Banca de DEFESA: FERNANDA MONSERRAT ROJAS CUADRA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : FERNANDA MONSERRAT ROJAS CUADRA
DATE: 06/08/2026
TIME: 15:00
LOCAL: Auditorio I do DIMAp
TITLE:

Discrete Sugeno integrals on triangular fuzzy numbers equipped with an admissible order and a proliferation index of Macrocystis pyrifera

KEY WORDS:

 triangular fuzzy numbers, Sugeno integral, capacity, admissible order, averaging functions, macrocystis pyrifera.

PAGES: 75
BIG AREA: Ciências Exatas e da Terra
AREA: Ciência da Computação
SUBÁREA: Matemática da Computação
SUMMARY:

Fuzzy set theory, introduced by Zadeh, encompasses the so-called fuzzy numbers, which can be understood as an extension of the classical concept of real numbers, allowing the quantitative modeling of imprecise situations. Among these classes, triangular fuzzy numbers stand out, characterized by a simple representation through an ordered triple of real numbers, which makes them particularly suitable for applications, computational implementations, and theoretical analyses. For this reason, this dissertation focuses on triangular fuzzy numbers. However, unlike the set of real numbers, the set of triangular fuzzy numbers does not admit a natural total order compatible with its structure. This limitation has motivated the development of admissible orders, which provide a useful framework for extending several mathematical concepts to the fuzzy setting.

The discrete Sugeno integral constitutes a fundamental tool for information aggregation under uncertainty. Nevertheless, its classical formulation does not directly address the setting of triangular fuzzy numbers when considered under arbitrary admissible orders, a gap that remains insufficiently explored in the literature. In this sense, this dissertation introduces the notion of a triangular fuzzy capacity, extending the classical concept of capacity, and proposes an adaptation of the discrete Sugeno integral for functions taking values in triangular fuzzy numbers, incorporating admissible orders into its definition.

Based on this construction, fundamental properties of the proposed $(\preceq,\TFNR)$-Sugeno integrals, where $\preceq$ is an admissible order on triangular fuzzy numbers, are investigated. In addition to the theoretical development, an application is presented based on spectral variables obtained through remote sensing from the Sentinel-2, Landsat 8, and Landsat 9 satellites and modeled as triangular fuzzy numbers, with the aim of constructing a presence index for Macrocystis pyrifera (kelp). This index is used to assess the feasibility and usefulness of the proposed approach for detecting kelp under uncertainty.

COMMITTEE MEMBERS:
Presidente - 2212166 - BENJAMIN RENE CALLEJAS BEDREGAL
Interno - 2645969 - ANDERSON PAIVA CRUZ
Externo à Instituição - NICOLAS EDUARDO ZUMELZU CÁRCAMO - UMAG
Externo à Instituição - YURILEV CHALCO-CANO