Bedregal, Benjamin René CallejasSantiago, Landerson Bezerra2023-04-192023-04-192023-03-02SANTIAGO, Landerson Bezerra. Negações e implicações fuzzy multidimensionais. Orientador: Benjamín René Callejas Bedregal. 2023. 81f. Tese (Doutorado em Ciência da Computação) - Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Natal, 2023.https://repositorio.ufrn.br/handle/123456789/52202Multidimensional fuzzy sets are a new extension of fuzzy sets on which the membership values of an element in the universe of discourse are vectors whose components are real numbers in the interval [0, 1], increasingly ordered. In the multidimensional fuzzy sets, distinct elements of the universe of discourse may have membership values with different numbers of components. The main application of this type of set are the multicriteria group decision making problems, in which, in the n-dimensional case, we have a set of criteria, which are always evaluated by a fixed number n of experts and able to identify the corresponding assignments for each of these specialists. 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(generated by omission or exclusion of opinion of some of the experts). This thesis aims to investigate fuzzy negations and fuzzy implications on the set of increasingly ordered vectors on [0, 1] with respect to some partial order, that is, in the partially ordered set ⟨L∞([0, 1]), ≤⟩. 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, including an action of the group of automorphisms on fuzzy implications on L∞([0, 1]) that 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, concepts of inclusion and similarity measure in multidimensional fuzzy sets will be proposed and an application in decision-making problems is presented.Acesso AbertoConjuntos fuzzy multidimensionaisOrdens admissíveisAutomorfismosNegações naturaisProblemas de tomada de decisãoSomas ordinaisdoctoralThesisCNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::SISTEMAS DE COMPUTACAO