The three semantics of fuzzy sets
Fuzzy Sets and Systems - Special issue: fuzzy sets: where do we stand? Where do we go?
Group decision making procedure considering preference strength under incomplete information
Computers and Operations Research
An interactive procedure for multiple criteria group decision making with incomplete information
Proceedings of the 23rd international conference on on Computers and industrial engineering
A utility range-based interactive group support system for multiattribute decision making
Computers and Operations Research
IEEE Transactions on Fuzzy Systems
Group Decision-Making Model With Incomplete Fuzzy Preference Relations Based on Additive Consistency
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A web based consensus support system for group decision making problems and incomplete preferences
Information Sciences: an International Journal
Expert Systems with Applications: An International Journal
Advances in Artificial Intelligence
A new incomplete preference relations based approach to quality function deployment
Information Sciences: an International Journal
Incomplete interval fuzzy preference relations and their applications
Computers and Industrial Engineering
Incomplete preference relations: An upper bound condition
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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This note analyzes two methods for calculating missing values of an incomplete reciprocal fuzzy preference relation. The first method by Herrera-Viedma et al. 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 et al.'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 et al.'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.