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Previous issue date: 2016-12-08 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Este trabalho tem o objetivo de introduzir uma nova classe de medidas de inclus?o difusa entre conjuntos difusos. Esta nova abordagem foi baseada nas axiomatiza??es mais conhecidas com a vantagem de utilizar o m?todo de constru??o de tais medidas agregando os operadores de implica??o. Esses operadores satisfazem algumas propriedades que t?m sido amplamente investigadas na literatura, de forma que, por exemplo, a medida de inclus?o proposta por Goguen torna-se um caso particular da nossa proposta de medida de inclus?o. Apresentamos tamb?m diferentes m?todos de constru??o utilizando automorfismos e provamos que com tais medidas podemos construir n?o s? medidas de entropia, mas tamb?m dist?ncias, fun??es p?nalti e medidas de similaridade entre conjuntos difusos. / The idea of inclusion for fuzzy sets was firstly introduced by L.
Zadeh in 1965 and since then many other studies proposed alternatives
to indicate a degree to which a fuzzy set is included into another
fuzzy set, called an inclusion degree or a subsethood measure. In this
work we present a new class of fuzzy subsethood measures between
fuzzy sets. We introduce a new definition of a fuzzy subsethood measure
as an intersection of other axiomatizations by aggregating fuzzy
implication operators. We also provide some construction methods
to obtain these fuzzy subsethood measures. With our approach we
recover some of the classical measures which have been discussed
in the literature, as the one given by Goguen. We also show how
we can use our developments to generate fuzzy entropies, fuzzy distances,
penalty functions and similarity measures. Finally we study some fuzzy indexes generated from this new class of fuzzy subsethood
measures.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/23644 |
| Date | 08 December 2016 |
| Creators | Santos, H?lida Salles |
| Contributors | 90688384404, http://lattes.cnpq.br/4601263005352005, Palmeira, Eduardo Silva, 99145642591, http://lattes.cnpq.br/9061067320839776, Rocha, Marcus Pinto da Costa da, 15438902291, http://lattes.cnpq.br/7169569605967930, Santiago, Regivan Hugo Nunes, 30680581200, http://lattes.cnpq.br/7536988783793885, Reiser, Renata Hax Sander, 42930995068, http://lattes.cnpq.br/3283691152621834, Sola, Humberto Bustince, Bedregal, Benjamin Rene Callejas |
| Publisher | PROGRAMA DE P?S-GRADUA??O EM SISTEMAS E COMPUTA??O, UFRN, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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