scholarly journals A Model for Determining Weight Coefficients by Forming a Non-Decreasing Series at Criteria Significance Levels (NDSL)

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 745
Author(s):  
Mališa Žižović ◽  
Dragan Pamučar ◽  
Goran Ćirović ◽  
Miodrag M. Žižović ◽  
Boža D. Miljković
Keyword(s):  
Decision Makers ◽  
Pairwise Comparisons ◽  
Small Range ◽  
Analytic Hierarchy ◽  
Original Algorithm ◽  
Real World Problem ◽  
Significance Levels ◽  
Hierarchy Process ◽  
Weight Coefficients ◽  
Best Worst Method

In this paper, a new method for determining weight coefficients by forming a non-decreasing series at criteria significance levels (the NDSL method) is presented. The NDLS method includes the identification of the best criterion (i.e., the most significant and most influential criterion) and the ranking of criteria in a decreasing series from the most significant to the least significant criterion. Criteria are then grouped as per the levels of significance within the framework of which experts express their preferences in compliance with the significance of such criteria. By employing this procedure, fully consistent results are obtained. In this paper, the advantages of the NDSL model are singled out through a comparison with the Best Worst Method (BWM) and Analytic Hierarchy Process (AHP) models. The advantages include the following: (1) the NDSL model requires a significantly smaller number of pairwise comparisons of criteria, only involving an n − 1 comparison, whereas the AHP requires an n(n − 1)/2 comparison and the BWM a 2n − 3 comparison; (2) it enables us to obtain reliable (consistent) results, even in the case of a larger number of criteria (more than nine criteria); (3) the NDSL model applies an original algorithm for grouping criteria according to the levels of significance, through which the deficiencies of the 9-degree scale applied in the BWM and AHP models are eliminated. By doing so, the small range and inconsistency of the 9-degree scale are eliminated; (4) while the BWM includes the defining of one unique best/worst criterion, the NDSL model eliminates this limitation and gives decision-makers the freedom to express the relationships between criteria in accordance with their preferences. In order to demonstrate the performance of the developed model, it was tested on a real-world problem and the results were validated through a comparison with the BWM and AHP models.

scholarly journals A New Model for Determining Weight Coefficients of Criteria in MCDM Models: Full Consistency Method (FUCOM)

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 393 ◽  
Author(s):  
Dragan Pamučar ◽  
Željko Stević ◽  
Siniša Sremac
Keyword(s):  
Pairwise Comparison ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Proposed Model ◽  
Optimal Values ◽  
Definition Of ◽  
Hierarchy Process ◽  
Consistency Method ◽  
Weight Coefficients ◽  
Best Worst Method

In this paper, a new multi-criteria problem solving method—the Full Consistency Method (FUCOM)—is proposed. The model implies the definition of two groups of constraints that need to satisfy the optimal values of weight coefficients. The first group of constraints is the condition that the relations of the weight coefficients of criteria should be equal to the comparative priorities of the criteria. The second group of constraints is defined on the basis of the conditions of mathematical transitivity. After defining the constraints and solving the model, in addition to optimal weight values, a deviation from full consistency (DFC) is obtained. The degree of DFC is the deviation value of the obtained weight coefficients from the estimated comparative priorities of the criteria. In addition, DFC is also the reliability confirmation of the obtained weights of criteria. In order to illustrate the proposed model and evaluate its performance, FUCOM was tested on several numerical examples from the literature. The model validation was performed by comparing it with the other subjective models (the Best Worst Method (BWM) and Analytic Hierarchy Process (AHP)), based on the pairwise comparisons of the criteria and the validation of the results by using DFC. The results show that FUCOM provides better results than the BWM and AHP methods, when the relation between consistency and the required number of the comparisons of the criteria are taken into consideration. The main advantages of FUCOM in relation to the existing multi-criteria decision-making (MCDM) methods are as follows: (1) a significantly smaller number of pairwise comparisons (only n − 1), (2) a consistent pairwise comparison of criteria, and (3) the calculation of the reliable values of criteria weight coefficients, which contribute to rational judgment.

