scales ◽  
Pairwise Comparison Matrix ◽  
Future Directions ◽  
Comparison Matrix ◽  
Comprehensive Literature Review

The measurement scales, consistency index, inconsistency issues, missing judgment estimation and priority derivation methods have been extensively studied in the pairwise comparison matrix (PCM). Various approaches have been proposed to handle these problems, and made great contributions to the decision making. This paper reviews the literature of the main developments of the PCM. There are plenty of literature related to these issues, thus we mainly focus on the literature published in 37 peer reviewed international journals from 2010 to 2015 (searched via ISI Web of science). We attempt to analyze and classify these literatures so as to find the current hot research topics and research techniques in the PCM, and point out the future directions on the PCM. It is hoped that this paper will provide a comprehensive literature review on PCM, and act as informative summary of the main developments of the PCM for the researchers for their future research.

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 SISTEM PENDUKUNG KEPUTUSAN PENERIMAAN BEASISWA BIDIKMISI DI UINSA DENGAN MENGGUNAKAN ANALYTICAL HIERARCHY PROCESS (AHP)

2021 ◽  
Vol 10 (2) ◽  
pp. 188
Author(s):  
Mila Iflakhah ◽  
Moh. Hafiyusholeh
Keyword(s):  
Decision Making ◽  
Analytical Hierarchy Process ◽  
Science And Technology ◽  
Pairwise Comparison ◽  
Primary Data ◽  
Eigenvalues And Eigenvectors ◽  
Pairwise Comparison Matrix ◽  
Screening Process ◽  
Comparison Matrix ◽  
Hierarchy Process

<p class="AfiliasiCxSpFirst" align="left"><strong>Abstrak:</strong></p><p class="AfiliasiCxSpMiddle">            Beasiswa merupakan pemberian bantuan biaya pendidikan kepada mahasiswa yang mampu dalam bidang akademik tetapi tidak dalam perekonomian. Namun masih sering terjadi kendala dalam pemrosesan seleksi pendaftar beasiswa, yaitu banyaknya kriteria yang harus diperhatikan dan banyaknya data pendaftar sehingga pengambilan keputusan menjadi relatif lebih sulit. Tujuan dari penelitian ini adalah memberikan alternatif dalam pengambilan keputusan penerima bantuan beasiswa untuk mahasiswa fakultas sains dan teknologi UINSA dengan menggunakan metode <em>Analytical Hierarchy Process (</em>AHP). Data yang diolah adalah data primer yang diperoleh dari angket. Data yang telah terkumpul selanjutnya dianalisis dengan matriks perbandingan berpasangan untuk menentukan nilai eigen dan vektor eigen. Hasil penelitian menunjukkan bahwa dari 39 pendaftar diperoleh 12 pendaftar yang menjadi prioritas dalam mendapatkan beasiswa Bidikmisi. Berturut-turut mahasiswa dengan kode Z1, Z2, Z5, Z7, Z10, Z19, Z20, Z21, Z23, Z29, Z32, Z35 dengan masing-masing bobot sebesar 0.34%, 0.27%, 0.27%, 0.28%, 0.36%, 0.33%, 0.29%, 0.31%, 0.34%, 0.29%, 0.27%, 0.35%.</p><p class="AfiliasiCxSpMiddle" align="left"> </p><p class="AfiliasiCxSpLast" align="left"><strong>Kata Kunci</strong>:</p><p>Vektor<em> </em>Eigen<em>, Analytical Hierarchy Process </em>(AHP)<em>, </em>Nilai<em> </em>Eigen</p><p> </p><p class="AfiliasiCxSpFirst" align="left"><strong><em>Abstract:</em></strong></p><p class="AfiliasiCxSpMiddle"><em>The scholarship is the provision of tuition assistance to students who are capable of academics but have difficulties economically. However, some obstacles are often found throughout the screening process of scholarship applicants, such as the number of criteria to fulfill and the number of registrant data that results in difficulties in making a decision</em><em>. </em><em>This study aims to provide an alternative in decision making on the screening process of scholarship applicants for students from the Faculty of Science and Technology at the Universitas Islam Negeri Sunan Ampel by using the Analytical Hierarchy Process (AHP)</em><em>. </em><em>The data processed are from the primary data obtained from questionnaires. The data obtained were analyzed by using a pairwise comparison matrix to determine the eigenvalues and eigenvectors. The results indicate that of 39 registrants, 12 of them became a priority in getting the Bidikmisi scholarship</em><em>. </em><em>Consecutively, students with codes</em><em> Z1, Z2, Z5, Z7, Z10, Z19, Z20, Z21, Z23, Z29, Z32, Z35 </em><em>have the score of</em><em> 0.34%, 0.27%, 0.27%, 0.28%, 0.36%, 0.33%, 0.29%, 0.31%, 0.34%, 0.29%, 0.27%, 0.35%.</em><em></em></p><p class="AfiliasiCxSpMiddle" align="left"><strong><em> </em></strong></p><p class="AfiliasiCxSpLast" align="left"><strong><em>Keywords</em></strong><em>:</em></p><em>Eigenvector, Analytical Hierarchy Process</em> (AHP), <em>Eigenvalue</em>

