scholarly journals An Ordinal Consistency Indicator for Pairwise Comparison Matrix

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2183
Author(s):  
Ting Kuo
Keyword(s):  
Pairwise Comparison ◽  
Multicriteria Decision Making ◽  
Necessary Condition ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Consistency Test ◽  
Practical Applications ◽  
Ordinal Consistency ◽  
Hierarchy Process ◽  
Surprising Fact

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.

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.

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 COVID-19 Susceptibility Mapping Using Multicriteria Evaluation

2020 ◽  
Vol 14 (4) ◽  
pp. 521-537 ◽  
Author(s):  
Showmitra Kumar Sarkar
Keyword(s):  
Pairwise Comparison ◽  
Secondary Data ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Government Organizations ◽  
Multicriteria Evaluation ◽  
Susceptibility Index ◽  
Effective Decision ◽  
Effective Decision Making ◽  
Hierarchy Process

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.

scholarly journals Matrix of pairwise comparison: decision making with the analytic network process

2019 ◽  
Vol 110 ◽  
pp. 02042
Author(s):  
Aliya Akhmadullina ◽  
Svetlana Vasilyeva ◽  
Tatyana Yakovleva ◽  
Svetlana Vopiyashina ◽  
Raisa Kraineva
Keyword(s):  
Decision Making ◽  
Environmental Planning ◽  
Pairwise Comparison ◽  
Multicriteria Decision Making ◽  
Analytic Network Process ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Network Process ◽  
Qualitative Factors ◽  
The Right

This article describes a method for analyzing hierarchies; identifies the problems with inconsistent judgments. The proof is given that the most effective tool allowing one to make the right decisions with inconsistencies is the introduction of the eigenvector on environmental planning and management. The Analytic Hierarchy Process (AHP) is a method for decision making, which includes qualitative factors. In this method, ratio scales are obtained from ordinal scales, which are derived from individual judgments for qualitative factors using the pairwise comparison matrix. This paper describes the applicability of a multicriteria decision-making method, specifically, the analytic network process.

scholarly journals Ranking All DEA-Efficient DMUs Based on Cross Efficiency and Analytic Hierarchy Process Methods

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Dariush Akbarian
Keyword(s):  
Analytic Hierarchy Process ◽  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Dea Models ◽  
Dea Efficiency ◽  
One Step ◽  
The Cross ◽  
The One ◽  
Hierarchy Process

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.

Electronic Market Credit Risk Evaluation for Agricultural Products Based on Analytic Hierarchy Process

2011 ◽  
Vol 99-100 ◽  
pp. 852-856
Author(s):  
You Zhu Li ◽  
De Hua He
Keyword(s):  
Analytic Hierarchy Process ◽  
Credit Risk ◽  
Risk Evaluation ◽  
Pairwise Comparison ◽  
Agricultural Products ◽  
Electronic Market ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
Hierarchy Process

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.

scholarly journals APPLYING THE ANALYTIC HIERARCHY PROCESS TO OIL SANDS ENVIRONMENTAL COMPLIANCE RISK MANAGEMENT

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
Izak Johannes Roux ◽  
Dr. Christos Makrigeorgis
Keyword(s):  
Analytic Hierarchy Process ◽  
Oil Sands ◽  
Pairwise Comparison ◽  
Environmental Compliance ◽  
Analytic Hierarchy ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
Risk Criteria ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

<p>In 2013, oil companies in Alberta, Canada invested $32 billion in new oil-sands projects.  Despite the size of this investment, there is a demonstrable deficiency in the uniformity and understanding of environmental legislation requirements that translate into increased project compliance risks. In this paper, we applied the Analytic Hierarchy Process (AHP) to develop a priority list of environmental regulatory compliance risk criteria for oil-sands projects.  AHP belongs to the family of multicriteria decision-making (MCDM) techniques that utilizes a pairwise comparison matrix solicited from subject matter experts (SMEs) in the field as input.  The overall methodology itself consisted of 4 phases: (1) identification of the initial list of N potential environmental compliance risk criteria and verification of these criteria via a pilot survey; (2) formation of a pairwise comparison survey in the form of an N(N-1)/2 comparison matrix based on the verified criteria; (3) administration of the pairwise comparison matrix to a sample of 16 industry-specific SME’s; and (4) the application of the AHP method using SuperDecisions as a tool on the collected sample to rank the identified risk criteria. Our demonstrated results can potentially inform Alberta oil sands industry leaders about the ranking and utility of specific compliance risks as understood by experts and enable a more focused environmental compliance action to help increase legislative and public trust.</p>

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