MAZUREK, Jiří and Konrad KULAKOWSKI. On the derivation of weights from incomplete pairwise comparisons matrices via spanning trees with crisp and fuzzy confidence levels. International Journal of Approximate Reasoning. 2022, Neuveden, No 150, p. 242-257. ISSN 0888-613X. Available from: https://dx.doi.org/10.1016/j.ijar.2022.08.014.
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Basic information
Original name On the derivation of weights from incomplete pairwise comparisons matrices via spanning trees with crisp and fuzzy confidence levels
Authors MAZUREK, Jiří (203 Czech Republic, guarantor, belonging to the institution) and Konrad KULAKOWSKI (616 Poland).
Edition International Journal of Approximate Reasoning, 2022, 0888-613X.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10201 Computer sciences, information science, bioinformatics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW URL
RIV identification code RIV/47813059:19520/22:A0000288
Organization unit School of Business Administration in Karvina
Doi http://dx.doi.org/10.1016/j.ijar.2022.08.014
UT WoS 000860466600003
Keywords in English Pairwise comparisons; Fuzzy numbers; Priority vector; Spanning tree; Multiple-criteria decision making
Tags International impact, Reviewed
Links GA21-03085S, research and development project.
Changed by Changed by: Miroslava Snopková, učo 43819. Changed: 11/4/2023 11:07.
Abstract
In this paper, we propose a new method for the derivation of a priority vector from an incomplete pairwise comparisons (PC) matrix. We assume that each entry of a PC matrix provided by an expert is also evaluated in terms of the expert’s confidence in a partic- ular judgment. Then, from corresponding graph representations of a given PC matrix, all spanning trees are found. For each spanning tree, a unique priority vector is obtained with the weight corresponding to the confidence levels of entries that constitute this tree. At the end, the final priority vector is obtained through an aggregation of priority vectors achieved from all spanning trees. Confidence levels are modeled by real (crisp) numbers and triangular fuzzy numbers. Numerical examples and comparisons with other methods are also provided. Last, but not least, we introduce a new formula for an upper bound of the number of spanning trees, so that a decision maker gains knowledge (in advance) on how computationally demanding the proposed method is for a given PC matrix
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