# The Analytic Hierarchy Process: Structuring, Measurement, and Synthesis

John Wang (Montclair State University, USA), Chandana Chakraborty (Montclair State University, USA) and Huanyu Ouyang (The People’s Hospital of Jiangxi Provence, China)
DOI: 10.4018/978-1-59904-843-7.ch003

## Abstract

The challenges of evaluation and decision making are encountered in every sphere of life and on a regular basis. The nature of the required decisions, however, may vary between themselves. While some decisions may reflect individual solutions on simple problems, others may indicate collaborative solutions on complex issues. Regardless of their distinctive nature, all decisions are outcomes of a mental process. The process involves careful evaluation of merits of all the available options leading ultimately to the choice of a single solution. Numerous efforts have been made in the literature to develop decision models ideal for choosing the best solution for a given problem. The dilemma in using these decision models, however, can hardly be avoided. With differences in underlying methodology, each model serves a specific decision-making need of the decision maker. In the absence of a universal framework suitable for handling a variety of problems, decision makers are often required to identify the model best suited for their particular need. Furthermore, they need to take account of the advantages and disadvantages associated with the chosen model.

## Key Terms in this Chapter

Eigenvector: An Eigenvector is a nonzero vector that is mapped by a given linear transformation of a vector space onto a vector that is the product of a scalar multiplied by the original vector.

Eigenvalue: An eigenvalue is a scalar associated with a given linear transformation of a vector space and having the property that there is some nonzero vector that when multiplied by the scalar is equal to the vector obtained by letting the transformation operate on the vector.

Synthesis: Synthesis is the combining of separate elements to form a coherent whole.

Criteria: These are one of the three main parts of the AHP that need to be defined before solving a problem. A criterion is a standard on which your judgments are based.

Hierarchy: It is a system of ranking and organizing in which each component is a subordinate to another component directly above or below depending on the layout.

Alternatives: They are multiple choices from which you have to choose one based upon their weights on the different criteria. The alternative with the highest overall rating is selected as the most efficient choice in an AHP.

Rank Reversal: This is one of the secondary problems related to AHP that occurs when the rankings for the alternatives are changed with either the addition of or removal of an alternative.

Consistency Measure (CM): Also known as consistency ratio or consistency index, it is an estimated arithmetical indicator of the inconsistencies or intransitivity in a set of pair-wise ratings.

