*Decoupling of Attributes and Aggregation for Fuzzy Number Ranking DOI: http://dx.doi.org/10.5772/intechopen.109992*

methods in literature have implicated multiple attributes in their ranking intuition. The multi-attribute approach has two phases: the selection of attributes and the formulation of the aggregation function. The selection of attributes determines what information is deemed relevant for FNR, and the aggregation function controls the trade-off of the attribute values of fuzzy numbers. In this work, we propose three attributes (i.e., representative x-value, range and membership ratio) as three possible dimensions to evaluate a fuzzy number. In aggregation, we formulate the discount factors for range and membership ratio to modify the representative x-value of a fuzzy number for FNR. The proposed method has been illustrated via numerical examples to reveal the rationale of using multiple attributes to articulate the intuition behind FNR.

In future work, there can be two directions to consider: practice and theory. In the practice direction, we can develop more methodical guidance toward the selection and formulations of attributes and the aggregation procedures. In particular, we can formalize the ranking intuition in terms of the selected attributes and the trade-off rationale through the aggregation approach for different FNR problems. Along this effort, we can also compare the ranking results from this multi-attribute approach with other FNR approaches. In the theory direction, while this chapter has initially explored the tension between information content and the satisfaction of the FNR axioms. This tension should call for more mathematical analyses such as classification of information content for FNR and relaxation of axioms for expanded information basis.
