On the derivation of weights from incomplete pairwise comparisons matrices via spanning trees with ...

@article{64366,
   author = {Mazurek, Jiří and Kulakowski, Konrad},
   article_number = {150},
   doi = {http://dx.doi.org/10.1016/j.ijar.2022.08.014},
   keywords = {Pairwise comparisons; Fuzzy numbers; Priority vector; Spanning tree; Multiple-criteria decision making},
   language = {eng},
   issn = {0888-613X},
   journal = {International Journal of Approximate Reasoning},
   title = {On the derivation of weights from incomplete pairwise comparisons matrices via spanning trees with crisp and fuzzy confidence levels},
   url = {https://www.sciencedirect.com/science/article/pii/S0888613X22001268},
   volume = {Neuveden},
   year = {2022}
}

TY  - JOUR
ID  - 64366
AU  - Mazurek, Jiří - Kulakowski, Konrad
PY  - 2022
TI  - On the derivation of weights from incomplete pairwise comparisons matrices via spanning trees with crisp and fuzzy confidence levels
JF  - International Journal of Approximate Reasoning
VL  - Neuveden
IS  - 150
SP  - 242-257
EP  - 242-257
SN  - 0888613X
KW  - Pairwise comparisons
KW  - Fuzzy numbers
KW  - Priority vector
KW  - Spanning tree
KW  - Multiple-criteria decision making
UR  - https://www.sciencedirect.com/science/article/pii/S0888613X22001268
N2  - In this paper, we propose a new method for the derivation of a priority vector from an incomplete pairwise comparisons (PC) matrix. We assume that each entry of a PC matrix provided by an expert is also evaluated in terms of the expert’s confidence in a partic- ular judgment. Then, from corresponding graph representations of a given PC matrix, all spanning trees are found. For each spanning tree, a unique priority vector is obtained with the weight corresponding to the confidence levels of entries that constitute this tree. At the end, the final priority vector is obtained through an aggregation of priority vectors achieved from all spanning trees. Confidence levels are modeled by real (crisp) numbers and triangular fuzzy numbers. Numerical examples and comparisons with other methods are also provided. Last, but not least, we introduce a new formula for an upper bound of the number of spanning trees, so that a decision maker gains knowledge (in advance) on how computationally demanding the proposed method is for a given PC matrix
ER  - 

MAZUREK, Jiří a Konrad KULAKOWSKI. On the derivation of weights from incomplete pairwise comparisons matrices via spanning trees with crisp and fuzzy confidence levels. \textit{International Journal of Approximate Reasoning}. 2022, Neuveden, č.~150, s.~242-257. ISSN~0888-613X. Dostupné z: https://dx.doi.org/10.1016/j.ijar.2022.08.014.