## Complete Chapter List

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Foreword
Jean-Charles Pomerol
Preface
Acknowledgment
Chapter 1
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Chapter 2
Zita Zoltay Paprika
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Chapter 3
John Wang, Chandana Chakraborty, Huanyu Ouyang
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Sven A. Carlsson
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Ricardo Colomo Palacios, Juan Miguel Gómez Berbís, Ángel García Crespo
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Maria Eugénia Captivo, João Clímaco, Sérgio Fernandes
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Amit V. Deokar, Omar F. El-Gayar
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Sergio F. Ochoa, José A. Pino
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Malcolm J. Beynon
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Thomas Madritsch, Michael May, Herwig Ostermann, Roland Staudinger
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Alexandre Gachet, Ralph Sprague
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Patrick Brézillon, Jean-Charles Pomerol
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Pascale Zaraté
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Dashboards for Management  (pages 116-123)
Werner Beuschel
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John Wang, James Yao, Qiyang Chen
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Patrick Humphreys
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A. Dolgui, O. Guschinskaya, N. Guschinsky, G. Levin
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A. Dolgui, O. Guschinskaya, N. Guschinsky, G. Levin
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Ivan Bruha
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Viviane Barbosa Diniz, Marcos R.S. Borges, José Orlando Gomes, José H. Canós
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Hannu Kivijärvi, Markku Tuominen
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Udo Richard Averweg
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Patrick Humphreys
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Daniel J. Power
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James Yao, John Wang, Qiyang Chen, June Lu
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Dina Neiger, Leonid Churilov
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Zhen Chen, Heng Li, Qian Xu, Szu-Li Sun
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Omar F. El-Gayar, Amit V. Deokar
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DS/AHP  (pages 278-285)
Malcolm J. Beynon
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Chapter 33
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Ran M. Bittmann, Roy M. Gelbard
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Norman Pendegraft, Mark Rounds
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Gloria E. Phillips-Wren, Manuel Mora, Guisseppi Forgionne
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Giusseppi Forgionne, Stephen Russell
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Margaret W. Wood, David C. Rine
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David Sammon
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Simon Woodworth, Joe Cunningham
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G. Kouamou, C. Pettang
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Fátima C.C. Dargam
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Fuzzy Decision Trees  (pages 382-390)
Malcolm J. Beynon
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P. Serra, R. A. Ribeiro, R. Marques Pereira, R. Steel, M. Niezette, A. Donati
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Games of Strategy  (pages 402-409)
Geraldine Ryan, Seamus Coffey
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John Wang, Dajin Wang, Aihua Li
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Alexey Petrovsky
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Frédéric Adam, Jean-Charles Pomerol, Patrick Brézillon
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Marcelo Índio dos Reis, Marcos R.S. Borges, José Orlando Gomes
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Fergal Carton
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Manual Mora, Ovsei Gelman, Guisseppi Forgionne, Francisco Cervantes
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John McAvoy, Tom Butler
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Peter O’Donnell, Rob Meredith
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Cristina Casado Lumbreras, Ricardo Colomo Palacios, Juan Miguel Gómez Berbís
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Ramon Brena, Carlos Chesñevar
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Dina Neiger, Leonid Churilov
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Gloria E. Phillips-Wren
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Ilya Ashikhmin, Eugenia Furems, Alexey Petrovsky, Michael Sternin
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R.A. Ribeiro, I.L. Nunes
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Pandian Vasant, Hrishikesh S. Kale
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Peer-Olaf Siebers, Uwe Aickelin
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Knowledge Based DSS  (pages 565-575)
Michel R. Klein
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James D. Jones
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Camille Rosenthal-Sabroux, Michel Grundstein, Fernando Iafrate
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James D. Jones
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Stephan Scheuerer
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Osvaldo García de la Cerda, Renato Orellana Muermann
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Peer-Olaf Siebers, Uwe Aickelin, Helen Celia, Chris Clegg
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Csaba Csáki
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Brad Morantz, Thomas Whalen, G. Peter Zhang
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Chris Schlueter Langdon
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Manual Mora, Francisco Cervantes, Guisseppi Forgionne, Ovsei Gelman
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Tan Yigitcanlar, Jung Hoon Han, Sang Ho Lee
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Tan Yigitcanlar, Omur Saygin
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João Carlos Namorado Clímaco, João Carlos Soares de Mello, Lidia Angulo Meza
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Luis Antunes, Ana Respício, João Balsa, Helder Coelho
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Geraldine Ryan, Edward Shinnick
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N. Chugunov, G. Shepelyov, M. Sternin
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PROMETHEE  (pages 743-750)
Malcolm J. Beynon
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Malcolm J. Beynon
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Todd McElroy
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Edward Shinnick, Geraldine Ryan
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Rough Set Theory  (pages 783-789)
Malcolm J. Beynon
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Dorrie DeLuca, Joseph S. Valacich
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Software Agents  (pages 798-806)
Stanislaw Stanek, Maciej Gawinecki, Malgorzata Pankowska, Shahram Rahimi
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C.W. Holsapple
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Mattias Strand, Sven A. Carlsson
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Robert Fitzgerald, John Findlay
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Hanan Yaniv, Susan Crichton
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Hanan Yaniv
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Pat Finnegan, Jeremy Hayes
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Giusseppi Forgionne, Stephen Russell
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David Sammon
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David Sammon
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Giusseppi Forgionne, Stephen Russell
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Chapter 107