Banca de DEFESA: LUCÉLIA MARQUES LIMA DA ROCHA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : LUCÉLIA MARQUES LIMA DA ROCHA
DATA : 05/12/2016
HORA: 09:00
LOCAL: Auditorio do CCET
TÍTULO:

Homogeneity and Pseudo-Homogeneity of interval T-Norms and interval-valued Atanassov's Intuicionistics T-norms

PALAVRAS-CHAVES:

T-norms, Homogeneity, Pseudo-homogeneity, interval-valued Atanassov's Intuitionistic, Fuzzy Logic, Admissibles orders, interval representation.

PÁGINAS: 120
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Ciência da Computação
SUBÁREA: Metodologia e Técnicas da Computação
ESPECIALIDADE: Sistemas de Informação
RESUMO:

The set theory can't deal adequately with subjective linguistic terms, for example, "approximately '', "around '', "young '', among others. It was then, Lotfi A. Zadeh in 1965 suggested a generalization of set theory called fuzzy sets theory (FST), where in the passage membership to the non-memberhip was gradual and not abrupt, thus allowing to represent the uncertainty and inaccuracy of such linguistic terms.

From the first moment it was clear that the FST was an exceptional tool to represent human knowledge. But Zadeh has shown that sometimes in decision-making processes, this knowledge is best represented by some generalizations or extensions of the fuzzy sets theory. Thus, there are several fuzzy extensions in literature, in which we can mention the interval-valued fuzzy sets theory (IVFST) where membership degrees are subintervals of [0,1], which was introduced in 1975
independently by Zadeh and other researchers.

Another extension of the FST was introduced by Krassimir Atanassov in 1983, which was called Atanassov's intuitionists fuzzy set theory (AIFST) that if characterized by considering both a membership degree as a non-membership degree. In 1989, Atanassov himself with G. Gargov proposed to consider intervals for both membership degrees as the non-membership. This latest extension is called  interval-valued Atanassov's intuitionistics fuzzy set theory (IVAIFST).

Introduced by Menger in the context of the probabilistic metric space theory, a triangular norm or t-norm is a kind special associative function over a unit interval closed  [0,1]  and is used to define the intersection of fuzzy sets and has been used in various applications of FST such as rule-based fuzzy systems, decision making, fuzzy morphology, fuzzy formal languages, etc. This concept has also been generalized to different extensions of FST, however there are no records that have it has been made for IVAIFST. This thesis introduced the notion of t-standards for TCFIAIV.

Thus, the Atanassov's intuitionists fuzzy sets are a natural generalization of fuzzy sets, and these are useful in applications in many situations of the day-to-day, such as decision making, digital image processing, among others. However, for these applications can not only use these sets, but we can also apply the concepts of homogeneity, of which play a key role in certain situations.

Homogeneity is an analytical property that has theoretically been studied over time and in particular the homogeneity of
t-norms has been studied exhaustively. In the literature there are several generalizations of the concept of homogeneity functions and among them there is the notion of pseudo-homogeneity introduced by Aifang Xie, Liu Yong Su and Huawen in order to generalize the quasi-homogeneous functions. In particular, pseudo-homogeneous t-norms were studied. In this sense, this thesis are presented new concepts regarding the homogeneity as well as the extension of the concept of the homogeneity and pseudo-homogeneity in  [0,1]  to interval homogeneity and interval pseudo-homogeneity, focusing mainly on the interval t-norms and interval-valued Atanassov's intuitionistics t-norms. We illustrate our results with examples of image processing and decision making.

MEMBROS DA BANCA:
Presidente - 2212166 - BENJAMIN RENE CALLEJAS BEDREGAL
Externo ao Programa - 1549905 - FAGNER LEMOS DE SANTANA
Externo ao Programa - 1345816 - REGIVAN HUGO NUNES SANTIAGO
Externo à Instituição - EDUARDO SILVA PALMEIRA - UESC-BA
Externo à Instituição - GRAÇALIZ PEREIRA DIMURO - FURG