Dubois and Prade (1978) present a method for performing algebraic operations on fuzzy numbers, extending classical tolerance analysis to fuzzy data. A fuzzy number is a fuzzy subset of the real line with a membership function that is monotonic around a mean value. The authors propose a fuzzification principle to extend operations like addition, subtraction, multiplication, and division to fuzzy numbers. They show that these operations can be performed with minimal computational effort, similar to handling error intervals in tolerance analysis. The approach allows known algorithms to be adapted to fuzzy data, with applications in various scientific domains. The paper defines fuzzy numbers and their properties, including their membership functions. It then discusses the sum of fuzzy numbers, showing that the membership function of the sum is derived from the minimum of the membership functions of the individual numbers. The authors also derive formulas for the product and quotient of fuzzy numbers, demonstrating that these operations can be performed using the fuzzification principle. They further extend the operations to the 'max' and 'min' functions, showing how to determine the fuzzy value of the maximum or minimum of two fuzzy numbers. The authors also discuss the practical implementation of these operations, showing that they can be performed efficiently using L-R fuzzy numbers, which are defined by their mean value and spreads. They demonstrate that the sum of two L-R fuzzy numbers is another L-R fuzzy number with updated mean and spreads. The paper also addresses the challenges of performing operations on fuzzy numbers with negative values and provides formulas for approximating the results. The authors conclude that fuzzy algebraic calculus is a generalization of tolerance analysis and can be applied in various scientific domains where quantities are vaguely known. They note that performing operations on fuzzy numbers requires only a moderate amount of additional computation compared to using classical numbers, making it a practical approach for handling uncertainty in data. The paper also references other studies and provides a foundation for further research in fuzzy set theory and its applications.Dubois and Prade (1978) present a method for performing algebraic operations on fuzzy numbers, extending classical tolerance analysis to fuzzy data. A fuzzy number is a fuzzy subset of the real line with a membership function that is monotonic around a mean value. The authors propose a fuzzification principle to extend operations like addition, subtraction, multiplication, and division to fuzzy numbers. They show that these operations can be performed with minimal computational effort, similar to handling error intervals in tolerance analysis. The approach allows known algorithms to be adapted to fuzzy data, with applications in various scientific domains. The paper defines fuzzy numbers and their properties, including their membership functions. It then discusses the sum of fuzzy numbers, showing that the membership function of the sum is derived from the minimum of the membership functions of the individual numbers. The authors also derive formulas for the product and quotient of fuzzy numbers, demonstrating that these operations can be performed using the fuzzification principle. They further extend the operations to the 'max' and 'min' functions, showing how to determine the fuzzy value of the maximum or minimum of two fuzzy numbers. The authors also discuss the practical implementation of these operations, showing that they can be performed efficiently using L-R fuzzy numbers, which are defined by their mean value and spreads. They demonstrate that the sum of two L-R fuzzy numbers is another L-R fuzzy number with updated mean and spreads. The paper also addresses the challenges of performing operations on fuzzy numbers with negative values and provides formulas for approximating the results. The authors conclude that fuzzy algebraic calculus is a generalization of tolerance analysis and can be applied in various scientific domains where quantities are vaguely known. They note that performing operations on fuzzy numbers requires only a moderate amount of additional computation compared to using classical numbers, making it a practical approach for handling uncertainty in data. The paper also references other studies and provides a foundation for further research in fuzzy set theory and its applications.