Fuzzy differential equations and fuzzy algebra with applications

• Grant number: 23/03927-0
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2023
• End date: October 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Vinícius Francisco Wasques
• Grantee: Vinícius Francisco Wasques
• Host Institution: Centro Nacional de Pesquisa em Energia e Materiais (CNPEM). Ministério da Ciência, Tecnologia e Inovação (Brasil). Campinas , SP, Brazil
• Associated researchers: Allan Edley Ramos de Andrade ; Estevão Esmi Laureano ; Francielle Santo Pedro Simões

Abstract

The fuzzy set theory was developed to analyze and characterize sets withvague frontiers. There are several ramifications within the area of fuzzy sets, in which this project dedicates to study two of them. The first one is the theory offuzzy differential equations (FDEs), in which the imprecision may be associated to the parameters involved, initial/boundary conditions or direction field. In modelling, some concepts are considered, such as fuzzy numbers, which extends the concept of real numbers, and also fuzzy derivatives and fuzzy integrals. Recently, it has been proved that the class of fuzzy numbers RF, under certain conditions, has the structureof a Banach space. This fact has brought several applications in dynamical systems. The condition mentioned above is associated with a fuzzy relationship called interactivity. This project focuses on exploring new results and applications from FDEs, consideringthe fuzzy relation of interactivity. In particular, this project will continue to study two distinct approaches thatare being explored by the candidate. The first considers the sup-J extension principle, which is a method that extends classical operators so that it is possible to have interactive (non-interactive) fuzzy numbers as inputs. The second is to explore dynamic systems, without effectivelyuse technical skills to solve classical differential equations, but instead consider the qualitative knowledge of the phenomenon and study it through a technique called p-fuzzy systems. The second area is the fuzzy algebra theory. In this fields it is possible to work in two perspectives. The first one is based on the algebraic structure of fuzzy numbers and arithmetic operations. The second perspective is based on the study of algebraic structures of fuzzy subsets of classical groups. For each approach, it is intended to apply the theoretic results in problems of exact and biological sciences, more specifically, in the areas of physics, chemistry and biology. (AU)

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

PINTO, NILMARA J. B.; WASQUES, VINICIUS F.; OLIVEIRA, WASHINGTON A.; BARROS, LAECIO C.. p-Fuzzy Newton-Raphson Method. INTELLIGENT AND FUZZY SYSTEMS, VOL 3, INFUS 2024, v. 1090, p. 9-pg., 2024-01-01. (20/09838-0, 23/03927-0)

WASQUES, VINICIUS FRANCISCO. A numerical approach to fuzzy partial differential equations with interactive fuzzy values: application to the heat equation. COMPUTATIONAL & APPLIED MATHEMATICS, v. 43, n. 6, p. 13-pg., 2024-09-01. (23/03927-0)

DE ANDRADE, ALLAN EDLEY RAMOS; WASQUES, VINICIUS FRANCISCO. Fixed-Point Theorems for Fuzzy Mappings. MATHEMATICS, v. 12, n. 14, p. 8-pg., 2024-07-01. (23/03927-0)

DE ANDRADE, ALLAN EDLEY RAMOS; WASQUES, VINICIUS FRANCISCO. The interactive fuzzy semigroup (R_IC,+_1/2) and its algebraic structure properties. FUZZY SETS AND SYSTEMS, v. 486, p. 15-pg., 2024-04-22. (23/03927-0)