scholarly journals On the Statistical Discrepancy and Affinity of Priority Vector Heuristics in Pairwise-Comparison-Based Methods

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1150
Author(s):  
Pawel Tadeusz Kazibudzki
Keyword(s):  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
Priority Vector ◽  
Approximation Quality ◽  
Statistical Measures ◽  
Eigenvalue Method ◽  
Mathematica Software ◽  
Hierarchy Process ◽  
Alternative Solutions

There are numerous priority deriving methods (PDMs) for pairwise-comparison-based (PCB) problems. They are often examined within the Analytic Hierarchy Process (AHP), which applies the Principal Right Eigenvalue Method (PREV) in the process of prioritizing alternatives. It is known that when decision makers (DMs) are consistent with their preferences when making evaluations concerning various decision options, all available PDMs result in the same priority vector (PV). However, when the evaluations of DMs are inconsistent and their preferences concerning alternative solutions to a particular problem are not transitive (cardinally), the outcomes are often different. This research study examines selected PDMs in relation to their ranking credibility, which is assessed by relevant statistical measures. These measures determine the approximation quality of the selected PDMs. The examined estimates refer to the inconsistency of various Pairwise Comparison Matrices (PCMs)—i.e., W = (wij), wij > 0, where i, j = 1,…, n—which are obtained during the pairwise comparison simulation process examined with the application of Wolfram’s Mathematica Software. Thus, theoretical considerations are accompanied by Monte Carlo simulations that apply various scenarios for the PCM perturbation process and are designed for hypothetical three-level AHP frameworks. The examination results show the similarities and discrepancies among the examined PDMs from the perspective of their quality, which enriches the state of knowledge about the examined PCB prioritization methodology and provides further prospective opportunities.

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 Fusion of BWM and AHP MCDM Methods to Choose the Most Suitable Secondary School for an Individual in the Context of Bangladesh

2019 ◽  
Vol 06 (03) ◽  
pp. 311-328
Author(s):  
N. S. M. Rezaur Rahman ◽  
Md. Abdul Ahad Chowdhury ◽  
Adnan Firoze ◽  
Rashedur M. Rahman
Keyword(s):  
Decision Making ◽  
Secondary School ◽  
Pairwise Comparison ◽  
User Preferences ◽  
Multi Criteria Decision Making ◽  
Analytic Hierarchy ◽  
Final Score ◽  
Hierarchy Process ◽  
Best Worst Method

Choosing the best schools from a group of schools is a multi-criteria decision-making (MCDM) problem. In this paper, we have represented a method that uses the fusion of two multi-criteria decision-making methods, Best–Worst Method (BWM) and Analytic Hierarchy Process (AHP), to rank some of the user preferred alternatives. The system considers the choice of the user and the quality of the alternatives to rank them. User preferences on the criteria are taken as inputs in the form of best–worst comparison vectors to measure the choice of the user. These values are applied to calculate the numeric weights of each of the criteria. These weights reflect the preference of the user. A dataset of secondary schools in Bangladesh has been compiled and used for automatic quantitative pairwise comparison on the alternatives to calculate the score of each alternative in every criterion, which reflects its quality in that criterion. These scores are calculated using AHP. The weights of the criteria as well as the scores of these alternatives in those criteria are then used to calculate the final score of the alternatives and to rank them accordingly. An extensive experimental analysis and comparative study is reported at the end of this paper.

scholarly journals The Triads Geometric Consistency Index in AHP-Pairwise Comparison Matrices

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 926 ◽  
Author(s):  
Juan Aguarón ◽  
María Teresa Escobar ◽  
José María Moreno-Jiménez ◽  
Alberto Turón
Keyword(s):  
Pairwise Comparison ◽  
Consistency Index ◽  
Analytic Hierarchy ◽  
Priority Vector ◽  
Decision Tools ◽  
Geometric Consistency ◽  
The Matrix ◽  
Stability Intervals ◽  
Definition Of ◽  
Hierarchy Process

The paper presents the Triads Geometric Consistency Index ( T - G C I ), a measure for evaluating the inconsistency of the pairwise comparison matrices employed in the Analytic Hierarchy Process (AHP). Based on the Saaty’s definition of consistency for AHP, the new measure works directly with triads of the initial judgements, without having to previously calculate the priority vector, and therefore is valid for any prioritisation procedure used in AHP. The T - G C I is an intuitive indicator defined as the average of the log quadratic deviations from the unit of the intensities of all the cycles of length three. Its value coincides with that of the Geometric Consistency Index ( G C I ) and this allows the utilisation of the inconsistency thresholds as well as the properties of the G C I when using the T - G C I . In addition, the decision tools developed for the G C I can be used when working with triads ( T - G C I ), especially the procedure for improving the inconsistency and the consistency stability intervals of the judgements used in group decision making. The paper further includes a study of the computational complexity of both measures ( T - G C I and G C I ) which allows selecting the most appropriate expression, depending on the size of the matrix. Finally, it is proved that the generalisation of the proposed measure to cycles of any length coincides with the T - G C I . It is not therefore necessary to consider cycles of length greater than three, as they are more complex to obtain and the calculation of their associated measure is more difficult.