Decision Evaluation of Harbin Metro Based on Fuzzy Theory

2013 ◽  
Vol 438-439 ◽  
pp. 1024-1027
Author(s):  
Xiao Guo Chen
Keyword(s):  
Comprehensive Evaluation ◽  
Fuzzy Theory ◽  
Evaluation Model ◽  
Fuzzy Comprehensive Evaluation ◽  
Decision Makers ◽  
Geological Environment ◽  
Analytic Hierarchy ◽  
Comprehensive Evaluation Model ◽  
Hierarchy Process ◽  
Weight Coefficients

The paper introduces some information about Harbin Metro line 1, makes the decision analysis on economies, environment, society and geological environment of Harbin Metro line 1 by some fuzzy comprehensive evaluation model, and gives the weight coefficients of indicators through analytic hierarchy process. The comprehensive evaluation result provides the basis for decision-makers during decision of metro projects.

scholarly journals On the features of the implementation of the interval method for analytic hierarchy process in the problem of assessing the effectiveness of the employment service

2020 ◽  
pp. 41-48
Author(s):  
N. F. Bogachenko ◽  
D. N. Lavrov
Keyword(s):  
Analytic Hierarchy Process ◽  
Interval Arithmetic ◽  
Pairwise Comparisons ◽  
Efficiency Function ◽  
Analytic Hierarchy ◽  
Employment Service ◽  
Interval Method ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process ◽  
Weight Coefficients

To determine the weight coefficients of the efficiency function of the employment service, the analytic hierarchy process and interval arithmetic were used. This made it possible to take into account the opinions of various experts without losing the consistency of the matrices of pairwise comparisons.

scholarly journals THE MAGIC OF THE ANALYTIC HIERARCHY PROCESS (AHP)

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Orrin Cooper
Keyword(s):  
Analytic Hierarchy Process ◽  
Decision Makers ◽  
Pairwise Comparisons ◽  
Ordinary People ◽  
Analytic Hierarchy ◽  
Scientific Justification ◽  
History Of ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process ◽  
Careful Investigation

Dr. Thomas Saaty developed the Analytic Hierarchy Process (AHP) with the underlying goal of making it simple and accessible to the lay user. In Saaty’s own words, the AHP is based on how “ordinary people process information” and “express the strength of their judgments” (Saaty, 1994, p. 37). Because he was successful in developing the AHP in accordance with these goals, when decision makers use the AHP their experience can feel magical as they find pairwise comparisons natural and can relate to the final priorities. Careful investigation of the axioms, theorems, and proofs shows that the AHP is more than just magic and provides scientific justification of the highest order. Five important components of the AHP and some background into the history of its development are summarized and highlighted from Saaty’s article, “How to Make a Decision: the Analytic Hierarchy Process” (Saaty, 1994). https://doi.org/10.13033/ijahp.v9i3.519

scholarly journals Assessing landscape plans with abbreviated pair-wise comparisons in the AHP (Analitic Hierarchy Process)

2019 ◽  
pp. 183-194
Author(s):  
Milena Lakicevic ◽  
Keith Reynolds ◽  
Bojan Srdjevic
Keyword(s):  
Graphical Representation ◽  
Decision Makers ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Advantages And Disadvantages ◽  
Management Plans ◽  
Elicitation Process ◽  
Elicitation Procedure ◽  
Hierarchy Process

