The incomplete Analytic Hierarchy Process and Bradley-Terry model: (in)consistency and information retrieval
| Autor: | László Gyarmati, Éva Orbán-Mihálykó, Csaba Mihálykó, Zsombor Szádoczki, Sándor Bozóki |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Artificial Intelligence Optimization and Control (math.OC) Computer Science - Information Theory Information Theory (cs.IT) General Engineering FOS: Mathematics QA75 Electronic computers. Computer science / számítástechnika számítógéptudomány Mathematics - Optimization and Control Computer Science Applications |
| DOI: | 10.48550/arxiv.2210.03700 |
| Popis: | Several methods of preference modeling, ranking, voting and multi-criteria decision making include pairwise comparisons. It is usually simpler to compare two objects at a time, furthermore, some relations (e.g., the outcome of sports matches) are naturally known for pairs. This paper investigates and compares pairwise comparison models and the stochastic Bradley-Terry model. It is proved that they provide the same priority vectors for consistent (complete or incomplete) comparisons. For incomplete comparisons, all filling in levels are considered. Recent results identified the optimal subsets and sequences of multiplicative/additive/reciprocal pairwise comparisons for small sizes of items (up to n = 6). Simulations of this paper show that the same subsets and sequences are optimal in case of the Bradley-Terry and the Thurstone models as well. This, somehow surprising, coincidence suggests the existence of a more general result. Further models of information and preference theory are subject to future investigation in order to identify optimal subsets of input data. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|