ANALYSIS OF THE ERROR IN THE STANDARD APPROXIMATION USED FOR MULTIPLICATION OF TRIANGULAR AND TRAPEZOIDAL FUZZY NUMBERS AND THE DEVELOPMENTOF A NEW APPROXIMATION

Triangular and trapezoidal fuzzy numbers are commonly used in many app lications. It is well known that the operators used for the non-linear operations such as multiplication, division, and inverse are approxim ations to the actual operators. It is also commonly assumed that the e rror introduced by the approximations is small and acceptable. This pa per examines the error of approximation for repeated use of the multip lication operand and shows it can be sufficiently large in simple circ umstances to produce erroneous results. The computational complexity o f the multiplication operation is analyzed and shown to be sufficientl y complex that a computationally simpler approximation is needed. As a consequence, the error produced by the approximation for the multipli cation operation is analyzed and a new approximation developed that is accurate for a large range of problems. An error expression is develo ped for the new approximation that can be used to determine when it is producing unacceptable results. (C) 1997 Elsevier Science B.V.