Analysis of the Error in the Standard Approximation Used for Multiplication of Triangular and Trapezoidal Fuzzy Numbers and the Development of a New Approximation

Workgroup for Intelligent Systems in Design and Manufacturing

Triangular and trapezoidal fuzzy numbers are commonly used in many applications. It is well known that the operators used for the non-linear operations such as multiplication, division, and inverse are approximations to the actual operators. It is also commonly assumed that the error introduced by the approximations is small and acceptable. This project has examined the error of approximation for repeated use of these operands and shown that it can be sufficiently large in simple circumstances to produce erroneous results. The computational complexity of the operations has been analyzed and shown to be sufficiently complex that a computationally simpler approximation was needed. As a consequence, the error produced by the approximation for the operations has been analyzed and new approximations developed that are accurate for a large range of problems. Error expressions have been developed for the new approximations that can be used to determine when they are producing unacceptable results.

• "Analysis of the Error in the Standard Approximation Used for Multiplication of Triangular and Trapezoidal Fuzzy Numbers and the Development of a New Approximation," with R. E. Giachetti, Fuzzy Sets and Systems, vol. 91, no. 1, Oct. 1997, pp. 1-13.

• "A Parametric Representation of Fuzzy Numbers and Their Arithmetic Operators," with R. E. Giachetti, Fuzzy Sets and Systems, vol., 91, no. 2, Oct. 1997, pp. 185-202.
  

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