Análisis de una metodología de ranking difuso utilizando números difusos trapezoidales con aplicaciones en Estadística

Resumen

Fuzzy numbers are mathematical entities that serve to generalize the notion of real number to a probabilistic or uncertain setting. Although the usual arithmetic with real numbers can be extended to the fuzzy context, the order in R is not easy to generalize. There are many methodologies for ranking (or classifying) fuzzy numbers, but none of them is universally accepted. In 2018, Rold_an López de Hierro, Roldán and Herrera presented a new fuzzy binary relationship between fuzzy numbers satisfying two important advantages: on the one hand, this relationship veri_es many reasonable properties that had been proposed by several authors previously; on the other hand, it provides consistent with human intuition rankings. Due to its feasible application in statistics and computation, the main aim of this report is to describe how this fuzzy binary relationship works on the family of all trapezoidal fuzzy numbers (including the subclasses that it contains) showing, at the same time, new properties of this novel ranking methodology. In addition, a new library in R (called rankingTwoTraFNs) has been introduced so that any interested researcher may test this algorithm for ranking fuzzy trapezoidal numbers in real contexts by using very few computational resources and avoiding the mathematical details of this methodology. Finally, a comparative study with other existing algorithms is carried out to show the reasonability of the obtained rankings and to illustrate the advantages of the proposed methodology.