scholarly journals Ranking Alternatives by Pairwise Comparisons Matrix and Priority Vector

2017 ◽  
Vol 64 (s1) ◽  
pp. 85-95 ◽  
Author(s):  
Jaroslav Ramík
Keyword(s):  
Decision Making ◽  
Essential Elements ◽  
Real Interval ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Priority Vector ◽  
Advantages And Disadvantages ◽  
Decision Making Problem ◽  
Ranking Of Alternatives ◽  
Hierarchy Process

Abstract The decision making problem considered here is to rank n alternatives from the best to the worst, using information given by the decision maker(s) in the form of an n×n pairwise comparisons (PC) matrix. We investigate pairwise comparisons matrices with elements from a real interval which is a traditional multiplicative approach used in Analytic hierarchy process (AHP). Here, we deal with two essential elements of AHP: measuring consistency of PC matrix and the method of eliciting the priority vector by which the final ranking of alternatives is derived. Classical approaches introduced by T. Saaty in AHP are compared with later approaches based on the AHP criticism published in the literature. Advantages and disadvantages of both approaches are highlighted and discussed.

scholarly journals FAHPSort: A Fuzzy Extension of the AHPSort Method

2018 ◽  
Vol 17 (04) ◽  
pp. 1119-1145 ◽  
Author(s):  
Jana Krejčí ◽  
Alessio Ishizaka
Keyword(s):  
Decision Making ◽  
Analytic Hierarchy Process ◽  
Pairwise Comparisons ◽  
Multi Criteria Decision Making ◽  
Powerful Method ◽  
Linguistic Terms ◽  
Ahp Method ◽  
Analytic Hierarchy ◽  
Decision Making Problem ◽  
Hierarchy Process

Analytic Hierarchy process (AHP) is a powerful method belonging to the full aggregation family of multi-criteria decision-making methods based on pairwise comparisons of objects. Since the information about the problem is usually not complete in real decision-making problems, it is difficult to express precisely the preferences on pairs of compared objects. This problem has been handled in the literature by introducing fuzziness into AHP. However, neither AHP nor its fuzzy extensions can deal with sorting decision-making problems, which form a significant part of decision-making problems. This paper presents the FAHPSort method — a fuzzy extension of the AHPSort method, which is an adaptation of the AHP method for sorting decision-making problems. The FAHPSort method handles the vagueness in the meaning of linguistic terms expressing the intensity of preference of one object over another one. Key properties of the FAHPSort method are described in the paper, and the method is illustrated in a decision-making problem.

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.

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.

A Enterprises Supplier Evaluating System Using Fuzzy-AHP

2013 ◽  
Vol 475-476 ◽  
pp. 1050-1054 ◽  
Author(s):  
Lan Cai ◽  
Shun Sheng Guo ◽  
Lu Ming Zhou
Keyword(s):  
Decision Making ◽  
Supplier Selection ◽  
Fuzzy Ahp ◽  
Evaluation Process ◽  
Systematic Design ◽  
Analytic Hierarchy ◽  
Qualitative And Quantitative ◽  
Decision Making Problem ◽  
Using Data ◽  
Hierarchy Process

Supplier selection is a multi-criteria decision making problem which includes evaluation factors. In order to select the best suppliers, it is crucial to considering the both qualitative and quantitative factors simultaneously. The analytic hierarchy Process is a kind of Decision-making method with the combination of quantity and quality. Combining with fuzzy algorithm, this paper established a supplier evaluating system based on ERP database, discussing many issues in the systematic design and developing the implement step. The system make the evaluation process transparent by using data mining and fuzzy-AHP algorithm, and avoid the disturbing from excessively subjective factors. Thus it can guarantee the fairness of the assessment. Finally, the example and conclusion are given.

scholarly journals TWO-STAGE PRIORITIZATION PROCEDURE FOR MULTIPLICATIVE AHP-GROUP DECISION MAKING

2020 ◽  
Vol 26 (2) ◽  
pp. 525-545
Author(s):  
Changsheng Lin ◽  
Gang Kou ◽  
Yi Peng ◽  
Fawaz E. Alsaadi
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Two Stage ◽  
Analytic Hierarchy ◽  
Priority Vector ◽  
The Individual ◽  
Collective Preference ◽  
Hierarchy Process ◽  
Multiplicative Ahp

