scholarly journals Constrained Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices by Nelder-Mead Algorithm

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 222
Author(s):  
Hailemariam Abebe Tekile ◽  
Michele Fedrizzi ◽  
Matteo Brunelli

Pairwise comparison matrices play a prominent role in multiple-criteria decision-making, particularly in the analytic hierarchy process (AHP). Another form of preference modeling, called an incomplete pairwise comparison matrix, is considered when one or more elements are missing. In this paper, an algorithm is proposed for the optimal completion of an incomplete matrix. Our intention is to numerically minimize a maximum eigenvalue function, which is difficult to write explicitly in terms of variables, subject to interval constraints. Numerical simulations are carried out in order to examine the performance of the algorithm. The results of our simulations show that the proposed algorithm has the ability to solve the minimization of the constrained eigenvalue problem. We provided illustrative examples to show the simplex procedures obtained by the proposed algorithm, and how well it fills in the given incomplete matrices.

Telematika ◽  
2017 ◽  
Vol 13 (2) ◽  
pp. 80
Author(s):  
Meiyanto Eko Sulisyo ◽  
Ristu Saptono

Bank Rakyat Indonesia (BRI) is a business entity which collects funds from the public in the form of deposits and distribute to the public in the form of the People 's Business Credit (KUR) or loan. Along with over time after KUR realized, there is no doubt BRI will be faced with the problems of risk, namely the risk of KUR problematic. There are several methods that can be used in making a decision to be able to solve the problem include the Analytical Hierarchy Process (AHP).AHP is used when the decision involves many factors, where the decision had difficulty in making the weight of each factor. Despite this problem the use of AHP in Multiple Criteria Decision Making (MCDM) approach has less to cope with uncertainties taken by decision-makers, when it should give a definite value in the pairwise comparison matrix therefore, to overcome the weaknesses of the existing AHP then developed a method namely Fuzzy Analytic Hierarchy Process (F-AHP). F-AHP method is the combination between fuzzy AHP approach. The results of research conducted using the Fuzzy Analytic Hierarchy Process (F-AHP) has a 100 % accuracy this is evidenced by the results obtained together with the calculation of banking. Calculation banking mention of 20 customers, acquired 14 accepted and rejected 6.


2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Zaher Sepehrian ◽  
Sahar Khoshfetrat ◽  
Said Ebadi

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.


2012 ◽  
Vol 7 (2) ◽  
pp. 59-70
Author(s):  
Martina Zeleňáková ◽  
Ibrahim Gargar ◽  
Pavol Purcz

Abstract Environmental hazards (natural and man-made) have always constituted problem in many developing and developed countries. Many applications proved that these problems could be solved through planning studies and detailed information about these prone areas. Determining time and location and size of the problem are important for decision makers for planning and management activities. It is important to know the risk represented by those hazards and take actions to protect against them. Multicriteria analysis methods - Analytic hierarchy process, Pairwise comparison, Ranking method are used to analyse which is the most dangerous hazard facing Libya country. The multicriteria analysis ends with a more or less stable ranking of the given alternatives and hence a recommendation as to which alternative(s) problems should be preferred. Regarding our problem of environmental risk assessment, the result will be a ranking or categorisation of hazards with regard to their risk level.


2016 ◽  
Vol 33 (03) ◽  
pp. 1650020
Author(s):  
L. N. Pradeep Kumar Rallabandi ◽  
Ravindranath Vandrangi ◽  
Subba Rao Rachakonda

The analytical hierarchy process (AHP) uses pairwise comparison matrix (PCM) to rank a known set of alternatives. Sometimes the comparisons made by the experts may be inconsistent which results in incorrect weights and rankings for the AHP. In this paper, a method is proposed which identifies inconsistent elements in a PCM and revises them iteratively until the inconsistency is reduced to an acceptable level. An error function similar to chi-square is used to identify the inconsistent elements which are revised with suitable values. The method is illustrated with some numerical examples mentioned in the literature and a comparative study of the results in terms of deviation from the PCM and preservation of original information is taken up. Monte Carlo simulation experiments over a large set of random matrices indicate that the proposed method converges for the moderately inconsistent matrices.


