Matemática Fuzzy: Teoria e Aplicações

Abstract

Fuzzy Mathematics is an area of Mathematics that presents a new approach to the classical notion of set, allowing to generalize concepts and results of classical Mathematics. This work aims to provide a comprehensive introduction to Fuzzy Mathematics, addressing the definition and properties of fuzzy sets, as well as their applicability, especially focused on biomathematics. We begin by focusing on the presentation of the fundamentals of Fuzzy Mathematics, in addition to brief comments on its predecessors. The concepts of fuzzy sets, operations with fuzzy sets and fuzzy numbers will be discussed, providing a deepening in relation to Zadeh's Extension Principle. We then proceeded to study bases for modeling population growth through Differential Equations. Next, we will address the area of interactive fuzzy numbers, exploring their potential for modeling problems, especially those related to biomathematics. In this context, we will study the properties of interactive fuzzy numbers, as well as their applications in mathematical modeling. Through concrete examples, we will illustrate how Fuzzy Mathematics and interactive fuzzy numbers are applied in real world situations, highlighting their relevance in decision making in environments of uncertainty and imprecision.