This paper demonstrates the application of the Analytic Hierarchy Pro?cess (AHP) in assessing landscape plans using the option of abbreviated pair-wise comparisons to simplify the weight elicitation process for decision makers. Whereas the standard AHP elicitation procedure requires a full set of pairwise comparisons among all criteria at each node of the decision hierarchy in order to derive criterion weights for the decision model, the abbreviated pairwise method uses a minimal spanning set of pairwise comparisons, and remaining comparisons are then derived by transitivity rules. In this paper is presented the abbreviated pairwise method with a case study in which alternative management plans are evaluated for the Zvezdarska forest of Belgrade, Serbia. The analysis was performed with the Criterium DecisionPlus software, which fully implements the AHP methodology, and provides useful diagnostics on AHP decision models. As a conclusion, some of the key advantages and disadvantages of the abbreviated pairwise variant of the AHP method are demonstrated. One of the key qualities of the Criterium DecisionPlus software is a clear and easy graphical representation of the results.

scholarly journals An Integrated Decision Support Model for Evaluating Public Transport Quality

2020 ◽  
Vol 10 (12) ◽  
pp. 4158 ◽  
Author(s):  
Sarbast Moslem ◽  
Ahmad Alkharabsheh ◽  
Karzan Ismael ◽  
Szabolcs Duleba
Keyword(s):  
Public Transport ◽  
Pairwise Comparison ◽  
Quality Criteria ◽  
Evaluation Process ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Urban Bus ◽  
Hierarchy Process ◽  
Bus Transport ◽  
Best Worst Method

Big cities suffer from serious complex problems such as air pollution, congestion, and traffic accidents. Developing public transport quality in such cities is considered an efficient remedy to obviate these critical issues. This paper aims to determine the significant supply quality criteria of public transportation. As a methodology, a hybrid Analytic Hierarchy Process (AHP) combined with the Best Worst Method (BWM) is applied. The proposed model is basically a hierarchy structure with at least a 5 × 5 pairwise comparison matrix or larger. A real-world complex problem was examined to validate the created model (public transport quality improvement). An urban bus transport system in the Jordanian capital city, Amman, was used as a case study; three stakeholder groups (passengers, nonpassengers, and representatives of the local government) participated in the evaluation process. The conventional Analytic Hierarchy Process (AHP) leads to weak consistency in the case of existing 5 × 5 pairwise comparison matrices or larger, particularly in estimating complex problems. To avoid this critical issue in AHP, we used Best Worst Method (BWM) comparisons, which make the evaluation process easier for decision makers; moreover, it saves survey time and provides more consistency when compared to AHP pairwise comparisons. The model adopted highlighted the most significant service quality criteria that influence urban bus transport systems. Furthermore, the sensitivity analysis conducted detected the stability of the criteria ranking in the three levels of the hierarchical structure. Since the proposed AHP–BWM model (which is the sole example of this sort of combination) is independent from the decision attributes, it can be applied to arbitrary hierarchically structured decision problems with a relatively large number of pairwise comparisons.

An Evaluation Method for Inconsistency of the AHP Judgment Matrix

2002 ◽  
Author(s):  
Yuan Mao Huang ◽  
Hsin-Ni Ho
Keyword(s):  
Decision Making ◽  
Evaluation Method ◽  
Decision Makers ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Principal Eigenvector ◽  
The Matrix ◽  
Judgment Matrix ◽  
Index Value ◽  
Hierarchy Process

Applications of the analytic hierarchy process have been widespread in the field of decision-making for decades. In this process, decision-makers perform pairwise comparisons to form a judgment matrix, and its principal eigenvector is used to represent the priorities. Thus it is important to evaluate the degree of inconsistency in a judgment matrix to ensure the principal eigenvector reflects the true priorities among the alternatives. This study proposes the I3 circuit method, which is based on the graph theory, with a critical inconsistent index value of 3.75 to judge and evaluate consistency or the degree of inconsistency for judgment matrices. In addition, it can also spot the matrix entries that create the most inconsistency. With these advantages of the proposed method, decision-makers can easily evaluate the pairwise comparisons of a matrix and revise some entries of the matrix toward consistency if needed.

