Banca de QUALIFICAÇÃO: DIEGO MANUEL SOTO ZÚÑIGA

Uma banca de QUALIFICAÇÃO de MESTRADO foi cadastrada pelo programa.
STUDENT : DIEGO MANUEL SOTO ZÚÑIGA
DATE: 25/07/2025
TIME: 10:00
LOCAL: Auditorio do DIMAp I
TITLE:

Mean-Like Functions on Trapezoidal Fuzzy Numbers Endowed with an Admissible Order and the Problem of Establishing a Quality of Life Index for Cities

KEY WORDS:

Trapezoidal fuzzy numbers; Admissible order; Mean-like function; Discrete Choquet integral; Quality of life index.

PAGES: 80
BIG AREA: Ciências Exatas e da Terra
AREA: Ciência da Computação
SUBÁREA: Matemática da Computação
SPECIALTY: Modelos Analíticos e de Simulação
SUMMARY:

This work establishes the foundations of a theory of mean-like functions over trapezoidal fuzzy numbers endowed with an admissible order—that is, a linear order that refines a specific partial order. To this end, we investigated an admissible order over trapezoidal fuzzy numbers "compatible" with arithmetic operations. Recently, we generalized this work to triangular fuzzy numbers endowed with an admissible order. In this dissertation, we adapt this work to trapezoidal fuzzy numbers, adding new classes of mean-like functions, such as ordered weighted mean functions and discrete Choquet integrals, both over the set of trapezoidal fuzzy numbers endowed with an admissible order. We also investigated properties such as symmetry, homogeneity, comonotony, and self-identity. To demonstrate the applicability of this approach, we propose, as an illustrative example, the obtaining of a quality of life index in three Chilean cities, considering climatic variables. Given that these variables have distinct units, we developed a method for their treatment that transforms this information into fuzzy numbers and applies median-like functions to trapezoidal fuzzy numbers considering an admissible lexicographic order.

COMMITTEE MEMBERS:
Presidente - 2212166 - BENJAMIN RENE CALLEJAS BEDREGAL
Interno - 2645969 - ANDERSON PAIVA CRUZ
Externo à Instituição - NICOLAS EDUARDO ZUMELZU CÁRCAMO - UMAG
Externo à Instituição - ROBERTO ANTONIO DÍAZ MATAMALA - ULAGOS