Simplifying Lexicographic Orders to Rank Fuzzy Numbers: An Application in Banking Capital Adequacy

Abstract

[EN] Lexicographic orders produce a total order over a set of fuzzy numbers by comparing several real-valued functions of each fuzzy number under consideration following a strictly hierarchical method. Lexicographic orders present advantages such as simplicity, consistency with human intuition, and power of discrimination. In this paper, we move one step forward in the search for simplicity by proposing a simplified version of lexicographic orders that focuses on the defining parameters of fuzzy numbers instead of using more complex functions as is common in the existing methodologies. More precisely, we show that two lexicographic methods described in the literature for trapezoidal and triangular fuzzy numbers are equivalent to the lexicographic order of a reorganization of the vector of defining parameters, reducing the complexity of the methods. We illustrate our approach through numerical examples and a case study about capital adequacy in the banking sector.