General Pseudo Quasi-Overlap Functions on Lattices
The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric <i>n</i>-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we continue developing this topic...
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| Format: | Article |
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MDPI AG
2022-08-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/8/395 |
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| author | Rui Eduardo Brasileiro Paiva Benjamín René Callejas Bedregal |
| author_facet | Rui Eduardo Brasileiro Paiva Benjamín René Callejas Bedregal |
| author_sort | Rui Eduardo Brasileiro Paiva |
| collection | DOAJ |
| description | The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric <i>n</i>-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we continue developing this topic, this time focusing on another generalization, called general pseudo-overlap functions on lattices, which in a given classification system measures the degree of overlapping of several classes and for any given object where symmetry is an unnecessarily restrictive condition. Moreover, we also provide some methods of constructing these functions, as well as a characterization theorem for them. Also, the notions of pseudo-t-norms and pseudo-t-conorms are used to generalize the concepts of additive and multiplicative generators for the context of general pseudo-quasi-overlap functions on lattices and we explore some related properties. |
| first_indexed | 2024-03-09T10:01:15Z |
| format | Article |
| id | doaj.art-315f790cb2d8400388a0be114bdb051b |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T10:01:15Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-315f790cb2d8400388a0be114bdb051b2023-12-01T23:24:38ZengMDPI AGAxioms2075-16802022-08-0111839510.3390/axioms11080395General Pseudo Quasi-Overlap Functions on LatticesRui Eduardo Brasileiro Paiva0Benjamín René Callejas Bedregal1Instituto Federal de Educação, Ciência e Tecnologia do Ceará, Maracanaú 61939-140, BrazilDepartamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Natal 59078-970, BrazilThe notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric <i>n</i>-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we continue developing this topic, this time focusing on another generalization, called general pseudo-overlap functions on lattices, which in a given classification system measures the degree of overlapping of several classes and for any given object where symmetry is an unnecessarily restrictive condition. Moreover, we also provide some methods of constructing these functions, as well as a characterization theorem for them. Also, the notions of pseudo-t-norms and pseudo-t-conorms are used to generalize the concepts of additive and multiplicative generators for the context of general pseudo-quasi-overlap functions on lattices and we explore some related properties.https://www.mdpi.com/2075-1680/11/8/395aggregation functionsgeneral pseudo quasi-overlap functionsbounded latticesL-fuzzy setsadditive and multiplicative generators |
| spellingShingle | Rui Eduardo Brasileiro Paiva Benjamín René Callejas Bedregal General Pseudo Quasi-Overlap Functions on Lattices Axioms aggregation functions general pseudo quasi-overlap functions bounded lattices L-fuzzy sets additive and multiplicative generators |
| title | General Pseudo Quasi-Overlap Functions on Lattices |
| title_full | General Pseudo Quasi-Overlap Functions on Lattices |
| title_fullStr | General Pseudo Quasi-Overlap Functions on Lattices |
| title_full_unstemmed | General Pseudo Quasi-Overlap Functions on Lattices |
| title_short | General Pseudo Quasi-Overlap Functions on Lattices |
| title_sort | general pseudo quasi overlap functions on lattices |
| topic | aggregation functions general pseudo quasi-overlap functions bounded lattices L-fuzzy sets additive and multiplicative generators |
| url | https://www.mdpi.com/2075-1680/11/8/395 |
| work_keys_str_mv | AT ruieduardobrasileiropaiva generalpseudoquasioverlapfunctionsonlattices AT benjaminrenecallejasbedregal generalpseudoquasioverlapfunctionsonlattices |