Definition of Triangular Norms and Triangular Conorms on Subfamilies of Type-2 Fuzzy Sets
In certain stages of the application of a type-2 fuzzy logic system, it is necessary to perform operations between input or output fuzzy variables in order to compute the union, intersection, aggregation, complement, and so forth. In this context, operators that satisfy the axioms of t-norms and t-c...
| Autores: | , , , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Navarra |
| Repositorio: | Dadun. Depósito Académico Digital de la Universidad de Navarra |
| Idioma: | inglés |
| OAI Identifier: | oai:dadun.unav.edu:10171/121083 |
| Acceso en línea: | https://hdl.handle.net/10171/121083 |
| Access Level: | acceso abierto |
| Palabra clave: | Normal function Convex function Type-2 fuzzy set Interval type-2 fuzzy set t-norm t-conorm Function from [0-1] to [0-1] |
| Sumario: | In certain stages of the application of a type-2 fuzzy logic system, it is necessary to perform operations between input or output fuzzy variables in order to compute the union, intersection, aggregation, complement, and so forth. In this context, operators that satisfy the axioms of t-norms and t-conorms are of particular significance, as they are applied to model intersection and union, respectively. Furthermore, the existence of a range of these operators allows for the selection of the t-norm or t-conorm that offers the optimal performance, in accordance with the specific context of the system. In this paper, we obtain new t-norms and t-conorms on some important subfamilies of the set of functions from [0,1] to [0,1] . The structure of these families provides a more solid algebraic foundation for the applications. In particular, we define these new operators on the subsets of the functions that are convex, normal, and normal and convex, as well as the functions taking only the values 0 or 1 and the subset of functions whose support is a finite union of closed intervals. These t-norms and t-conorms are generalized to the type-2 fuzzy set framework. |
|---|