RAMÍK, Jaroslav. Condition of Order Preservation in Pairwise Comparisons Matrix. Online. In International Conference on Intelligent Decision Technologies. Cham, Switzerland: Springer, 2018, p. 283-292, 6 pp. ISBN 978-3-319-59420-0.
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Basic information
Original name Condition of Order Preservation in Pairwise Comparisons Matrix
Authors RAMÍK, Jaroslav (203 Czech Republic, guarantor, belonging to the institution).
Edition Cham, Switzerland, International Conference on Intelligent Decision Technologies, p. 283-292, 6 pp. 2018.
Publisher Springer
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/47813059:19520/18:00011195
Organization unit School of Business Administration in Karvina
ISBN 978-3-319-59420-0
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
This paper forms both theoretical and practical innovation basis for decision making process in micro and macro economics. The decision making problem considered here is to rank n alternatives from the best to the worst, using the information given by the decision maker(s) in the form of an n×n pairwise comparisons matrix. Here, we deal with pairwise comparisons matrices with fuzzy elements. Fuzzy elements of the pairwise comparisons matrix are applied whenever the decision maker is uncertain about the value of his/her evaluation of the relative importance of elements in question. We investigate pairwise comparisons matrices with elements from abelian linearly ordered group (alo-group) over a real interval which is a generalization of traditional multiplicative or additive approaches. The concept of reciprocity and consistency of pairwise comparisons matrices with fuzzy elements is well known. Here, we extend these concepts, namely to the strict as well as strong consistency of pairwise comparisons matrices with fuzzy elements (PCF matrices). We derive the necessary and sufficient conditions for strict/strong consistency and investigate their properties as well as some consequences to the problem of ranking the alternatives. Illustrating examples are presented and discussed.
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