Paper Info
Title
A note on two methods for estimating missing pairwise preference values.
Abstract
This note analyzes two methods for calculating missing values of an incomplete reciprocal fuzzy preference relation. The first method by Herrera-Viedma appeared in the IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics [vol. 37, no. 1 (2007) 176-189], while the second one by Fedrizzi and Giove appeared later in the European Journal of Operational Research [vol. 183 (2007) 303-313]. The underlying concept driving both methods is the additive consistency property. We show that both methods, although different, are very similar. Both methods derive the same estimated values for the independent-missing-comparison case, while they differ in the dependent-missing-comparison case. However, it is shown that a modification of the first method coincides with the second one. Regarding the total reconstruction of an incomplete preference relation, it is true that the second method performs worse than the first one. When Herrera-Viedma 's method is unsuccessful, Fedrizzi-Giove's method is as well. However, in those cases when Fedrizzi-Giove's method cannot guarantee the successful reconstruction of an incomplete preference relation, we have that Herrera-Viedma 's method can. These results lead us to claim that both methods should be seen as complementary rather than competitors in their application, and as such, we propose a reconstruction policy of incomplete fuzzy preference relations using both methods. By doing this, the only unsuccessful reconstruction case is when there is a chain of missing pairwise comparisons involving each one of the feasible alternatives at least once.
Year
DOI
Venue
2009
10.1109/TSMCB.2009.2023923
IEEE Transactions on Systems, Man, and Cybernetics, Part B
Keywords
Field
DocType
missing pairwise preference value,unsuccessful reconstruction case,incomplete preference relation,independent-missing-comparison case,incomplete reciprocal fuzzy preference,successful reconstruction,total reconstruction,reconstruction policy,missing pairwise comparison,dependent-missing-comparison case,incomplete fuzzy preference relation,fuzzy systems,uncertainty,computational intelligence,artificial intelligence,transitivity,consistency,fuzzy set theory,software engineering,additives,fuzzy sets,operations research,computer science,missing values,pairwise comparison
Reciprocal,Pairwise comparison,Preference relation,Fuzzy logic,Fuzzy set,Artificial intelligence,Missing data,Statistics,Machine learning,Cybernetics,Mathematics,Transitive relation
Journal
Volume
Issue
ISSN
39
6
1941-0492
Citations 
PageRank 
References 
28
1.05
12
Authors
3
Name
Order
Citations
PageRank
Francisco Chiclana16350284.13
Enrique Herrera-Viedma213105642.24
Sergio Alonso3166953.28