On Yager and Hamacher t-Norms and Fuzzy Metric Spaces

Recently, Gregori et al. have discussed (Fuzzy Sets Syst 2011;161:2193 2205) the so-called strong fuzzy metrics when looking for a class of completable fuzzy metric spaces in the sense of George and Veeramani and state the question of finding a non-strong fuzzy metric space for a continuous t-norm d...

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Detalles Bibliográficos
Autores: Castro Company, Francisco, Tirado Peláez, Pedro
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/50523
Acceso en línea:https://riunet.upv.es/handle/10251/50523
Access Level:acceso abierto
Palabra clave:T-norm
Yager t-norms
Hamacher t-norms
Fuzzy Metric Spaces
MATEMATICA APLICADA
Descripción
Sumario:Recently, Gregori et al. have discussed (Fuzzy Sets Syst 2011;161:2193 2205) the so-called strong fuzzy metrics when looking for a class of completable fuzzy metric spaces in the sense of George and Veeramani and state the question of finding a non-strong fuzzy metric space for a continuous t-norm different from the minimum. Later on, Gutíerrez-García and Romaguera solved this question (Fuzzy Sets Syst 2011;162:91 93) by means of two examples for the product and the Lukasiewicz t-norm, respectively. In this direction, they posed to find further examples of nonstrong fuzzy metrics for continuous t-norms that are greater than the product but different from minimum. In this paper, we found an example of this kind. On the other hand, Tirado established (Fixed Point Theory 2012;13:273 283) a fixed-point theorem in fuzzy metric spaces, which was successfully used to prove the existence and uniqueness of solution for the recurrence equation associated with the probabilistic divide and conquer algorithms. Here, we generalize this result by using a class of continuous t-norms known as ω-Yager t-norms.