scholarly journals AN INTERPRETATION OF THE AHP EIGENVECTOR SOLUTION FOR THE LAY PERSON

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
Stan Lipovetsky
Keyword(s):  
Decision Making ◽  
Linear Algebra ◽  
Iterative Process ◽  
Pairwise Comparison ◽  
Forthcoming Paper ◽  
Pairwise Comparison Matrix ◽  
Priority Vector ◽  
Comparison Matrix ◽  
Judgment Matrix

<p class="MsoBodyText" style="margin: 0in 0in 0pt;">An AHP priority vector represents the importance, preference, or likelihood of its elements with respect to a certain property or criterion and here we examine how that priority vector can be derived through an iterative process applied to the pairwise comparison matrix. Further, we show that the vector obtained in this way satisfies the definition for an eigenvector of the original judgment matrix. Practical managers using AHP in decision making would most likely be better able to appreciate this approach than they would a process phrased in the language of linear algebra. The overall priority vector for the alternatives in a hierarchy and, further, in a network, can be obtained in the same way by applying the iterative process to the supermatrix of the ANP. This claim is examined in depth in a forthcoming paper that will appear in this journal.</p><p class="MsoBodyText" style="margin: 0in 0in 0pt;">http://dx.doi.org/10.13033/ijahp.v2i2.42</p>

Using AHP Multiple Criteria Decision Making Approach for Selecting a Type of Industrial Plant at Risk on Fire

2015 ◽  
Vol 1125 ◽  
pp. 613-619
Author(s):  
Arroon Ketsakorn ◽  
W. Meethom
Keyword(s):  
Decision Making ◽  
At Risk ◽  
Multiple Criteria Decision Making ◽  
Pairwise Comparison ◽  
Multiple Criteria ◽  
Industrial Plant ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
Serious Injury

Fire can cause death, serious injury, and significant damage to properties. Industrial plants are dangerous places for fires. In the past, industrial fires have occurred more often than they should. Many industries are at high risk of fire due to the nature of work, and unfortunately it only takes one mistake to cause a serious life-threatening fire. The analytic hierarchy process (AHP) method is particularly suitable for modeling qualitative criteria and has found extensive applications in a wide variety of areas. In this paper we will focus on the AHP multiple criteria decision making approach for selecting a type of industrial plant at risk of fire in Thailand. The data were analyzed using Expert Choice11 software. Results showed that the type of 53 (Business related to plastic products) is reasonable for selection as a pilot plant for fire safety measurement with a corresponding consistency ratio of 0.06 C.R.≤0.09 for 4×4 pairwise comparison matrix. The pairwise comparison matrix is thought to have acceptable consistency and its normalized principle right eigenvector can be used as the weights of criteria. Limitations and future work of this study are also discussed.

Sign in / Sign up

Export Citation Format

Share Document