scholarly journals Optimal Inconsistency Repairing of Pairwise Comparison Matrices Using Integrated Linear Programming and Eigenvector Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Haiqing Zhang ◽  
Aicha Sekhari ◽  
Yacine Ouzrout ◽  
Abdelaziz Bouras
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Lower Bound ◽  
Fuzzy Ahp ◽  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Segment Tree ◽  
Hierarchy Process ◽  
Original Information

Satisfying consistency requirements of pairwise comparison matrix (PCM) is a critical step in decision making methodologies. An algorithm has been proposed to find a new modified consistent PCM in which it can replace the original inconsistent PCM in analytic hierarchy process (AHP) or in fuzzy AHP. This paper defines the modified consistent PCM by the original inconsistent PCM and an adjustable consistent PCM combined. The algorithm adopts asegment treeto gradually approach the greatest lower bound of the distance with the original PCM to obtain the middle value of an adjustable PCM. It also proposes a theorem to obtain the lower value and the upper value of an adjustable PCM based on two constraints. The experiments for crisp elements show that the proposed approach can preserve more of the original information than previous works of the same consistent value. The convergence rate of our algorithm is significantly faster than previous works with respect to different parameters. The experiments for fuzzy elements show that our method could obtain suitable modified fuzzy PCMs.

On Moderate Fuzzy Analytic Hierarchy Process Pairwise Comparison Model With Subcriteria

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.

Improved Consistency Ratio for Pairwise Comparison Matrix in Analytic Hierarchy Processes

2016 ◽  
Vol 33 (03) ◽  
pp. 1650020
Author(s):  
L. N. Pradeep Kumar Rallabandi ◽  
Ravindranath Vandrangi ◽  
Subba Rao Rachakonda
Keyword(s):  
Error Function ◽  
Pairwise Comparison ◽  
Large Set ◽  
Simulation Experiments ◽  
Analytic Hierarchy ◽  
Chi Square ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
Hierarchy Process ◽  
Original Information

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.

scholarly journals On Consistency in AHP and Fuzzy AHP

2017 ◽  
Vol 5 (2) ◽  
pp. 128-147 ◽  
Author(s):  
Fang Liu ◽  
Yanan Peng ◽  
Weiguo Zhang ◽  
Witold Pedrycz
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Fuzzy Ahp ◽  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
Hierarchy Process ◽  
Fuzzy Interval

Abstract The analytic hierarchy process (AHP) is used widely for analyzing decisions made in various real-world applications. Its basic idea is to construct a hierarchy of concepts encountered in a given decision problem and to choose the best alternative according to pairwise comparison matrices given by the decision maker. Under the assumption of fully rational economics, a reasonable decision should be consistent. It becomes an important issue on how to analyze and ensure the consistency of comparison matrices together with the judgments of the decision maker. The main objectives of the present paper are threefold. First, we review the basic idea and methods used to define the consistency and the transitivity of multiplicative reciprocal matrices, additive reciprocal matrices and comparison matrices with fuzzy interval and triangular fuzzy numbers. The existing controversy behind the applications of fuzzy set theory to the AHP in the literature is presented. Second, the consistency of the collective comparison matrices in group decision making based on AHP and fuzzy AHP is further analyzed. We point out that the weak consistency of preference relations with fuzzy numbers in fuzzy AHP and group decision making should be investigated comprehensively. Third, under the consideration of the vagueness in the process of evaluating the judgements, a new concept of fuzzy consistency of comparison matrices in the AHP is given.

scholarly journals LINEAR PROGRAMMING MODELS FOR ESTIMATING WEIGHTS IN ANALYTIC HIERARCHY PROCESS AND FOR OPTIMIZATION OF HUMAN RESOURCE ALLOCATION

2016 ◽  
Vol 8 (2) ◽  
Author(s):  
Gokulananda Patel ◽  
Godwin D Mjema ◽  
Kasio M Godwin
Keyword(s):  
Linear Programming ◽  
Analytic Hierarchy Process ◽  
Human Resource ◽  
Pairwise Comparison ◽  
Food Product ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Frame Work ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

The Analytic Hierarchy Process (AHP) provides a way to rank the alternatives by deriving priorities. In this paper we used Linear Programming (LP) models to estimate the weights of a pairwise comparison matrix derived within the frame work of the Analytic Hierarchy Process. The priorities obtained for the alternatives served as the coefficients of the objective function of linear programming to optimize a human resource problem at Bakhresa Food Product Limited (BFPL).

scholarly journals UTILIZATION OF F-AHP METHOD IN BRI FOR GIVING SELECTION OF KUR

Telematika ◽  
2017 ◽  
Vol 13 (2) ◽  
pp. 80
Author(s):  
Meiyanto Eko Sulisyo ◽  
Ristu Saptono
Keyword(s):  
Analytic Hierarchy Process ◽  
Fuzzy Ahp ◽  
Multiple Criteria Decision Making ◽  
Pairwise Comparison ◽  
Fuzzy Analytic Hierarchy Process ◽  
Ahp Method ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
The Public ◽  
Hierarchy Process

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.

scholarly journals SISTEM PENDUKUNG KEPUTUSAN DALAM PENILAIAN PRESTASI KERJA MENGGUNAKAN FUZZY-AHP DAN SAW

2019 ◽  
Vol 3 (2) ◽  
pp. 72
Author(s):  
Denni Kurniawan ◽  
Catur Nugroho
Keyword(s):  
Fuzzy Logic ◽  
Employee Performance ◽  
Fuzzy Ahp ◽  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Highest Weight ◽  
Weight Value ◽  
Simple Additive Weighting ◽  
Hierarchy Process

