RAMÍK, Jaroslav. Condition of Order Preservation in Pairwise Comparisons Matrix With Fuzzy Elements. Online. In 36-th International Conference Mathematical Methods in Economics 2018. Praha, CZ: Silesian Univeristy in Opava, SBA Karviná, 2018, p. 457-462. ISBN 978-80-7378-372-3.
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Basic information
Original name Condition of Order Preservation in Pairwise Comparisons Matrix With Fuzzy Elements
Authors RAMÍK, Jaroslav (203 Czech Republic, guarantor, belonging to the institution).
Edition Praha, CZ, 36-th International Conference Mathematical Methods in Economics 2018, p. 457-462, 6 pp. 2018.
Publisher Silesian Univeristy in Opava, SBA Karviná
Other information
Original language English
Type of outcome Proceedings paper
Field of Study 10103 Statistics and probability
Confidentiality degree is not subject to a state or trade secret
Publication form electronic version available online
RIV identification code RIV/47813059:19520/18:00011194
Organization unit School of Business Administration in Karvina
ISBN 978-80-7378-372-3
UT WoS 000427151400094
Keywords in English ranking alternatives; pairwise comparisons matrix; analytic hierarchy process; consistency
Changed by Changed by: RNDr. Daniel Jakubík, učo 139797. Changed: 21/11/2019 15:05.
Abstract
In this paper we deal with Preference Order Preservation (POP) condition of pairwise comparisons (PC) matrix with fuzzy elements. 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. We formulate the problem in a general setting investigating pairwise comparisons matrices with fuzzy elements from Abelian linearly ordered group (alo-group). Such an approach enables extensions of traditional multiplicative, additive or fuzzy approaches. Then we propose new order preservation concept based on alpha-cuts. We define the concept of consistency of PC matrix with fuzzy elements (PCF matrices), generalize the concept of the preference order preservation condition (POP condition) to PCF matrices defining weak POP and strong POP condition and derive sufficient conditions for POP condition to be met. Finally, we discuss a numerical example in order to illustrate the proposed concepts and properties.
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