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

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.

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

<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>

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

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.

Materials selection criteria weighting method using analytic hierarchy process (AHP) with simplest questionnaire and modifying method of inconsistent pairwise comparison matrix

The analytic hierarchy process has been widely used to determine subjective weights of materials selection criteria in materials selection using multi-criteria decision-making. However, the analytic hierarchy process has some drawbacks: it is difficult to construct a pairwise comparison matrix and meet the consistency requirement. First, we propose a new simplest questionnaire to perform the pairwise comparison without confusion, conventionally and easily. Next, we propose an improved modifying method for inconsistent pairwise comparison matrix according to the following principles: (1) the elements of the reconstructed pairwise comparison matrix should be nine-point scales, (2) the number and modifying the amount of the modified elements should be as small as possible and (3) the deviation between the original and reconstructed pairwise comparison matrixes should be as small as possible. The outline of the proposed modifying method is as follows: (1) calculate the consistency ration decrements of all the pairwise comparison matrixes reconstructed by modifying every element of the original pairwise comparison matrix to the lower and upper adjacent nine-point scales and (2) find the element with the maximum consistency ratio decrement and modify it to the lower or upper adjacent scale. To illustrate the effectiveness, we apply the proposed methods to determine the criteria weights for selecting the best phase change material used in a solar domestic hot water system, and apply the proposed modifying method to some examples from the published papers, and compare the performances with some previous methods. The simplest questionnaire and improved modifying method help materials designers and engineers to apply the analytic hierarchy process method in materials design and optimization problems, much more actively.

On a Maximum Eigenvalue of Third-Order Pairwise Comparison Matrix in Analytic Hierarchy Process and Convergence of Newton’s Method

Nowadays, the analytic hierarchy process is an established method of multiple criteria decision making in the field of Operations Research. Pairwise comparison matrix plays a crucial role in the analytic hierarchy process. The principal (maximum magnitude) eigenvalue of the pairwise comparison matrix can be utilized for measuring the consistency of the decision maker’s judgment. The simple transformation of the maximum magnitude eigenvalue is known to be Saaty’s consistency index. In this short note, we shed light on the characteristic polynomial of a pairwise comparison matrix of third order. We will show that the only real-number root of the characteristic equation is the maximum magnitude eigenvalue of the third-order pairwise comparison matrix. The unique real-number root appears in the area where it is greater than 3, which is equal to the order of the matrix. By applying usual Newton’s method to the characteristic polynomial of the third-order pairwise comparison matrix, we see that the sequence generated from the initial value of 3 always converges to the maximum magnitude eigenvalue.

Earthquake Vulnerability Mapping using Binary Comparison Matrix and Analytical Hierarchical Process (AHP) in Lalmatia, Dhaka

From the historical records, geological evident and recent trends in earthquake, it is evident that Bangladesh is in a high-risk zone of earthquake hazard. The recent results of the CDMP, if a huge earthquake greater or equal to seven magnitude happened in this country, would lead to a serious human tragedy due to the defective structure. In Lalmatia, Dhaka study area there are various types of structures as like as RCC, masonry, semi-pucca etc. and the area has different old and newly filled soil development. This study considered the characteristics of RCC building elements and their behaviors to assess the risk against earthquake vulnerability in Lalmatia using the Turkish method. Next building vulnerability from Turkish Method used as one total vulnerability factor. In the method of this research, a pair wise comparison matrix for a numerical relationship between two elements and the Analytical Hierarchical Process (AHP) model has been applied to decide in weight and to get rank of the vulnerability factors. By weighted sum vector among the six factors and calculating vulnerability index (VI), the overall vulnerability were identified in Lalmatia. Using Geographic Information System (GIS) and defining an ordinal scale of calculated result, the vulnerability status of single buildings of the study area is presented here. This research tells that 8.23% buildings are highly vulnerable and 14.24% buildings are moderately vulnerable to earthquake. About 77.53% buildings are less vulnerable. As the study area is in a major urban center (Dhaka City), the scenario of unplanned urbanization increases the overall vulnerability to higher scale.

Construction of Consistent Comparison Matrix by Macharis’ Method Revisit

A famous paper that has been cited more than four hundred times tried to combine (a) the preference ranking organization method for enrichment evaluations (PROMETHEE) and (b) the analytic hierarchy process (AHP) to construct a new method for multicriteria decision-making problems. The paper developed a consistent comparison matrix for their AHP by the defined first row and then they allowed the expert to change several entries in the comparison matrix. Hence, how to construct a new comparison matrix that is (i) consistent and (ii) satisfying the assigned values by the expert becomes a challenging problem. A recent article provided a reply to the above problem by the construction of all entries for the comparison matrix. However, they did not follow the original design proposed by the famous paper. In this paper, we present a new approach with a proposition that satisfies the original design of the famous paper and also achieves two goals (i) and (ii). The research gap of proof is fulfilled by this paper. Our findings explain that the original construction of the famous paper to develop a consistent comparison matrix only by the first row with several assigned values by an expert is indeed workable under two additional restrictions proposed by the recent article. We believe that after our proposition, researchers have the confidence to execute the original design of the paper that has been cited more than four hundred times.

Analisis Kelayakan Pendirian Pusat Distribusi Provinsi (PDP) Jawa Barat

The purpose of this study was to analyze the feasibility of establishing a Provincial Distribution Center (PDP) in Purwakarta Regency, West Java which was assessed from the aspects of the Potential of Production Centers and Commodity Demand, Infrastructure, Socio-Economic Conditions, Environmental Conditions, Regional Spatial Plans, Regulations, Land and Actors. Distribution / Logistics Services. This research used Pairwise Comparison Matrix method. It was concluded that, Purwakarta Regency was deemed appropriate and sufficient in determining the criteria as a Provincial Distribution Center.