Banca de DEFESA: LANDERSON BEZERRA SANTIAGO

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : LANDERSON BEZERRA SANTIAGO
DATE: 02/03/2023
TIME: 14:00
LOCAL: Laboratorio de Ensino DIMAp
TITLE:

Multidimensional Fuzzy Negations and Implications

KEY WORDS:

Multidimensional fuzzy sets, Admissible orders, Automorphisms, Natural ne-
gations, Decision-making problems, Ordinal sums.

PAGES: 62
BIG AREA: Ciências Exatas e da Terra
AREA: Ciência da Computação
SUBÁREA: Teoria da Computação
SPECIALTY: Lógicas e Semântica de Programas
SUMMARY:

Multidimensional fuzzy sets is a new extension of fuzzy sets on which the membership values of an element in the universe of discourse are increasingly ordered vectors on the set of real numbers in the interval [0, 1]. The main application of this type of set are the multi-criteria group decision making problems, in which, in the n-dimensional case, we have a set of situations, which are always evaluated by a fixed number n of experts. The multidimensional case is used when some of these experts refrain to evaluate some of these situations and, therefore, may be suitable for solving multi-criteria group decision making problems with incomplete information. This thesis aims to investigate fuzzy negations and fuzzy implications on the set of increasingly ordered vectors on [0, 1], i.e. on L∞ ([0, 1]), with respect to some partial order. In this thesis we study partial orders, giving special attention to admissible orders on L∞ ([0, 1]). In addition, some properties and methods to construct and generate such operators from fuzzy negations and fuzzy implications, respectively, are provided (in particular, a notion of ordinal sums of n-dimensional fuzzy negations and ordinal sums of multidimensional fuzzy negations will be proposed with respect to specific partial orders) and we demonstrate that an action of the group of automorphisms on fuzzy implications on L∞ ([0, 1]) preserves several original properties of the implication. Using a specific type of representable multidimensional fuzzy implication, we are able to generate a class of multidimensional fuzzy negations called natural m-negations. In the end, an application in decision-making problems is presented.

COMMITTEE MEMBERS:
Presidente - 2212166 - BENJAMIN RENE CALLEJAS BEDREGAL
Interno - 1345816 - REGIVAN HUGO NUNES SANTIAGO
Externo à Instituição - ANNAXSUEL ARAUJO DE LIMA - IFRN
Externo à Instituição - EDUARDO SILVA PALMEIRA - UESC-BA
Externa à Instituição - RENATA HAX SANDER REISER - UFPel
Externo à Instituição - THADEU RIBEIRO BENÍCIO MILFONT - UFERSA