An original approach to ranking fuzzy numbers by inclusion index and Bitset Encoding
Résumé
A variety of methods for ranking fuzzy sets has been suggested. Generally, these methods fall under two main categories: a fuzzy-real sets mapping, a dominance relation of one fuzzy set over another. The original approach proposed in this paper belongs to the second category, as the ranking is based on the degree of inclusion in the MIN of two fuzzy numbers. The novelty lies mainly in the intuitive connection between the topological relationship of fuzzy shapes (triangles, trapezoids, etc.) and the measure of inclusion or dominance referred as inclusion index. This connection led to the classification of different topological relationships into classes identified by a binary pattern. This operation is referred to as Bitset Encoding. Consequently, the outcome of a ranking is already decided for most cases by merely identifying its pattern. Ultimately, the method is validated by the axiomatic system of Wang and Kerre and proven to be a reliable, efficient and strong potential alternative to the other prominent methods.