Employee appraisal is one of the company's efforts to evaluate employee performance and productivity. As the result, the company can also give awards to employees who are considered gives high contribution to company.  However, it is not easy to measure employee performance, because most them only based on the leaders valuation which is subjective and do not based on standards. The objective of this study is to develop a system to assess employee performance by using a combination of Fuzzy Logic, Analytic Hierarchy Process (AHP) and Simple Additive Weighting (SAW) methods. The AHP is a method of weighting in based on multi-criteria decisions. This method uses a pairwise comparison matrix to  calculate the weight value. The Fuzzy logic is used to overcome the problem, where the AHP method is indicated still have subjectivity in criteria evaluation. After calculation based on combination of Fuzzy-AHP methods, the final result of employee performance will determined by using SAW method. The employee with the highest weight value will considered as the most productive employee and also gives the best performance in the company.

JUDGMENT NUMBER REDUCTION: AN ISSUE IN THE ANALYTIC HIERARCHY PROCESS

2010 ◽  
Vol 09 (01) ◽  
pp. 175-189 ◽  
Author(s):  
LONG-TING WU ◽  
XIA CUI ◽  
RU-WEI DAI
Keyword(s):  
Decision Making ◽  
Analytic Hierarchy Process ◽  
Pairwise Comparison ◽  
Random Variable ◽  
Analytic Hierarchy ◽  
Priority Vector ◽  
Judgment Error ◽  
Scale Error ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

The Analytic Hierarchy Process (AHP) uses pairwise comparison to evaluate alternatives' advantages to a certain criterion. For decision-making problem with many different criteria and alternatives, pairwise comparison causes a prolonged decision-making period and rises fatigue in decision-makers' mentality. A question of practical value is if there exists a way to reduce judgment number and what influence the reduction will have on the overall evaluation of alternative ratings. To answer this question, we introduce scale error and judgment error into AHP judgment matrix. By expanding the scales defined in the AHP, scale error is eliminated. Taking judgment error as random variable, a new estimator to calculate priority vector is presented. In the end, an example is proved to show lowering judgment number will increase the probability of larger errors appearing in priority vector computation.

scholarly journals PENERAPAN METODE FUZZY AHP DALAM PENENTUAN SEKTOR YANG BERPENGARUH TERHADAP PEREKONOMIAN PROVINSI BALI

2016 ◽  
Vol 5 (2) ◽  
pp. 59
Author(s):  
TJOKORDA GDE AGUNG FRISKA ADNYANA ◽  
G. K. GANDHIADI ◽  
DESAK PUTU EKA NILAKUSMAWATI
Keyword(s):  
Manufacturing Industry ◽  
Fuzzy Ahp ◽  
Weighted Average ◽  
Pairwise Comparison ◽  
Primary Group ◽  
Tertiary Sector ◽  
Analytic Hierarchy ◽  
Consistency Ratio ◽  
Analytic Hierarchy Process Method ◽  
Hierarchy Process

The aim of this research is to apply Fuzzy Analytic Hierarchy Process method to determine the dominant sectors of economy Bali Province. This research used survey data from respondents who understand about economy of Bali Province and Gross Regional Domestic Product (GRDP). The research variables consist of criteria and sub-criteria. The criteria consist of primary sector, secondary, and tertiary, while the sub-criteria consist of 9 sectors of the GRDP. Data processing is done by calculating the weighted average and arrange them into pairwise comparison matrices. Furthermore, the consistency ratio is checked. If consistency ratio less than 0.100 (), the elements of matrices is changed into triangular fuzzy scale and processed with synthetic extent to get the priority. Based on the result of research, the economy of Bali are dominated by tertiary sector in sector group, agriculture and forestry in sub-primary group, manufacturing industry in sub-secondary group, and trade, hotel and restaurant in sub-tertiary group.

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.

Fuzzy Analytic Hierarchy Process and Its Application to E-Marketplace Selection

2013 ◽  
pp. 26-44 ◽  
Author(s):  
Beyza Ahlatcioglu Ozkok ◽  
Elisa Pappalardo
Keyword(s):  
Decision Making ◽  
Analytic Hierarchy Process ◽  
Fuzzy Ahp ◽  
Multi Criteria Decision Making ◽  
Linguistic Variables ◽  
Analytic Hierarchy ◽  
Multi Attribute Decision Making ◽  
Electronic Parts ◽  
Hierarchy Process

Making decisions is a part of daily life. The nature of decision-making includes multiple and usually conflicting criteria. Multi Criteria Decision-Making (MCDM) problems are handled under two main headings: Multi Attribute Decision Making (MADM) and Multi Objective Decision Making (MODM). Analytic Hierarchy Process (AHP) is a widely used multi-criteria decision making approach and has successfully been applied to many practical problems. Traditional AHP requires exact or crisp judgments (numbers). However, due to the complexity and uncertainty involved in real world decision problems, decision makers might be more reluctant to provide crisp judgments than fuzzy ones. Furthermore, even when people use the same words, individual judgments of events are invariably subjective, and the interpretations that they attach to the same words may differ. This is why fuzzy numbers and fuzzy sets have been introduced to characterize linguistic variables. Here, the authors overview the most known fuzzy AHP approaches and their application, and they present a case study to select an e-marketplace for a firm, which produces and sells electronic parts of computers in Turkey.

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