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## Banca de DEFESA: THADEU RIBEIRO BENICIO MILFONT

STUDENT : THADEU RIBEIRO BENICIO MILFONT
DATE: 03/12/2021
TIME: 14:00
LOCAL: Sala Virtual no Google Meets
TITLE:

Ordered n-dimensional fuzzy graphs

KEY WORDS:

n-Dimensional Fuzzy Graphs, Metrics on n-Dimensional Fuzzy Graphs, n-Dimensional Aggregation Functions, Admissible Orders, Ordered Semi-vector Spaces,  Aggregation of  n-Dimensional fuzzy graphs.

PAGES: 132
BIG AREA: Ciências Exatas e da Terra
AREA: Ciência da Computação
SUBÁREA: Teoria da Computação
SPECIALTY: Lógicas e Semântica de Programas
SUMMARY:

A fuzzy graph is a fuzzy relation between the elements of a set, they are ideal for modeling uncertain data about these sets. The fuzzy graphs appear frequently in the literature, among them, stands out the fuzzy graph of Rosenfeld, based on fuzzy sets of
Zadeh, and its extensions, such as: interval-valued fuzzy graphs, bi-polar fuzzy graphs and m-polar fuzzy graphs. The applications of these concepts are vast: cluster analysis, pattern classification, database theory, social science, neural networks, decision analysis, among others. As well as fuzzy graphs, studies on admissible orders and their extensions are frequent. Originally, admissible orders were introduced in the context of interval-valued fuzzy sets by H. Bustince et al. and since then they have been widely investigated. Recently, this notion has been studied in other types of fuzzy sets, such as interval-valued intuitionistic fuzzy sets, hesitant fuzzy sets, multidimensional fuzzy sets and n-dimensional fuzzy sets. In this context, this work proposes to extend the fuzzy graph of Rosenfeld to interval-valued n-dimensional fuzzy graphs, based on n-dimensional fuzzy sets, as well as, for the admissible interval-valued n-dimensional fuzzy graphs, that we equip with an admissible ordered semi-vector space. We present some methods to generate admissible orders in the n-dimensional fuzzy set and the concept of n-dimensional aggregation functions with respect to an admissible order. We extend the concept of ordered semi-vector space in a semi-field of non-negative real numbers to an arbitrary weak semi-field. We define in a set of admissible interval n-dimensional fuzzy graphs the concept of ordered semi-vector space, whit this, we introduced in this set the concept of admissible interval n-dimensional fuzzy graphs aggregation function. Several properties of these concepts were investigated, in addition to presenting some applications.

BANKING MEMBERS:
Presidente - 2212166 - BENJAMIN RENE CALLEJAS BEDREGAL
Interno - 1345816 - REGIVAN HUGO NUNES SANTIAGO
Externo à Instituição - IVAN MEZZOMO - UFERSA
Externo à Instituição - MATHEUS DA SILVA MENEZES - UFERSA
Externa à Instituição - RENATA HAX SANDER REISER - UFPel