Comparative Assessment of the Stability of AHP and FAHP Methods
| Autor: | Edmundas Kazimeras Zavadskas, Valentinas Podvezko, Irina Vinogradova-Zinkevič |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization Physics and Astronomy (miscellaneous) General Mathematics Analytic hierarchy process 02 engineering and technology Fuzzy logic 020901 industrial engineering & automation 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) Fuzzy number uncertainty Mathematics Mathematical model lcsh:Mathematics fuzzy Analytic Hierarchy Process stability Multiple-criteria decision analysis Analytic Hierarchy Process lcsh:QA1-939 symmetric and asymmetric fuzzy numbers Ranking Chemistry (miscellaneous) Decision matrix 020201 artificial intelligence & image processing Pairwise comparison |
| Zdroj: | Symmetry, Vol 13, Iss 479, p 479 (2021) Symmetry; Volume 13; Issue 3; Pages: 479 |
| ISSN: | 2073-8994 |
| Popis: | Mathematical models describing physical, technical, economic, and other processes can be used to analyze these processes and predict their results, providing that these models are stable and their results are stable relative to the model parameters used. Small changes in the values of the model parameters correspond to small changes in the results. Multicriteria decision-making models need to check the results’ stability against the models’ main components: the values of the criteria weights and the elements of the decision matrix. In this article, we study the stability of models associated with the calculation of criteria weights. For the analysis, the most commonly used models are taken—the Analytic Hierarchy Process (AHP) method and the fuzzy Analytic Hierarchy Process (FAHP) method, in which fuzzy numbers are used under conditions of data uncertainty. Both mathematically well-based methods verify the consistency of the expert evaluations. The method of statistical simulation (Monte Carlo) is the basis for studying the results’ stability. The study checks the experts’ provided evaluations’ consistency, calculates the criteria weights, and evaluates their relative errors after a slight change in the estimates of the pairwise comparisons of the criteria provided by the experts. The matrix of comparisons of the FAHP method is constructed based on the entire expert group’s assessments. It estimates the boundaries of variance in the fuzzy criteria weights. This paper estimates the stability of the criteria’ weights associated with the mathematical methods themselves and the experts’ estimates. The results are useful to study the stability of specific MCDM methods when ranking alternatives. |
| Databáze: | OpenAIRE |
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