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Previous issue date: 2013-12-06 / In the literature there are several proposals of fuzzi cation of lattices
and ideals concepts. Chon in (Korean J. Math 17 (2009), No. 4,
361-374), using the notion of fuzzy order relation de ned by Zadeh,
introduced a new notion of fuzzy lattice and studied the level sets of
fuzzy lattices, but did not de ne a notion of fuzzy ideals for this type
of fuzzy lattice.
In this thesis, using the fuzzy lattices de ned by Chon, we de ne fuzzy
homomorphism between fuzzy lattices, the operations of product, collapsed
sum, lifting, opposite, interval and intuitionistic on bounded
fuzzy lattices. They are conceived as extensions of their analogous
operations on the classical theory by using this de nition of fuzzy
lattices and introduce new results from these operators.
In addition, we de ne ideals and lters of fuzzy lattices and concepts
in the same way as in their characterization in terms of level and
support sets. One of the results found here is the connection among
ideals, supports and level sets. The reader will also nd the de nition
of some kinds of ideals and lters as well as some results with respect
to the intersection among their families.
Moreover, we introduce a new notion of fuzzy ideals and fuzzy lters
for fuzzy lattices de ned by Chon. We de ne types of fuzzy ideals
and fuzzy lters that generalize usual types of ideals and lters of
lattices, such as principal ideals, proper ideals, prime ideals and maximal
ideals. The main idea is verifying that analogous properties in
the classical theory on lattices are maintained in this new theory of
fuzzy ideals. We also de ne, a fuzzy homomorphism h from fuzzy lattices
L and M and prove some results involving fuzzy homomorphism
and fuzzy ideals as if h is a fuzzy monomorphism and the fuzzy image
of a fuzzy set ~h(I) is a fuzzy ideal, then I is a fuzzy ideal. Similarly,
we prove for proper, prime and maximal fuzzy ideals. Finally, we
prove that h is a fuzzy homomorphism from fuzzy lattices L into M
if the inverse image of all principal fuzzy ideals of M is a fuzzy ideal
of L.
Lastly, we introduce the notion of -ideals and - lters of fuzzy lattices
and characterize it by using its support and its level set. Moreover,
we prove some similar properties in the classical theory of -
ideals and - lters, such as, the class of -ideals and - lters are
closed under intersection. We also de ne fuzzy -ideals of fuzzy lattices,
some properties analogous to the classical theory are also proved
and characterize a fuzzy -ideal on operation of product between
bounded fuzzy lattices L and M and prove some results.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/18692 |
| Date | 06 December 2013 |
| Creators | Mezzomo, Ivan |
| Contributors | CPF:90688384404, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4781417E7, Prolo, Carlos Augusto, CPF:38899973091, http://lattes.cnpq.br/3828418008457501, Mesquita, Marcos Eduardo Ribeiro do Valle, CPF:27869691828, http://lattes.cnpq.br/7809380690711656, Santiago, Regivan Hugo Nunes, CPF:30680581200, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4790032Z4, Reiser, Renata Hax Sander, CPF:42930995068, http://lattes.cnpq.br/3283691152621834, Bedregal, Benjamin Ren? Callejas |
| Publisher | Universidade Federal do Rio Grande do Norte, Programa de P?s-Gradua??o em Sistemas e Computa??o, UFRN, BR, Ci?ncia da Computa??o |
| Source Sets | IBICT Brazilian ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| 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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