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A new method for ranking fuzzy numbers and its application to group decision making
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Zhang, Feng, Ignatius, Joshua, Lim, Chee Peng and Zhao, Yajun (2014) A new method for ranking fuzzy numbers and its application to group decision making. Applied Mathematical Modelling, 38 (4). pp. 1563-1582. doi:10.1016/j.apm.2013.09.002 ISSN 0307-904X.
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Official URL: https://doi.org/10.1016/j.apm.2013.09.002
Abstract
In this paper, a new method for comparing fuzzy numbers based on a fuzzy probabilistic preference relation is introduced. The ranking order of fuzzy numbers with the weighted confidence level is derived from the pairwise comparison matrix based on 0.5-transitivity of the fuzzy probabilistic preference relation. The main difference between the proposed method and existing ones is that the comparison result between two fuzzy numbers is expressed as a fuzzy set instead of a crisp one. As such, the ranking order of n fuzzy numbers provides more information on the uncertainty level of the comparison. Illustrated by comparative examples, the proposed method overcomes certain unreasonable (due to the violation of the inequality properties) and indiscriminative problems exhibited by some existing methods. More importantly, the proposed method is able to provide decision makers with the probability of making errors when a crisp ranking order is obtained. The proposed method is also able to provide a probability-based explanation for conflicts among the comparison results provided by some existing methods using a proper ranking order, which ensures that ties of alternatives can be broken.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Engineering > WMG (Formerly the Warwick Manufacturing Group) | ||||
Journal or Publication Title: | Applied Mathematical Modelling | ||||
Publisher: | Elsevier | ||||
ISSN: | 0307-904X | ||||
Official Date: | 2014 | ||||
Dates: |
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Volume: | 38 | ||||
Number: | 4 | ||||
Page Range: | pp. 1563-1582 | ||||
DOI: | 10.1016/j.apm.2013.09.002 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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