A Soft Hierarchical Process Approach for Decision Making in A Supply Chain

2015 ◽  
Vol 4 (1and2) ◽  
Author(s):  
Rajeev Dhingra ◽  
Preetvanti Singh
Keyword(s):  
Decision Making ◽  
Process Approach ◽  
Decision Makers ◽  
Analytic Hierarchy ◽  
Conflicting Objectives ◽  
Realistic View ◽  
Hierarchy Process ◽  
Pair Wise Comparison ◽  
Supplier Selection Problem ◽  
Selection Of

Decision problems are usually complex and involve evaluation of several conflicting criteria (parameters). Multi Criteria Decision Making (MCDM) is a promising field that considers the parallel influence of all criteria and aims at helping decision makers in expressing their preferences, over a set of predefined alternatives, on the basis of criteria (parameters) that are contradictory in nature. The Analytic Hierarchy Process (AHP) is a useful and widespread MCDM tool for solving such type of problems, as it allows the incorporation of conflicting objectives and decision makers preferences in the decision making. The AHP utilizes the concept of pair wise comparison to find the order of criteria (parameters) and alternatives. The comparison in a pairwise manner becomes quite tedious and complex for problems having eight alternatives or more, thereby, limiting the application of AHP. This paper presents a soft hierarchical process approach based on soft set decision making which eliminates the least promising candidate alternatives and selects the optimum(potential) ones that results in the significant reduction in the number of pairwise comparisons necessary for the selection of the best alternative using AHP, giving the approach a more realistic view. A supplier selection problem is used to illustrate the proposed approach.

scholarly journals A Multi-Criteria Decision Support Concept for Selecting the Optimal Contractor

2021 ◽  
Vol 11 (4) ◽  
pp. 1660 ◽  
Author(s):  
Ivan Marović ◽  
Monika Perić ◽  
Tomaš Hanak
Keyword(s):  
Decision Making ◽  
Decision Support ◽  
Project Performance ◽  
Decision Makers ◽  
Construction Project Management ◽  
Analytic Hierarchy ◽  
Conflicting Demands ◽  
Decision Making Problem ◽  
Scientific Approach ◽  
Hierarchy Process

A way to minimize uncertainty and achieve the best possible project performance in construction project management can be achieved during the procurement process, which involves selecting an optimal contractor according to “the most economically advantageous tender.” As resources are limited, decision-makers are often pulled apart by conflicting demands coming from various stakeholders. The challenge of addressing them at the same time can be modelled as a multi-criteria decision-making problem. The aim of this paper is to show that the analytic hierarchy process (AHP) together with PROMETHEE could cope with such a problem. As a result of their synergy, a decision support concept for selecting the optimal contractor (DSC-CONT) is proposed that: (a) allows the incorporation of opposing stakeholders’ demands; (b) increases the transparency of decision-making and the consistency of the decision-making process; (c) enhances the legitimacy of the final outcome; and (d) is a scientific approach with great potential for application to similar decision-making problems where sustainable decisions are needed.

scholarly journals A decision support method for evaluating database designs

2012 ◽  
Vol 9 (1) ◽  
pp. 81-106 ◽  
Author(s):  
Erki Eessaar ◽  
Marek Soobik
Keyword(s):  
Decision Support ◽  
Data Model ◽  
Processing System ◽  
Transaction Processing ◽  
Database Management System ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Hierarchy Process ◽  
Decision Support Method

It is possible to produce different database designs based on the same set of requirements to a database. In this paper, we present a decision support method for comparing different database designs and for selecting one of them as the best design. Each data model is an abstract language that can be used to create many different databases. The proposed method is flexible in the sense that it can be used in case of different data models, criteria, and designs. The method is based on the Analytic Hierarchy Process and uses pairwise comparisons. We also present a case study about comparing four designs of SQL databases in case of PostgreSQL? database management system. The results depend on the context where the designs will be used. Hence, we evaluate the designs in case of two different contexts - management of measurements data and an online transaction processing system.

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