Desirable Properties of Weighting Vector in Pairwise Comparisons Matrix With Fuzzy Elements

@inproceedings{45862,
   author = {Ramík, Jaroslav},
   address = {Brno, Czech Republic,},
   booktitle = {38th International Conference on Mathematical Methods in Economics},
   editor = {Kapounek, S., Vránová, H. (eds.)},
   keywords = {multi-criteria optimization; pair-wise comparisons matrix; fuzzy elements; alo-group; consistency; priority vector},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Brno, Czech Republic,},
   isbn = {978-80-7509-734-7},
   pages = {481-487},
   publisher = {Mendel University Brno},
   title = {Desirable Properties of Weighting Vector in Pairwise Comparisons Matrix With Fuzzy Elements},
   year = {2020}
}

TY  - JOUR
ID  - 45862
AU  - Ramík, Jaroslav
PY  - 2020
TI  - Desirable Properties of Weighting Vector in Pairwise Comparisons Matrix With Fuzzy Elements
PB  - Mendel University Brno
CY  - Brno, Czech Republic,
SN  - 9788075097347
KW  - multi-criteria optimization
KW  - pair-wise comparisons matrix
KW  - fuzzy elements
KW  - alo-group
KW  - consistency
KW  - priority vector
N2  - We deal with pairwise comparisons matrix with fuzzy elements (FPCM). Fuzzy elements are appropriate whenever the decision maker (DM) is uncertain about the value of his/her evaluation of the relative importance of elements in question, or, when aggregating crisp pairwise comparisons of a group of decision makers in the group DM problem. The problem is formulated in a general setting investigating pairwise comparisons matrices with elements from abelian linearly ordered group (alo-group). Such an approach enables extensions of traditional multiplicative, additive or fuzzy approaches. Continuing our research in \cite{Ramik2018}, here we propose a new order preservation concept based on alpha-cuts. Then we define an innovative concept of (weak) consistency of FPCMs, propose some desirable properties of priority vectors, and derive necessary and sufficient conditions for the existence of coherent vector (CV) and intensity vector (IV) of a FPCM. Finally, we formulate the optimization problem and derive the priority vector with the desirable properties. Illustrating examples are presented and discussed.
ER  - 

RAMÍK, Jaroslav. Desirable Properties of Weighting Vector in Pairwise Comparisons Matrix With Fuzzy Elements. In Kapounek, S., Vránová, H. (eds.). \textit{38th International Conference on Mathematical Methods in Economics}. Brno, Czech Republic,: Mendel University Brno. s.~481-487. ISBN~978-80-7509-734-7. 2020.