A note on the information content of a consistent pairwise comparison judgment matrix of an AHP decision maker

1993 ◽  
Vol 34 (2) ◽  
pp. 99-108 ◽  
Author(s):  
Elizabeth E. Noble ◽  
Pedro P. Sanchez
Keyword(s):  
Information Content ◽  
Decision Maker ◽  
Pairwise Comparison ◽  
Comparison Judgment ◽  
Judgment Matrix

scholarly journals Words from the Managing Editor

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
Rozann Saaty
Keyword(s):  
Analytic Hierarchy Process ◽  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
Comparison Judgment ◽  
The Subject ◽  
Judgment Matrix ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

<p><span>At the ISAHP 2009 meeting in Pittsburgh, Thomas L. Saaty offered a challenge to the attendees to explain the eigenvector solution of the pairwise comparison judgment matrix that is the basis of the Analytic Hierarchy Process so that it would be understandable to any intelligent layman. He wrote an essay himself on it during the meeting, and submitted it as his offering. A second essay on the subject, also during the meeting, was written by Stan Lipovetsky. These two papers appear in this issue of the journal. </span></p><p><span>Rozann Saaty</span></p><p><span>http://dx.doi.org/10.13033/ijahp.v2i2.86<br /></span></p>

FAIR CONSISTENCY EVALUATION FOR RECIPROCAL RELATIONS AND IN GROUP DECISION MAKING

2009 ◽  
Vol 05 (02) ◽  
pp. 407-420 ◽  
Author(s):  
MICHELE FEDRIZZI ◽  
MATTEO BRUNELLI
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Group Decision Making ◽  
Evaluation Method ◽  
Group Decision ◽  
Pairwise Comparison ◽  
Pairwise Comparisons ◽  
Reciprocal Relations ◽  
Decision Making Processes ◽  
Consistency Evaluation

In decision-making processes, it often occurs that the decision maker is asked to pairwise compare alternatives. His/her judgements over a set of pairs of alternatives can be collected into a matrix and some relevant properties, for instance, consistency, can be estimated. Consistency is a desirable property which implies that all the pairwise comparisons respect a principle of transitivity. So far, many indices have been proposed to estimate consistency. Nevertheless, in this paper we argue that most of these indices do not fairly evaluate this property. Then, we introduce a new consistency evaluation method and we propose to use it in group decision making problems in order to fairly weigh the decision maker's preferences according to their consistency. In our analysis, we consider two families of pairwise comparison matrices: additively reciprocal pairwise comparison matrices and multiplicatively reciprocal pairwise comparison matrices.

FARSJUM, A FUZZY SYSTEM FOR RANKING SPARSE JUDGMENT MATRICES: A CASE STUDY IN SOCCER TOURNAMENTS

2007 ◽  
Vol 15 (01) ◽  
pp. 115-129 ◽  
Author(s):  
M. R. GHOLAMIAN ◽  
S. M. T. FATEMI GHOMI ◽  
M. GHAZANFARI
Keyword(s):  
Pairwise Comparison ◽  
Major Constituent ◽  
Pairwise Comparisons ◽  
Ahp Method ◽  
World Cup ◽  
Analytic Hierarchy ◽  
Rank Reversal ◽  
Judgment Matrix ◽  
Hierarchy Process

The establishment of the priorities from pairwise comparison matrices is the major constituent of the Analytic Hierarchy Process (AHP). However, the number of pairwise comparisons necessary in real problems often becomes overwhelming. In such cases, generally the experts are not able to answer all questions and consequently sparse judgment matrix is generated which caused "equal ranks" and "rank reversal" based on AHP method. In this paper, a new ranking system (FARSJUM) is developed for such sparse judgment matrix. The system is constructed on fuzzy rules and fuzzy reasoning methods. The numerical example of world cup soccer tournament is brought to clarify the performance of the developed system comparing with AHP method in ranking the sparse judgment matrices.

Study on the Difficulty Sorting of Experimental Projects Based on the AHP

2011 ◽  
Vol 271-273 ◽  
pp. 363-367
Author(s):  
Lian Hui Liu ◽  
Juan He
Keyword(s):  
Analytic Hierarchy Process ◽  
Ahp Method ◽  
Analytic Hierarchy ◽  
Experimental Instruction ◽  
Comparison Judgment ◽  
Judgment Matrix ◽  
The Analytic Hierarchy Process ◽  
Set Up ◽  
Hierarchy Process

To classify the difficulty of the experiments is the basis of the effective mutlit-level experimental instruction. In this paper, we employ the analytic hierarchy process (AHP) method to compare and analyse the difficult of the experiments, and set up a corresponding comparison judgment matrix to the difficulty of the projects. We obtain some sortings of difficulty of experiments, which coincide with the fact. Our studies offer an effective way to the rational sorting of difficulty of experiments.

scholarly journals On Consistency in AHP and Fuzzy AHP

2017 ◽  
Vol 5 (2) ◽  
pp. 128-147 ◽  
Author(s):  
Fang Liu ◽  
Yanan Peng ◽  
Weiguo Zhang ◽  
Witold Pedrycz
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Fuzzy Ahp ◽  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
Hierarchy Process ◽  
Fuzzy Interval

Abstract The analytic hierarchy process (AHP) is used widely for analyzing decisions made in various real-world applications. Its basic idea is to construct a hierarchy of concepts encountered in a given decision problem and to choose the best alternative according to pairwise comparison matrices given by the decision maker. Under the assumption of fully rational economics, a reasonable decision should be consistent. It becomes an important issue on how to analyze and ensure the consistency of comparison matrices together with the judgments of the decision maker. The main objectives of the present paper are threefold. First, we review the basic idea and methods used to define the consistency and the transitivity of multiplicative reciprocal matrices, additive reciprocal matrices and comparison matrices with fuzzy interval and triangular fuzzy numbers. The existing controversy behind the applications of fuzzy set theory to the AHP in the literature is presented. Second, the consistency of the collective comparison matrices in group decision making based on AHP and fuzzy AHP is further analyzed. We point out that the weak consistency of preference relations with fuzzy numbers in fuzzy AHP and group decision making should be investigated comprehensively. Third, under the consideration of the vagueness in the process of evaluating the judgements, a new concept of fuzzy consistency of comparison matrices in the AHP is given.

A METHOD FOR IMPROVING THE CONSISTENCY OF JUDGEMENTS

2002 ◽  
Vol 10 (06) ◽  
pp. 677-686 ◽  
Author(s):  
M. T. LAMATA ◽  
J. I. PELAEZ
Keyword(s):  
Analytic Hierarchy Process ◽  
Decision Maker ◽  
Pairwise Comparison ◽  
Analytic Hierarchy ◽  
Alternative Method ◽  
Consistency Problem ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

The Analytic Hierarchy Process provides the decision maker with a method for improving the consistency of pairwise comparison matrices. Although it is one of the most commonly used method it presents some disadvantages related generally with the consistency problem. The purpose of this paper is to provide an alternative method for improving consistency and show how it can be applied to pairwise comparison matrices. The contribution to this method and also its limitations are shown at the end.

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