Mean-Like Functions on Trapezoidal Fuzzy Numbers Endowed with an Admissible Order
Trapezoidal fuzzy numbers; Admissible order; Mean-like function; Discrete Choquet integral.
This work establishes the foundations of a theory of mean-like functions over trapezoidal fuzzy numbers endowed with an admissible order—that is, a linear order that refines a specific partial order. To this end, we investigated an admissible order over trapezoidal fuzzy numbers "compatible" with arithmetic operations. Recently, we generalized this work to triangular fuzzy numbers endowed with an admissible order. In this dissertation, we ke functions, such as ordered weighted mean functions and discrete Choquet integrals, both over the set of trapezoidal fuzzy numbers endowed with an admissible order. We also investigated
properties such as symmetry, homogeneity, comonotony, and self-identity.