Estimating Missing Values in Incomplete Additive Fuzzy Preference Relations

Incomplete fuzzy linguistic preference relations under uncertain environments

“…In some cases, a decision-maker may develop a fuzzy preference relation with incomplete information due to lack of time and knowledge, and the decision-maker's limited experience related with the problem domain [41,42]. Some studies recently focused on this important research field [1,14,15,23,34,41]. Herrera-Viedma et al [15] proposed incomplete fuzzy preference relations for constructing decision matrices of pair wise comparisons from a set of n À 1 preference data based on additive transitivity.…”

“…A complete fuzzy or linguistic preference relation requires nÂðnÀ1Þ 2 judgments for a level with n criteria or alternatives. However, the complexity and uncertainty of real world decision problems may result in situations in which decision-makers cannot provide complete judgments due to time pressure, lack of knowledge or expertise with respect to the problem domain [41,42,44]; thus, decision-makers can utilize fuzzy or linguistic preference relations with incomplete judgments (called incomplete fuzzy or linguistic preference relations) [1,14,15,23,34,[41][42][43][44]. However, all of these studies focus on fuzzy or linguistic preference relations with crisp values, which do not reflect expert opinions when modeling imprecise judgments.…”

A note on group decision-making procedure based on incomplete reciprocal relations

“…A complete fuzzy preference relation of order n necessitates the completion of all n(n -1)/2 judgements in its entire top triangular portion. Sometimes, however, a decision maker (DM) may develop a fuzzy preference relation with incomplete information because of (1) time pressure, lack of knowledge, and the DM's limited expertise related with problem domain Lee et al 2007;Xu 2004Xu , 2005Xu and Chen 2008); (2) when the number of the alternatives, n, is large it may be practically impossible, or at least unacceptable from the point of view of the decision maker, to perform all the n(n -1)/2 required comparisons to complete the pairwise comparison matrices (Fedrizzi and Giove 2007); (3) It can be convenient/necessary to skip some direct critical comparison between alternatives, even if the total number of alternatives is small (Fedrizzi and Giove 2007). (4) An expert would not be able to efficiently express any kind of preference degree between two or more of the available options.…”

Group Decision Making with Incomplete Interval-valued Fuzzy Preference Relations Based on the Minimum Operator

“…Kerre All the above researches focused on the IVFPRs with complete information. However, in DM problems such situations are unavoidable in which an expert does not have comprehensive information of the problem because of time constraint, lack of knowledge and the expert's limited expertise within the problem domain [1,3,5,10,19,22,24,33]. Consequently, the expert may not be able to give his/her opinion about specific traits of the problem, and hence an incomplete preference relation would be constructed.…”