Banca de DEFESA: ANA SHIRLEY MONTEIRO DA SILVA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : ANA SHIRLEY MONTEIRO DA SILVA
DATE: 16/10/2025
TIME: 14:00
LOCAL: DIMAp
TITLE:

Extension of Functions Defined on Bounded Posets via Retractions and its Properties

KEY WORDS:

Extensions; reductions; retractions; sections; quasi-vector spaces.

PAGES: 120
BIG AREA: Ciências Exatas e da Terra
AREA: Ciência da Computação
SUBÁREA: Teoria da Computação
SPECIALTY: Lógicas e Semântica de Programas
SUMMARY:

This thesis addresses the problem of extension and reduction of fuzzy operators defined on partially ordered sets, a topic of relevance in fuzzy logic due to its connection with the preservation of structures and properties. The work is inspired by the method of Palmeira and Bedregal, who used retractions and sections to propose an extension method (up to isomorphism) for fuzzy operators on bounded lattices. We generalize this method to partially ordered sets, developing a methodology for extensions and, in an innovative manner, introducing the notion of function reduction, conceived as the dual perspective of extension: instead of expanding the domain, reducing it. We also characterize conditions for the preservation of classes and properties of fuzzy operators and establish a partial duality between extension and reduction. Moreover, we introduce the notions of quasi-vector spaces, partially ordered quasi-vector spaces, and conditional monotonicity for functions defined on these spaces, opening new perspectives for applications in fuzzy logic and related areas.

COMMITTEE MEMBERS:
Presidente - 1345816 - REGIVAN HUGO NUNES SANTIAGO
Interno - 2212166 - BENJAMIN RENE CALLEJAS BEDREGAL
Externo ao Programa - 1139450 - VALDIGLEIS DA SILVA COSTA - UFRNExterno à Instituição - HUMBERTO BUSTINCE SOLA - UPNA
Externa à Instituição - HELIDA SALLES SANTOS - FURG
Externo à Instituição - FLAULLES BOONE BERGAMASCHI - UESB
Externa à Instituição - GRAÇALIZ PEREIRA DIMURO