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

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

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.

scholarly journals Determination of Environmental Factors for the Implementation of the Exploitability Index in Industrial Aggregate Mining Using Multi-Criteria Analysis

2021 ◽  
Vol 10 (4) ◽  
pp. 196
Author(s):  
Julio Manuel de Luis-Ruiz ◽  
Benito Ramiro Salas-Menocal ◽  
Gema Fernández-Maroto ◽  
Rubén Pérez-Álvarez ◽  
Raúl Pereda-García
Keyword(s):  
Environmental Factors ◽  
Environmental Factor ◽  
Human Life ◽  
Accurate Estimation ◽  
Analytic Hierarchy ◽  
Main Components ◽  
Hierarchy Process ◽  
Made In

The quality of human life is linked to the exploitation of mining resources. The Exploitability Index (EI) assesses the actual possibilities to enable a mine according to several factors. The environment is one of the most constraining ones, but its analysis is made in a shallow way. This research is focused on its determination, according to a new preliminary methodology that sets the main components of the environmental impact related to the development of an exploitation of industrial minerals and its weighting according to the Analytic Hierarchy Process (AHP). It is applied to the case of the ophitic outcrops in Cantabria (Spain). Twelve components are proposed and weighted with the AHP and an algorithm that allows for assigning a normalized value for the environmental factor to each deposit. Geographic Information Systems (GISs) are applied, allowing us to map a large number of components of the environmental factors. This provides a much more accurate estimation of the environmental factor, with respect to reality, and improves the traditional methodology in a substantial way. It can be established as a methodology for mining spaces planning, but it is suitable for other contexts, and it raises developing the environmental analysis before selecting the outcrop to be exploited.

scholarly journals An Empirical Investigation into Physician Preferences in Drug Prescription: An Integrated Methodology of AHP and QFD

2016 ◽  
Vol 8 (5) ◽  
pp. 81
Author(s):  
Farzana Elahi ◽  
Shamsad Ahmed ◽  
Mahbubul Haque ◽  
Nazreen Chowdhury
Keyword(s):  
Quality Function Deployment ◽  
Drug Prescription ◽  
Future Research ◽  
Relationship Matrix ◽  
Analytic Hierarchy ◽  
Expert Choice ◽  
Integrated Methodology ◽  
Hierarchy Process ◽  
The Relationship

<p class="Default">In order to sustain in a competitive market like pharmaceutical in Bangladesh, it is important to get an insight into physicians’ preferences in prescribing the drugs. The aim of this work is to investigate and address the physician requirements through an integrated methodology of Analytic Hierarchy Process (AHP) and Quality Function Deployment (QFD). In this research, an expert panel has been interviewed to recognize the criteria affecting physicians’ decisions. The results from AHP derived through Expert Choice software demonstrate that from the viewpoint of physicians, out of the five criteria, quality of product offering is ranked highest in prescribing the drugs followed by the reputation of the company, relationship enjoyed with the company, etc. As for the technical aspects, derived from the relationship matrix of AHP and QFD, out of the sixteen, brand image is ranked first followed by the quality of raw and packaging materials, skilled production personnel etc. The contribution of this research is expected to enable the managers in the pharmaceutical companies to recognize the factors that influence physicians in prescribing drugs for the patients and help them find out challenging items with preeminent alternatives. Few suggestions for future research are also put forward. <strong></strong></p>

A Method of the Comprehensive Evaluation of Surface Integrity in Micro- and Nano-Machining

2007 ◽  
Author(s):  
Guicheng Wang ◽  
Chunyan Zhang ◽  
Hongjie Pei ◽  
Yunming Zhu ◽  
Chungen Shen ◽  
...  
Keyword(s):  
Surface Integrity ◽  
Evaluation System ◽  
Metal Cutting ◽  
Comprehensive Evaluation ◽  
Rapid Development ◽  
Analytic Hierarchy ◽  
Ultra Precision ◽  
Edge Quality ◽  
Hierarchy Process

The surface quality is always the crucial element of machined quality in precision ultra-precision metal cutting. A new concept that the surface integrity should include the edge quality of parts is put forward In this paper, the weight value of a series of characteristic parameters of surface integrity are calculated with using analytic hierarchy process, three basic methods of evaluating surface integrity are presented, and the comprehensive evaluation system has been formed which will theoretically play a great important role on rapid development in the precision machining.

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 Evaluating and ranking the circular supply chain implementation enablers

2021 ◽  
Author(s):  
Swapnil Lahane ◽  
◽  
Himanshu Prajapati ◽  
Ravi Kant ◽  
◽  
...  
Keyword(s):  
Supply Chain ◽  
Manufacturing Industry ◽  
Global Climate ◽  
Pairwise Comparison ◽  
Decision Makers ◽  
Analytic Hierarchy ◽  
Effective Implementation ◽  
Manufacturing Organizations ◽  
Scarcity Of Resources ◽  
Hierarchy Process

This research aims to evaluate and rank the Circular Supply Chain (CSC) enablers for the effective implementation of CSC management. From the literature and input received from industrial experts, 30 CSC enablers are identified. Further, the selected CSC enablers are classified into seven main categories. This research employs the Pythagorean fuzzy analytic hierarchy process (PF-AHP) technique to prioritize the selected CSC enablers based on pairwise comparison of criteria and sub-criteria. The effectiveness of the proposed method is illustrated with the help of responses received from an Indian manufacturing industry. The result reveals that global climate pressure and ecological scarcity of resources is the most significant enabler and the environment management certifications and systems is the least important enabler. The result of the present study will assist the practitioners / decision makers in implementing CSC in manufacturing organizations by adopting the ranking obtained in a systematic way.

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