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Understanding the Analytic Hierarchy Process

Understanding the Analytic Hierarchy Process

Authors
Publisher Taylor & Francis Ltd
Year 11/11/2020
Pages 242
Version hardback
Readership level Professional and scholarly
ISBN 9781138032323
Categories Product design, Decision theory: general, Probability & statistics
$214.87 (with VAT)
790.00 PLN / €176.16 / £151.34
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Book description

One of the best-known methods of multi-criteria decision-making is the Analytic Hierarchy Process (AHP). This method provides a convenient and versatile framework for modeling multi-criteria decision problems, evaluating alternatives, and deriving final priorities. Rather than imposing a "correct" decision, AHP allows the user to create a ranking of alternatives, then choose the one which is the best (or among the best). At the core of AHP is a pairwise comparisons (PC) method. This is an old technique known in various forms since at least the Middle Ages. AHP uses and develops the PC method. The aim of Understanding the Analytic Hierarchy Process is to provide the reader with a critical guide to AHP. In this book, the AHP method is considered primarily as a mathematical technique supporting the decision-making process. Key Features Collects the ideas underpinning the AHP method and discusses them together with many improvements and extensions present in the literature. As a result, the reader will receive a much more complete picture of the method. Aimed at theorists and advanced practitioners from a wide range of scientific fields, including the social, management, and technical sciences. Highlights the intuitive assumptions underlying the mathematical methods that make up AHP and the pairwise comparisons method. Provides software code for readers who wish to practice AHP analysis using the Wolfram Language.

Understanding the Analytic Hierarchy Process

Table of contents

1. AHP as a decision-making method. 1.1. Why we need decision-making methods. 1.2. AHP basics. 1.3. Neat examples. 2. PC Matrices. 2.1. Cardinal PC Matrix. 2.2. Ordinal PC Matrix. 2.3. Incomplete PC matrix. 2.4. PC matrix as a graph. 2.5. Graph as a matrix. 2.6. Additive PC matrix. 2.7. Fuzzy PC matrix. 3. Prioritization methods. 3.1. Eigenvalue Method. 3.2. Geometric mean method. 3.3. Optimization methods. 3.4. Weighted column sum methods. 3.5. Towards comparing prioritization methods. 4. Prioritization methods for incomplete PC matrices. 4.1. Eigenvalue method for incomplete PC matrices. 4.2. Geometric mean method for incomplete PC matrices. 4.3. Logarithmic Least Square Method. 4.4. Optimization methods. 4.5. Other optimization methods. 5. Rating scale. 5.1. The concept of a rating scale. 5.2. Rating scales for AHP. 6. Inconsistency. 6.1. Introduction. 6.2. Preliminaries. 6.3. Quantifying inconsistency. 6.4. Properties of inconsistency indices. 7. Inconsistency of incomplete PC matrices. 7.1. Introduction. 7.2. Preliminaries. 7.3. Quantifying inconsistency. 7.4. Incompleteness and inconsistency. 8. Group Decisions. 8.1. Aggregation methods. 8.2. Consensus methods. 8.3. Compatibility index. 9. Ordinal inconsistency. 9.1. Condition of order preservation. 9.2. Kendall Babington-Smith inconsistency index. 10. Fuzzy AHP. 10.1. Fuzzy LLSM. 10.2. Order of alternatives in the fuzzy ranking. 10.3. Exact solution based on fuzzy preferences. 10.4. Other methods and discussion. 11. Heuristic Rating Estimation. 11.1. The idea of HRE. 11.2. Additive HRE. 11.3. Existence of a solution for additive HRE. 11.4. Geometric HRE. 11.5. Existence of a solution for geometric HRE. 11.6. Is geometric HRE optimal? 11.7. Illustrative examples. Bibliography. Index

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