Join and meet operations for type-2 fuzzy sets with non-convex secondary memberships

In this paper we will present two theorems for the join and meet operations for general type-2 fuzzy sets with arbitrary secondary memberships, which can be non-convex and/or non-normal type-1 fuzzy sets. These results will be used to derive the join and meet operations of the more general descripti...

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Detalles Bibliográficos
Autores: Ruiz, Gonzalo, Hagras, Hani, Pomares, Héctor, Rojas, Ignacio, Bustince Sola, Humberto
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2016
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/32796
Acceso en línea:https://hdl.handle.net/2454/32796
Access Level:acceso abierto
Palabra clave:General type-2 fuzzy logic
Nonconvex fuzzy sets
Type-2 fuzzy logic
Descripción
Sumario:In this paper we will present two theorems for the join and meet operations for general type-2 fuzzy sets with arbitrary secondary memberships, which can be non-convex and/or non-normal type-1 fuzzy sets. These results will be used to derive the join and meet operations of the more general descriptions of interval type-2 fuzzy sets presented in [1], where the secondary grades can be non-convex. Hence, this work will help to explore the potential of type-2 fuzzy logic systems which use the general forms of interval type-2 fuzzy sets which are not equivalent to interval valued fuzzy sets. Several examples for both general type-2 and the more general forms of interval type-2 fuzzy sets are presented.