Understanding the Analytic Hierarchy Process

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