RAMÍK, Jaroslav. Desirable Properties of Weighting Vector in Pairwise Comparisons Matrix With Fuzzy Elements. Online. In Kapounek, S., Vránová, H. (eds.). 38th International Conference on Mathematical Methods in Economics. Brno, Czech Republic,: Mendel University Brno, 2020, p. 481-487. ISBN 978-80-7509-734-7.
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Basic information
Original name Desirable Properties of Weighting Vector in Pairwise Comparisons Matrix With Fuzzy Elements
Name in Czech Požadované vlastnosti váhového vektoru v matici párových porovnání s fuzzy prvky
Authors RAMÍK, Jaroslav (203 Czech Republic, guarantor, belonging to the institution).
Edition Brno, Czech Republic, 38th International Conference on Mathematical Methods in Economics, p. 481-487, 7 pp. 2020.
Publisher Mendel University Brno
Other information
Original language English
Type of outcome Proceedings paper
Field of Study 10102 Applied mathematics
Country of publisher Czech Republic
Confidentiality degree is not subject to a state or trade secret
Publication form electronic version available online
RIV identification code RIV/47813059:19520/20:A0000121
Organization unit School of Business Administration in Karvina
ISBN 978-80-7509-734-7
Keywords (in Czech) vícekriteriální optimalizace; matice párových porovnání; fuzzy prvky; alo-grupyů konzistenceů prioritní vektor
Keywords in English multi-criteria optimization; pair-wise comparisons matrix; fuzzy elements; alo-group; consistency; priority vector
Tags International impact, Reviewed
Links GA18-01246S, research and development project.
Changed by Changed by: prof. RNDr. Jaroslav Ramík, CSc., učo 48844. Changed: 23/1/2021 20:59.
Abstract
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.
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