| Texto completo | |
| Autor(es): |
Sussner, Peter
Número total de Autores: 1
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| Tipo de documento: | Artigo Científico |
| Fonte: | IEEE TRANSACTIONS ON FUZZY SYSTEMS; v. 33, n. 9, p. 15-pg., 2025-09-01. |
| Resumo | |
The secondary membership functions (MFs) of type-2 (T2) fuzzy sets (FSs) are generally assumed to be convex, normal, and upper semicontinuous. Although not explicitly stated, this fact can be detected by taking a look at the alpha-cuts of their join and meet in vertical-slice format. These two operations induce [0,1](F), i.e., the complete lattice of the convex normal upper semicontinuous FSs on [0,1] together with the so-called convolution order. In this article, we deduce the alpha-cut representations of suprema and infima over finite and infinite sets that occur in the inference mechanisms of general type-2 (GT2) fuzzy inference systems (FISs). We continue by developing a complete, albeit not distributive, lattice structure for the class of all convex upper semicontinuous FSs on [0,1], denoted F-CU, which permits designing T2 FISs involving T2 FSs whose secondary MFs are not necessarily normal. Using our formulae of the alpha-cuts of suprema and infima in [0,1](F) and F-CU, whose elements we describe using so-called anti-dilations, we prove that [0,1](F) is a closed sublattice of F-CU. We also expand on the lattice-theoretical relations between [0,1](F) and the complete lattices of the convex (strictly) normal FSs. In addition, we show that [0,1](F) and F(CU )contain complete sublattices of (extended) interval type-2 (IT2) FSs. With these results at hand, it becomes easy to perform the transitions FISs under the minimum t-norm -> (closed) IT2 FISs -> GT2 FISs currently used in practice -> GT2 FISs having not necessarily normal secondary MFs. (AU) | |
| Processo FAPESP: | 20/09838-0 - BI0S - Brazilian Institute of Data Science |
| Beneficiário: | João Marcos Travassos Romano |
| Modalidade de apoio: | Auxílio à Pesquisa - Programa Centros de Pesquisa Aplicada |