Vague and fuzzy t-norms and t-conorms
t-norms and t-conorms are the natural connectives “and” and “or” in fuzzy logic. The unit interval with a t-norm or a t-conorm is a special monoid and some submonoids like discrete t-norms and t-conorms have been proved useful in many cases. In the first part of this article these submonoids will be...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/365019 |
| Acceso en línea: | https://hdl.handle.net/2117/365019 https://dx.doi.org/10.1016/j.fss.2021.07.008 |
| Access Level: | acceso abierto |
| Palabra clave: | Fuzzy logic t-norms t-conorm Indistinguishability operator Fuzzy monoid Fuzzy t-subnorm Fuzzy t-subconorm Vague monoid Vague t-norm Vague t-conorm Lògica difusa Àrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàtica |
| Sumario: | t-norms and t-conorms are the natural connectives “and” and “or” in fuzzy logic. The unit interval with a t-norm or a t-conorm is a special monoid and some submonoids like discrete t-norms and t-conorms have been proved useful in many cases. In the first part of this article these submonoids will be fuzzified to fuzzy t-subnorms and fuzzy t-subconorms in order to deal with imprecision. As particular examples we will provide fuzzifications of the classical and the Lukasiewicz three-valued conjunctions. The second part of the article will define and study vague t-norms and t-conorms as fuzzy operations where is the degree in which z is ( respectively) where T (S) is a t-norm (t-conorm). |
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