Banca de QUALIFICAÇÃO: JUSCELINO PEREIRA DE ARAUJO

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : JUSCELINO PEREIRA DE ARAUJO
DATE: 14/11/2024
TIME: 13:00
LOCAL: Remoto
TITLE:

On φ-extensions and fuzzy number functions

KEY WORDS:

Zadeh’s Extension Principle, Aggregation Function, φ-Extension, Fuzzy Number, Semiring.

PAGES: 60
BIG AREA: Ciências Exatas e da Terra
AREA: Ciência da Computação
SUBÁREA: Teoria da Computação
SPECIALTY: Lógicas e Semântica de Programas
SUMMARY:

This work studies the generalizations of Zadeh's Extension Principle through the change of the minimum function by another aggregation function. The mathematical details involved are studied in order to assure that real number functions are extended to functions of fuzzy numbers whose image only contains fuzzy numbers. The notion of $\varphi$-extension was introduced in order to formalize the definition of these extended mappings in a way to avoid inconsistencies with the definition of fuzzy number used. Some algebraic properties are explored aiming to understand how characteristics of a real number function are present in its extended versions. Some applications of $\varphi$-extensions are also studied, like the extensions of binary operations of real numbers. Particularly, a new definition of the product operation of fuzzy numbers is used to define a semiring of positive trapezoidal fuzzy number. Some properties of this semiring are explored.

COMMITTEE MEMBERS:
Presidente - 1345816 - REGIVAN HUGO NUNES SANTIAGO
Interno - 2212166 - BENJAMIN RENE CALLEJAS BEDREGAL
Externa à Instituição - RENATA HAX SANDER REISER - UFPel