On the Monte Carlo weights in multiple criteria decision analysis

@article{64368,
   author = {Mazurek, Jiří and Strzalka, Dominik},
   article_number = {10},
   keywords = {Monte Carlo simulations; weights; multiple criteria decision making},
   language = {eng},
   issn = {1932-6203},
   journal = {PLOS ONE},
   title = {On the Monte Carlo weights in multiple criteria decision analysis},
   url = {https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0268950},
   volume = {17},
   year = {2022}
}

TY  - JOUR
ID  - 64368
AU  - Mazurek, Jiří - Strzalka, Dominik
PY  - 2022
TI  - On the Monte Carlo weights in multiple criteria decision analysis
JF  - PLOS ONE
VL  - 17
IS  - 10
SP  - 1-18
EP  - 1-18
SN  - 19326203
KW  - Monte Carlo simulations
KW  - weights
KW  - multiple criteria decision making
UR  - https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0268950
N2  - In multiple-criteria decision making/aiding/analysis (MCDM/MCDA) weights of criteria constitute a crucial input for finding an optimal solution (alternative). A large number of methods were proposed for criteria weights derivation including direct ranking, point allocation, pairwise comparisons, entropy method, standard deviation method, and so on. However, the problem of correct criteria weights setting persists, especially when the number of criteria is relatively high. The aim of this paper is to approach the problem of determining criteria weights from a different perspective: we examine what weights’ values have to be for a given alternative to be ranked the best. We consider a space of all feasible weights from which a large number of weights in the form of n−tuples is drawn randomly via Monte Carlo method. Then, we use predefined dominance relations for comparison and ranking of alternatives, which are based on the set of generated cases. Further on, we provide the estimates for a sample size so the results could be considered robust enough. At last, but not least, we introduce the concept of central weights and the measure of its robustness (stability) as well as the concept of alternatives’ multi-dominance, and show their application to a real-world problem of the selection of the best wind turbine.
ER  - 

MAZUREK, Jiří a Dominik STRZALKA. On the Monte Carlo weights in multiple criteria decision analysis. \textit{PLOS ONE}. 2022, roč.~17, č.~10, s.~1-18. ISSN~1932-6203.