Study of uncertainties in physical phenomena via fuzzy sets theor

• Grant number: 21/03896-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2021
• End date: December 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Vinícius Francisco Wasques
• Grantee: Yngrid Zacharias Delgato
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

The fuzzy sets theory was introduced by Zadeh in 1965. From this theory an object can belong to a set with a certain degree of association, allowing to deal in a mathematical and computational way the uncertainty inherent to phenomena of nature. This project focuses on a subclass of fuzzy sets called fuzzy numbers (RF), which extends the definition of a real number. Fuzzy numbers play an important role in the study of Fuzzy Differential Equations (FDEs), which can be used to model phenomena that have uncertain parameters and / or state variables described by fuzzy numbers. There are several ways to deal with FDEs, one of them is given by the extension principle of the analytical solution, which allows to extend classical solutions of Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) to fuzzy solutions. This project will consider two types of extension principles, the Zadeh extension principle and the sup-J extension principle. In the second case, FDEs describe the behavior of fuzzy processes with memory, that is, fuzzy functions that associate real values in RF whose future values are correlated with past or current values. Fuzzy processes with memory incorporate a relationship between fuzzy numbers called interactivity. This project will study the analytical solutions for FDEs and the implications of the proposed approach in the theory of FDEs. In addition, a comparison will be made between the solutions via the Zadeh extension principle and the sup-J extension principle. Finally, the theoretical results will be applied in dynamical systems that model problems in the area of Physics. More precisely, in thermodynamics.

Scientific publications

(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)

DELGATO, YNGRID ZACHARIAS; WASQUES, VINICIUS FRANCISCO. A study of the heat transfer in materials with interval and fuzzy values via extension principle. COMPUTATIONAL & APPLIED MATHEMATICS, v. 41, n. 8, p. 22-pg., 2022-12-01. (21/03896-1)