Ranking inconsistency among fuzzy, numeric, and cognitive aggregations

In traditional surveys, opinions collected from questionnaires are transformed into numeric values. To synthesize the opinions of a group, usually the mean and variance of the numeric ratings are computed. Instead of transforming opinions into numbers, fuzzy set theory represents opinions using fuzzy sets. To synthesize opinions, the fuzzy sets are manipulated by aggregation operators. Both numeric and fuzzy methods are used to produce an abstract model intended to represent human decision. This paper compared three methods: numbers, fuzzy sets, and human cognition, in the aggregation of two opinions, and has found that their orderings are not consistent. Human cognition deviates from the numeric mean in a systematic way. Although fuzzy sets can effectively represent the vagueness of linguistic evaluations, fuzzy aggregation operations fail to capture the behavior of cognitive aggregation of two opinions.