Banca de DEFESA: RUI EDUARDO BRASILEIRO PAIVA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : RUI EDUARDO BRASILEIRO PAIVA
DATA : 05/08/2019
HORA: 10:00
LOCAL: DIMAp
TÍTULO:

A lattice extension for Overlaps and naBL-algebras

PALAVRAS-CHAVES:

Overlap, Quasi-overlap, Scott toplogy, Fuzzy Logic, naBL-algebras.

PÁGINAS: 122
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Ciência da Computação
SUBÁREA: Teoria da Computação
ESPECIALIDADE: Lógicas e Semântica de Programas
RESUMO:

Overlap functions were introduced as a class of bivariate aggregation functions on [0, 1] to be applied in the image processing field. Many researchers have begun to develop overlap functions to explore their potential in different scenarios, such as problems involving classification or decision making. Recently, a non-associative generalization of Hájek’s BL-algebras (naBL-algebras) were investigated from the perspective of overlap functions as a residuated application. In this work, we generalize the notion of overlap functions for the lattice context and introduce a weaker definition, called a quasi-overlap, that arises from definition, called a quasi-overlap, that arises from the removal of the continuity condition. To this end, the main properties of (quasi-) overlaps over bounded lattices, namely: convex sum, migrativity, homogeneity, idempotency, and cancellation law are investigated, as well as an overlap characterization of Archimedian overlap functions is presented. In addition, we formalized the residual principle for the case of quasi-overlap functions on lattices and their respective induced implications, as well as revealing that the class of quasi-overlap functions that fulfill the residual principle is the same class of continuous functions according to topology of Scott. As a consequence, we provide a new generalization of the notion of naBL-algebras based on overlap over lattices.

MEMBROS DA BANCA:
Presidente - 1345816 - REGIVAN HUGO NUNES SANTIAGO
Interno - 2251108 - UMBERTO RIVIECCIO
Externo à Instituição - FLAULLES BOONE BERGAMASCHI - UESB
Externo à Instituição - JORGE PETRUCIO VIANA - UFF
Externo à Instituição - MARCO CERAMI - UFBA