Indistinguishability operators and generalized distances: the transformation problem revisited
[EN] In this paper we characterize those functions that induce a fuzzy preorder from a quasi-pseudo-metric even when the considered t-norm is not continuous. On the one hand, we prove that they must be decreasing and fulfill a special property of dominance with respect to the ordinary addition and t...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:dnet:riunet______::142686fac247bcd434ff8abb78fc81d9 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/234708 |
| Access Level: | acceso abierto |
| Palabra clave: | Fuzzy preorder Indistinguishability operator Quasi-pseudo-metric T-norm Asymmetric T-triangular triplet Monotonicity Dominance Additive generator Pseudo-inverse |
| Sumario: | [EN] In this paper we characterize those functions that induce a fuzzy preorder from a quasi-pseudo-metric even when the considered t-norm is not continuous. On the one hand, we prove that they must be decreasing and fulfill a special property of dominance with respect to the ordinary addition and the t-norm T under consideration. On the other hand, we have shown that they must transform asymmetric triangular triplets into asymmetric T-triangular triplets. Moreover, we also study the case in which fuzzy preorders are exactly indistinguishability operators. Concretely, we show that the monotonicity of the function and the previously mentioned dominance are sufficient but not necessary conditions. In addition, we prove that such functions must transform triangular triplets into T-triangular triplets. The developed theory is illustrated by means of appropriate examples. Furthermore, we prove that the well-known technique based on the use of the pseudo-inverses of the additive generators of continuous and Archimedean t-norms is recovered as a particular case of the new one presented here. |
|---|