A Monte Carlo Study of Pairwise Comparisons (original) (raw)

Some Critical Issues in Making Decisions with Pairwise Comparisons

Proceedings of the International Symposium on the Analytic Hierarchy Process, 1994

Pairwise comparisons are the core of the AHP and provide an intuitive and efficient method in eliciting information for multi-criteria decision-making (MCDM) applications. However, there are a number of critical issues related to their application in solving a MCDM problem. The main challenges are: (i) how to quantify them, (ii) how to process the resulted reciprocal matrices, and (iii) how to process the decision matrices. This paper presents some of the alternative approaches proposed to solve the previous problems and discusses their relative effectiveness and limitations.

Methods of Evaluation and Improvement of Consistency of Expert Pairwise Comparison Judgments

2015

The notion of consistency is used to evaluate the contradiction level of expert pairwise comparison judgments and their suitability for the purpose of calculation of weights of decision alternatives. Several consistency coefficients and criteria are used to measure inconsistency of a pairwise comparison matrix (PCM). Traditional approach to increase consistency of expert information is to organize a feedback with an expert. However, it is not always possible due to financial and time limitations. The paper deals with methods of improvement (increase) PCM consistency without participation of an expert. Computer simulation is used to provide a comparative study of these methods. It is shown that taking an inadmissibly inconsistent PCM, for example, with the consistency ratio equal to CR=0.2 or CR=0.3, methods of improvement PCM consistency help to decrease inconsistency up to admissible level CR≤0.1 for n≥5. Results reveal that these methods, unfortunately, are not always effective, t...

Of Evaluation and Improvement of Consistency of Expert Pairwise Comparison Judgments

2015

Reduction of Pairwise Comparisons in Decision Making Via a Duality Approach

1999

ABSTRACT: Although pairwise comparisons have been seen by many as an effective and intuitive way for eliciting qualitative data for multi-criteria decision making problems, a major drawback is that the number of the required comparisons increases quadratically with the number of the entities to be compared. Thus, often even data for medium size decision problems may be impractical to be elicited via pairwise comparisons. The more the comparisons are, the higher is the likelihood that the decision maker will introduce erroneous data. This paper introduces a dual formulation to a given multi-criteria decision making problem, which can significantly alleviate the previous problems. Some theoretical results establish that this is possible when the number of alternatives is greater than the number of decision criteria plus one. KEY WORDS: Pairwise comparisons, multi-criteria decision making, the Analytic Hierarchy Process (AHP), duality. Some Background Information This paper deals with ...

Important Facts and Observations about Pairwise Comparisons (the special issue edition

This study has been inspired by numerous requests for clarification from researchers who often confuse Saaty's Analytic Hierarchy Process (AHP) with the pairwise comparisons (PC) method, taking AHP as the only representation of PC. This study should be regarded as an interpretation and clarification of past investigations of PC. In addition, this article is a reflection on general PC research at a higher level of abstraction: the philosophy of science. It delves into the foundations and implications of pairwise comparisons. Some results of this study are based on a recently published work by Koczkodaj and Szwarc. Finally, open problems have also been reported for future research.

Consistency of the decision-maker in pair-wise comparisons

International Journal of Management and Decision Making, 2006

Most authors assume that the natural behaviour of the decision-maker is being inconsistent. This paper investigates the main sources of inconsistency and analyses methods for reducing or eliminating inconsistency. Decision support systems can contain interactive modules for that purpose. In a system with consistency control, there are three stages. First, consistency should be checked: a consistency measure is needed. Secondly, approval or rejection has to be decided: a threshold value of inconsistency measure is needed. Finally, if inconsistency is 'high', corrections have to be made: an inconsistency reducing method is needed. This paper reviews the difficulties in all stages. An entirely different approach is to elaborate a decision support system in order to force the decision-maker to give consistent values in each step of answering pair-wise comparison questions. An interactive questioning procedure resulting in consistent (sub) matrices has been demonstrated.

Analysis of pairwise comparison matrices: an empirical research

Pairwise comparison (PC) matrices are used in multi-attribute decision problems (MADM) in order to express the preferences of the decision maker. Our research focused on testing various characteristics of PC matrices. In a controlled experiment with university students (N = 227) we have obtained 454 PC matrices. The cases have been divided into 18 subgroups according to the key factors to be analyzed. Our team conducted experiments with matrices of different size given from different types of MADM problems. Additionally, the matrix elements have been obtained by different questioning procedures differing in the order of the questions. Results are organized to answer five research questions. Three of them are directly connected to the inconsistency of a PC matrix. Various types of inconsistency indices have been applied. We have found that the type of the problem and the size of the matrix had impact on the inconsistency of the PC matrix. However, we have not found any impact of the questioning order. Incomplete PC matrices played an important role in our research. The decision makers behavioral consistency was as well analyzed in case of incomplete matrices using indicators measuring the deviation from the final order of alternatives and from the final score vector.

Pairwise comparison matrices: an empirical research

2011

Our research focused on testing various characteristics of pairwise comparison (PC) matrices in controlled experiments. About 270 students have been involved in the test exercises and the final pool contained 450 matrices. Our team conducted experiments with matrices of different size obtained from different types of MADM problems. The matrix elements have been generated by different questioning orders, too. The cases have been divided into 18 subgroups according to the key factors to be analyzed. The testing environment made it possible to analyze the dynamics of inconsistency as the number of elements increased in a given case. Various types of inconsistency indices have been applied. The consequent behavior of the decision maker has also been analyzed in case of incomplete matrices using indicators to measure the deviation from the final ranking of alternatives and from the final score vector.

A Monte Carlo Study of Pairwise Comparisons (original) (raw)

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