This paper introduces a simplified approach to understanding and working with type-2 fuzzy sets, which are used to model and minimize uncertainties in fuzzy logic systems. Type-2 fuzzy sets are more complex than type-1 fuzzy sets because their membership functions are themselves fuzzy, allowing them to represent uncertainties in the system. However, they are more difficult to understand and use due to their three-dimensional nature, lack of clear terminology, and reliance on the Extension Principle for operations like union, intersection, and complement. To address these challenges, the paper defines a small set of terms that enable precise communication and definition of type-2 fuzzy sets. It introduces the concept of the "footprint of uncertainty," which helps visualize the uncertainty in type-2 fuzzy sets. A new representation for type-2 fuzzy sets is also proposed, using "wavy slices" that simplify the handling of these sets. The paper then presents a new Representation Theorem that allows the derivation of formulas for the union, intersection, and complement of type-2 fuzzy sets without using the Extension Principle. This approach simplifies the operations by using embedded type-2 fuzzy sets and t-norms or t-conorms for combining membership grades. The paper also discusses the application of these concepts to interval type-2 fuzzy sets, which are the most commonly used type-2 fuzzy sets. These sets have secondary grades equal to 1, making them easier to handle and compute. The paper concludes that the new approach makes type-2 fuzzy sets easier to understand and use, validating the use of the Extension Principle through alternative derivations. The results demonstrate that type-2 fuzzy sets can effectively model uncertainties in fuzzy logic systems, making them valuable tools in various applications such as classification, control, and decision-making.This paper introduces a simplified approach to understanding and working with type-2 fuzzy sets, which are used to model and minimize uncertainties in fuzzy logic systems. Type-2 fuzzy sets are more complex than type-1 fuzzy sets because their membership functions are themselves fuzzy, allowing them to represent uncertainties in the system. However, they are more difficult to understand and use due to their three-dimensional nature, lack of clear terminology, and reliance on the Extension Principle for operations like union, intersection, and complement. To address these challenges, the paper defines a small set of terms that enable precise communication and definition of type-2 fuzzy sets. It introduces the concept of the "footprint of uncertainty," which helps visualize the uncertainty in type-2 fuzzy sets. A new representation for type-2 fuzzy sets is also proposed, using "wavy slices" that simplify the handling of these sets. The paper then presents a new Representation Theorem that allows the derivation of formulas for the union, intersection, and complement of type-2 fuzzy sets without using the Extension Principle. This approach simplifies the operations by using embedded type-2 fuzzy sets and t-norms or t-conorms for combining membership grades. The paper also discusses the application of these concepts to interval type-2 fuzzy sets, which are the most commonly used type-2 fuzzy sets. These sets have secondary grades equal to 1, making them easier to handle and compute. The paper concludes that the new approach makes type-2 fuzzy sets easier to understand and use, validating the use of the Extension Principle through alternative derivations. The results demonstrate that type-2 fuzzy sets can effectively model uncertainties in fuzzy logic systems, making them valuable tools in various applications such as classification, control, and decision-making.