SOME REMARKS ON THE MAXIMUM EIGENVALUE OF 3RD ORDER PAIRWISE COMPARISON MATRICES IN AHP

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.

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Tournaments, transitivity and pairwise comparison matrices

Journal of the Operational Research Society ◽

10.1038/sj.jors.2600572 ◽

1998 ◽

Vol 49 (6) ◽

pp. 616-624 ◽

Cited By ~ 2

Author(s):

S I Gass

Keyword(s):

Pairwise Comparison

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Penilaian Kinerja Dosen Dengan Menggunakan Metode AHP Studi Kasus di STIE Ahmad Dahlan Jakarta

Liquidity ◽

10.32546/lq.v2i1.136 ◽

2018 ◽

Vol 2 (1) ◽

pp. 100-109

Author(s):

Ellya Sestri

Keyword(s):

Decision Making ◽

Performance Appraisal ◽

Technological Progress ◽

Pairwise Comparison ◽

Relative Importance ◽

Faculty Performance ◽

Business World ◽

The Face ◽

Hierarchy Process ◽

Rule Out

An increasingly rapid technological progress in the era of globalization in the business world, so do not rule out the possibility that a decision-making is something that is very vital in determining the decisions to be taken in the face of competitive business world. Decision making can be influenced by several aspects, this can affect the speed of decision making by the decision maker in which decisions must be quick and accurate. Lecturer Performance Assessment Using the Analytical Hierarchy Process is a decision support system that aims to assess faculty performance according to certain criteria. This system of faculty performance appraisal criteria to map a hierarchy, where each hierarchy will be performed pairwise comparison, the pairwise comparisons between criteria, so to get a comparison of the relative importance of criteria with each other. The results of this comparison is then analyzed to obtain the priority of each criterion. Once completed and performed an assessment of alternative options to be compared and calculated to obtain the best alternatives according to established criteria.

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Optimal topology for maximum eigenvalue using density-dependent material model

10.2514/6.1996-1627 ◽

1996 ◽

Cited By ~ 1

Author(s):

B. Wang ◽

C. Lu ◽

R. Yang

Keyword(s):

Material Model ◽

Optimal Topology ◽

Maximum Eigenvalue ◽

Density Dependent

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

Jurnal Rekayasa Lingkungan ◽

10.29122/jrl.v9i1.1986 ◽

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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Model and Method for Contributor’s Quality Assessment in Community Image Tagging Systems

Information and Control Systems ◽

10.31799/1684-8853-2018-4-45-51 ◽

2018 ◽

pp. 45-51

Author(s):

A. V. Ponomarev

Keyword(s):

Large Scale ◽

Wide Spectrum ◽

Preference Relation ◽

Pairwise Comparison ◽

Ground Truth ◽

Comparison Method ◽

Characteristic Matrix ◽

Image Tagging ◽

Proposed Model

Introduction: Large-scale human-computer systems involving people of various skills and motivation into the information processing process are currently used in a wide spectrum of applications. An acute problem in such systems is assessing the expected quality of each contributor; for example, in order to penalize incompetent or inaccurate ones and to promote diligent ones.Purpose: To develop a method of assessing the expected contributor’s quality in community tagging systems. This method should only use generally unreliable and incomplete information provided by contributors (with ground truth tags unknown).Results:A mathematical model is proposed for community image tagging (including the model of a contributor), along with a method of assessing the expected contributor’s quality. The method is based on comparing tag sets provided by different contributors for the same images, being a modification of pairwise comparison method with preference relation replaced by a special domination characteristic. Expected contributors’ quality is evaluated as a positive eigenvector of a pairwise domination characteristic matrix. Community tagging simulation has confirmed that the proposed method allows you to adequately estimate the expected quality of community tagging system contributors (provided that the contributors' behavior fits the proposed model).Practical relevance: The obtained results can be used in the development of systems based on coordinated efforts of community (primarily, community tagging systems).

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On Moderate Fuzzy Analytic Hierarchy Process Pairwise Comparison Model With Subcriteria

International Research Journal of Engineering IT & Scientific Research ◽

10.21744/irjeis.v2i3.41 ◽

2016 ◽

Vol 2 (3) ◽

pp. 54

Author(s):

G. Marimuthu ◽

G. Ramesh

Keyword(s):

Decision Making ◽

Analytic Hierarchy Process ◽

Fuzzy Ahp ◽

Pairwise Comparison ◽

Decision Models ◽

Fuzzy Analytic Hierarchy Process ◽

Analysis Method ◽

Analytic Hierarchy ◽

Comparison Model ◽

Hierarchy Process

Decisions usually involve the getting the best solution, selecting the suitable experiments, most appropriate judgments, taking the quality results etc., using some techniques. Every decision making can be considered as the choice from the set of alternatives based on a set of criteria. The fuzzy analytic hierarchy process is a multi-criteria decision making and is dealing with decision making problems through pairwise comparisons mode [10]. The weight vectors from this comparison model are obtained by using extent analysis method. This paper concern with an alternate method of finding the weight vectors from the original fuzzy AHP decision model (moderate fuzzy AHP model), that has the same rank as obtained in original fuzzy AHP and ideal fuzzy AHP decision models.

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