In this paper, we propose two-stage prioritization procedure (TSPP) for multiplicative Analytic Hierarchy Process-group decision making (AHP-GDM), which involves determining the group priority vector based on the individual pair-wise comparison matrices (PCMs), simultaneously considering the consensus and consistency of the individual PCMs. The first stage of the TSPP involves checking and revising the individual PCMs for reaching the acceptable consensus and consistency. The second stage of the TSPP involves estimating the group priority vector using Bayesian approach. The main characteristics of the proposed TSPP are as follows: 1) It makes full use of the prior information as well as the sample information during the Bayesian revision of the individual PCMs and the Bayesian estimation of the group priority vector; 2) It ensures that the revised individual PCMs reach the acceptable consensus and consistency; 3) It enriches the aggregation methods for the collective preference in multiplicative AHP-GDM. Finally, two numerical examples are used to evaluate the applicability and effectiveness of the proposed TSPP by the comparisons with several other methods.

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.

A novel hybrid two-step group multi-attribute assessment model of stairs shape for two-story individual dwelling houses

2015 ◽  
Author(s):  
Zenonas Turskis ◽  
Birutė Juodagalvienė
Keyword(s):  
Decision Making ◽  
Analytic Hierarchy Process ◽  
Hybrid Model ◽  
Assessment Model ◽  
Analytic Hierarchy ◽  
Decision Making Problem ◽  
Multi Attribute Decision Making ◽  
Measurement Units ◽  
The Cost ◽  
Hierarchy Process

The article deals with a novel hybrid two-step group multi-attribute assessment model of stairs shape for two-story individual dwelling houses. There exist many available shapes of stairs for two-story dwelling houses. Selection among shapes and construction of stairs is a multi-attribute decision making problem in nature. It depends on a lot of different conflicting attributes, that have different optimisation direction, different measurement units. A determinated set of the main attributes to assess the alternatives includes the following: Stairwell Area, The Total Area of Climbing, “Climbing Lane" Area, The Cost of Stairs, and Ergonomics. The values of attributes and importance of attributes are determined by grey numbers. The paper presents a novel original hybrid model, which is based on two different multi-attribute decision making methods: ARAS-G (Additive Ratio Assessment) and AHP (Analytic Hierarchy Process).

scholarly journals THE LEGACY OF THE ANALYTIC HIERARCHY/NETWORK PROCESS

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Luis G Vargas
Keyword(s):  
Decision Making ◽  
Analytic Hierarchy Process ◽  
Cognitive Processes ◽  
Brain Activity ◽  
Fundamental Equation ◽  
Pairwise Comparisons ◽  
Analytic Hierarchy ◽  
Network Process ◽  
Hierarchy Process ◽  
Process Group

There is no doubt that the Analytic Hierarchy Process is in itself a remarkable contribution to the field of decision making.  In this paper, I have tried to point out what I consider to be Tom Saaty’s three most important contributions within his Analytic Hierarchy Process: group decision making, conflict resolution and the fundamental equation of pairwise comparisons.  The third contribution occupied him most of his life in an attempt to connect pairwise comparisons with brain activity related to cognitive processes.  https://doi.org/10.13033/ijahp.v9i3.541

scholarly journals PRIORITY VECTOR ESTIMATION: CONSISTENCY, COMPATIBILITY, PRECISION

2020 ◽  
Vol 12 (3) ◽  
Author(s):  
Stan Lipovetsky
Keyword(s):  
Decision Making ◽  
Robust Estimation ◽  
Multiple Criteria Decision Making ◽  
Data Consistency ◽  
Matrix Approximation ◽  
Analytic Hierarchy ◽  
Practical Applications ◽  
Priority Vector ◽  
Vector Estimation ◽  
Hierarchy Process

Various methods of priority vector estimation are known in the Analytic Hierarchy Process (AHP). They include the classical eigenproblem method given by Thomas Saaty, developments in least squares and the multiplicative approach, robust estimation based on transformation of the pairwise ratios to the shares of preferences, and other approaches. In this paper, the priority vectors are completed with validation of data consistency, comparisons of vectors’ compatibility, and estimation of precision for matrix approximation by vectors. The numerical results for different data sizes and consistency show that the considered methods reveal useful features, are simple and convenient, and capable of facilitating practical applications of the AHP in solving various multiple-criteria decision making problems.

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