The papers below have both been accepted for focus sessions at the International Fuzzy Systems Association World Congress to be held in Edmonton, Alberta, Canada.
Title: Aggregating fuzzy implications to measure group consensus
Authors: G. Beliakov, T. Calvo and S. James
We approach the problem of measuring consensus for a set of real inputs by aggregating the fuzzy implication degrees between each pair of inputs. We compare our operator with existing consensus measures in terms of their satisfaction of desirable properties. The appeal of such an approach lies in the interpretability and flexibility that results from component-wise construction which we modeled on the Bonferroni mean. We also outline some intentions for future research.
Title: Learning aggregation weights from 3-tuple comparison sets
Authors: G. Beliakov, S. James and D. Nimmo
An important task in multiple-criteria decision making is how to learn the weights and parameters of an aggregation function from empirical data. We consider this in the context of quantifying ecological diversity, where such data is to be obtained as a set of pairwise comparisons specifying that one community should be considered more diverse than another. A problem that arises is how to collect a sufficient amount of data for reliable model determination without overloading individuals with the number of comparisons they need to make. After providing an algorithm for determining criteria weights and an overall ranking from such information, we then investigate the improvement in accuracy if ranked 3-tuples are supplied instead of pairs. We found that aggregation models could be determined accurately from significantly fewer 3-tuple comparisons than pairs.
The R code relating to these papers will be made available soon.