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n-Dimensional (S,N)-implications
The n-dimensional fuzzy logic (n-DFL) has been contributed to overcome the insufficiency of traditional fuzzy logic in modeling imperfect and imprecise information, coming from different opinions of many experts by considering the possibility to model not only ordered but also repeated membership de...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Elsevier Inc.
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7422844/ https://www.ncbi.nlm.nih.gov/pubmed/32834472 http://dx.doi.org/10.1016/j.ijar.2020.07.002 |
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author | Zanotelli, Rosana Reiser, Renata Bedregal, Benjamin |
author_facet | Zanotelli, Rosana Reiser, Renata Bedregal, Benjamin |
author_sort | Zanotelli, Rosana |
collection | PubMed |
description | The n-dimensional fuzzy logic (n-DFL) has been contributed to overcome the insufficiency of traditional fuzzy logic in modeling imperfect and imprecise information, coming from different opinions of many experts by considering the possibility to model not only ordered but also repeated membership degrees. Thus, n-DFL provides a consolidated logical strategy for applied technologies since the ordered evaluations provided by decision makers impact not only by selecting the best solutions for a decision making problem, but also by enabling their comparisons. In such context, this paper studies the n-dimensional fuzzy implications (n-DI) following distinct approaches: (i) analytical studies, presenting the most desirable properties as neutrality, ordering, (contra-)symmetry, exchange and identity principles, discussing their interrelations and exemplifications; (ii) algebraic aspects mainly related to left- and right-continuity of representable n-dimensional fuzzy t-conorms; and (iii) generating n-DI from existing fuzzy implications. As the most relevant contribution, the prospective studies in the class of n-dimensional interval (S,N)-implications include results obtained from t-representable n-dimensional conorms and involutive n-dimensional fuzzy negations. And, these theoretical results are applied to model approximate reasoning of inference schemes, dealing with based-rule in n-dimensional interval fuzzy systems. A synthetic case-study illustrates the solution for a decision-making problem in medical diagnoses. |
format | Online Article Text |
id | pubmed-7422844 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Elsevier Inc. |
record_format | MEDLINE/PubMed |
spelling | pubmed-74228442020-08-13 n-Dimensional (S,N)-implications Zanotelli, Rosana Reiser, Renata Bedregal, Benjamin Int J Approx Reason Article The n-dimensional fuzzy logic (n-DFL) has been contributed to overcome the insufficiency of traditional fuzzy logic in modeling imperfect and imprecise information, coming from different opinions of many experts by considering the possibility to model not only ordered but also repeated membership degrees. Thus, n-DFL provides a consolidated logical strategy for applied technologies since the ordered evaluations provided by decision makers impact not only by selecting the best solutions for a decision making problem, but also by enabling their comparisons. In such context, this paper studies the n-dimensional fuzzy implications (n-DI) following distinct approaches: (i) analytical studies, presenting the most desirable properties as neutrality, ordering, (contra-)symmetry, exchange and identity principles, discussing their interrelations and exemplifications; (ii) algebraic aspects mainly related to left- and right-continuity of representable n-dimensional fuzzy t-conorms; and (iii) generating n-DI from existing fuzzy implications. As the most relevant contribution, the prospective studies in the class of n-dimensional interval (S,N)-implications include results obtained from t-representable n-dimensional conorms and involutive n-dimensional fuzzy negations. And, these theoretical results are applied to model approximate reasoning of inference schemes, dealing with based-rule in n-dimensional interval fuzzy systems. A synthetic case-study illustrates the solution for a decision-making problem in medical diagnoses. Elsevier Inc. 2020-11 2020-08-12 /pmc/articles/PMC7422844/ /pubmed/32834472 http://dx.doi.org/10.1016/j.ijar.2020.07.002 Text en © 2020 Elsevier Inc. All rights reserved. Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active. |
spellingShingle | Article Zanotelli, Rosana Reiser, Renata Bedregal, Benjamin n-Dimensional (S,N)-implications |
title | n-Dimensional (S,N)-implications |
title_full | n-Dimensional (S,N)-implications |
title_fullStr | n-Dimensional (S,N)-implications |
title_full_unstemmed | n-Dimensional (S,N)-implications |
title_short | n-Dimensional (S,N)-implications |
title_sort | n-dimensional (s,n)-implications |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7422844/ https://www.ncbi.nlm.nih.gov/pubmed/32834472 http://dx.doi.org/10.1016/j.ijar.2020.07.002 |
work_keys_str_mv | AT zanotellirosana ndimensionalsnimplications AT reiserrenata ndimensionalsnimplications AT bedregalbenjamin ndimensionalsnimplications |