Banca de DEFESA: FERNANDO NERES DE OLIVEIRA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : FERNANDO NERES DE OLIVEIRA
DATE: 28/07/2023
TIME: 09:00
LOCAL: Auditório I DIMAP - https://meet.google.com/bdh-nudx-jzq
TITLE:

On new contrapositivisation techniques for (interval-valued) fuzzy (co)implications and their generalizations

KEY WORDS:

Contrapositivisation, Fuzzy implication, Fuzzy coimplication, Triangular norm, Triangular conorm, Fuzzy negation, ($S$,$N$)-Contrapositivisation, co-Upper contrapositivisation, co-Lower contrapositivisation, co-Medium contrapositivisation, co-($S$,$N$)-Contrapositivisation, Overlap function, Grouping function, ($G$,$N$)-Contrapositivisation, Quasi-overlap function, Quasi-grouping function, ($QO$,$QG$,$N$)-Contrapositivisation, Automorphism, Aggregation function, Aggregated contrapositivisation, Bi-aggregated contrapositivisation, Min-Max contrapositivisation, Best interval representation, Interval-valued upper contrapositivisation, Interval-valued lower contrapositivisation, Interval-valued medium contrapositivisation, Fuzzy logic, $N$-compatibility, Contrapositive symmetrization.

PAGES: 180
BIG AREA: Ciências Exatas e da Terra
AREA: Ciência da Computação
SUBÁREA: Teoria da Computação
SPECIALTY: Lógicas e Semântica de Programas
SUMMARY:

In this work, we introduce several contrapositivisation operators for fuzzy implications, we present a wide study of each of these operators with respect to the main properties routinely required by fuzzy implications, we prove that the classes of these contrapositivisators are invariant by automorphisms and present some conditions for the $N$-compatibility of the respective contrapositivisations, we propose some construction methods of classes of triangular norms (quasi-overlaps), triangular conorms (quasi-groupings) and aggregation functions from these contrapositivisators; we introduce the Min-Max contrapositivisation technique for fuzzy implications and some of its generalizations; we introduce four contrapositivisation operators for fuzzy coimplications so-called co-upper, co-lower, co-medium and co-($S$,$N$)- contrapositivisators, we characterize these operators from the point of view of the properties that are usually attributed to the fuzzy coimplications, we present sufficient conditions for the $N$-compatibility of the co-upper, co-lower, co-medium and co-($S$,$N$)- contrapositivisations, we show that the classes of co-upper, co-lower, co-medium and co-($S$,$N$)- contrapositivisators are closed under the action of automorphisms and we propose a construction method of triangular conorms from co-($S$,$N$)-contrapositivisators of ($T$,$N$)-coimplications and fuzzy negations; and finally, we propose the classes of interval-valued upper, lower and medium contrapositivisators and broadly characterize each one of them, we show that both classes are invariant by interval-valued automorphisms, we introduce the notion of $N$-compatibility for the respective interval-valued contrapositivisations and we prove that the best interval representations of real-valued upper, lower and medium contrapositivisators are, respectively, interval-valued upper, lower and medium contrapositivisators.

COMMITTEE MEMBERS:
Presidente - 1345816 - REGIVAN HUGO NUNES SANTIAGO
Interno - 2212166 - BENJAMIN RENE CALLEJAS BEDREGAL
Externo ao Programa - 2645969 - ANDERSON PAIVA CRUZ - UFRNExterna à Instituição - RENATA HAX SANDER REISER - UFPel
Externo à Instituição - RUI EDUARDO BRASILEIRO PAIVA - IFCE