Understanding the Analytic Hierarchy Process

1. Auflage 2020
ISBN: 978-1-138-03232-3
Verlag: Chapman and Hall/CRC

Buch, Englisch, 262 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 564 g

Reihe: Chapman & Hall/CRC Series in Operations Research

The aim of this book 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. This method provides a convenient and versatile framework for modelling 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.

Autoren/Hrsg.

Kulakowski, Konrad

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung
• Mathematik | Informatik Mathematik Stochastik Bayesianische Inferenz

Inhaltsverzeichnis

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

Über Autor(innen)

Konrad Kulakowski is an Associate Professor and Deputy Head of the Department of Applied Computer Science, Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering at the AGH University of Science and Technology (AGH UST). He received his Ph.D. and Habilitation in computer science from AGH UST. His research interests are focused on multiple-criteria decision-making methods, including AHP, and their applications, theory and practice of the pairwise comparison method, parallel programming, and algorithms. He serves as a reviewer of many international journals in operational research and computer science. He has organized several special sessions in International Conferences on Computer Science and Operational Research. He has also served as a member of program committees at numerous international IT and OR conferences and meetings.