2020 ◽  
Vol 14 (4) ◽  
pp. 521-537 ◽  
Author(s):  
Showmitra Kumar Sarkar

ABSTRACTObjective: The purpose of this research was to investigate coronavirus disease (COVID-19) susceptibility in districts of Bangladesh using multicriteria evaluation techniques.Methods: Secondary data were collected from different government organizations, 120 primary surveys were conducted for calculating weights, and results were validated through 12 key people’s interviews. Pairwise comparison matrixes were calculated for 9 factors and subfactors. The analytic hierarchy process used for calculating the susceptibility index and map was prepared based on the results.Results: According to the results, multiple causal factors might be responsible for COVID-19 spreading in Bangladesh. Dhaka might be vulnerable to COVID-19 due to a higher population, population density, and international collaboration. According to the pairwise comparison matrix, the consistency ratio for subfactors and factors was in the permissible limit (ie, less than 0.10). The highest factor weight of 0.2907 was found for the factors type of port. The maximum value for the susceptibility index was 0.435219362 for Chittagong, and the minimum value was 0.076174 for Naogaon.Conclusions: The findings of this research might help the communities and government agencies with effective decision-making.


2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Dariush Akbarian

The aim of this paper is to present an original approach for ranking of DEA-efficient DMUs based on the cross efficiency and analytic hierarchy process (AHP) methods. The approach includes two basic stages. In the first stage using DEA models the cross efficiency value of each DEA-efficiency DMU is specified. In the second stage, the pairwise comparison matrix generated in the first stage is utilized to rank scale of the units via the one-step process of AHP. The advantage of this proposed method is its capability of ranking extreme and nonextreme DEA-efficient DMUs. The numerical examples are presented in this paper and we compare our approach with some other approaches.


2016 ◽  
Vol 27 (6) ◽  
pp. 874-888 ◽  
Author(s):  
Uday Hameed Farhan ◽  
Majid Tolouei-Rad ◽  
Adam Osseiran

Purpose The purpose of this paper is to develop a model of analytic hierarchy process (AHP), a multiple criteria decision-making method, to assist selecting suitable machine configurations for special purpose machines (SPMs) from available alternatives. Design/methodology/approach The necessary criteria and sub-criteria were identified and used in the developed model. The assessment process was carried out by constructing the hierarchy of four levels. Then, pairwise comparison matrices were created for each level to compute the weights for the alternatives. The model was programmed and implemented by software for practical use. Findings Different scenarios were obtained from the assessment process of the developed AHP model showing the influence of changing the relevant importance of the elements in the hierarchy on the selection of SPMs configurations. Selection of the suitable scenario was also affected by some factors of manufacturing preferences and industry recommendations such as cost and production rate. Originality/value This is a new application of AHP method which assists decision makers to select suitable configurations for SPMs, and reduce the time required for designing SPMs.


2011 ◽  
Vol 99-100 ◽  
pp. 852-856
Author(s):  
You Zhu Li ◽  
De Hua He

In the study, electronic market credit risk evaluation for agricultural products based on analytic hierarchy process is proposed.Firstly, the evaluation indexes are analyzed and the hierarchic tree is formulated based on the evaluation indexes.Then, pairwise comparison matrix is established,and the consistency of discriminant matrix is judged.When the consistency of discriminant matrix is satisfied,the weight vector of the indexes which are used to establish the pairwise comparison matrix are obtained. And weight of each index is obtained.Finally,final decision making is obtained. The experimental results show that the evaluation of electronic market credit risk evaluation for agricultural products based on analytic hierarchy process is effective.


Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2183
Author(s):  
Ting Kuo

The pairwise comparison (PC) matrix is often used to manifest human judgments, and it has been successfully applied in the analytic hierarchy process (AHP). As a PC matrix is formed by making paired reciprocal comparisons, symmetry is a striking characteristic of a PC matrix. It is this simple but powerful means of resolving multicriteria decision-making problems that is the basis of AHP; however, in practical applications, human judgments may be inconsistent. Although Saaty’s rule for the consistency test is commonly accepted, there is evidence that those so-called “acceptable” PC matrices may not be ordinally consistent, which is a necessary condition for a PC matrix to be accepted. We propose an ordinal consistency indicator called SDR (standard deviation of ranks), derive the upper bound of the SDR, suggest a threshold for a decision-maker to assess whether the ordinal consistency of a PC matrix is acceptable, and reveal a surprising fact that the degree of ordinal inconsistency of a small PC matrix may be more serious than a large one. We made a comparative analysis with some other indicators. Experimental results showed that the ordinal inconsistency measured by the SDR is invariant under heterogeneous judgment measurements with a varied spectrum of scales, and that the SDR is superior to the two compared indicators. Note that the SDR not only works for a multiplicative PC matrix but can also be used for additive and fuzzy PC matrices.


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