## Banca de QUALIFICAÇÃO: ANDERSON PAIVA CRUZ

DISCENTE: ANDERSON PAIVA CRUZ
DATA: 04/09/2012
HORA: 15:00
LOCAL: Sala de Reuiniões do DIMAp
TÍTULO:

Characterizations of the Three Main Fuzzy Implication Classes Satisfying the Boolean-like Laws y =< I(x,y) , I(x,I(y,x))=1 and I(x,I(y,z))=I(I(x,y), I(x,z)).

PALAVRAS-CHAVES:

Boolean-like laws; Fuzzy implications; Fuzzy Rule Based Systems; Fuzzy Set Theories.

PÁGINAS: 78
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Ciência da Computação
SUBÁREA: Teoria da Computação
ESPECIALIDADE: Lógicas e Semântica de Programas
RESUMO:

There is not only one acceptable fuzzy implication de nition nowadays. In a theoretical viewpoint, this fact evinces a lack of consensus
on the logical implication meaning in Boolean and fuzzy contexts. In a practical viewpoint, it induces the ignorance about which "implication operators" the software engineer can apply in a Fuzzy Rule Based System (FRBS) which in turn generates FRBSs less appropriated with respect to1 their appliance domain. In order to a better understanding about logical connectives, it is necessary to known which properties are satisfied ed for them. Therefore, towards to corroborate with fuzzy implication meaning and for a contribution to implement FRBSs more appropriated to their domain, several Boolean laws have been generalized and studied as equations or inequations in fuzzy logics. Those generalizations are called Boolean-like laws and a lot of them do not remain valid in any fuzzy semantics. In this scenario, this proposal brings an investigation of under which sucient and necessary conditions three Boolean-like laws - y =< I(x; y), I(x; I(y; x)) = 1 and I(x; I(y; z)) = I(I(x; y); I(x; z)) - holds for the three best-known classes of fuzzy implications and when they generated by automorphisms.

MEMBROS DA BANCA:
Presidente - 1345816 - REGIVAN HUGO NUNES SANTIAGO
Interno - 2212166 - BENJAMIN RENE CALLEJAS BEDREGAL
Externo à Instituição - GRAÇALIZ PEREIRA DIMURO - FURG