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@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. Online. In Kapounek, S., Vránová, H. (eds.). \textit{38th International Conference on Mathematical Methods in Economics}. Brno, Czech Republic,: Mendel University Brno, 2020, s.~481-487. ISBN~978-80-7509-734-7.
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