We suggest the use of piecewise monotonic interpolations to approximate and represent a fuzzy number (or interval) and to derive a procedure to control the absolute error associated to the arithmetic operations (+,-,⋅,:) between fuzzy numbers, in order to reduce the distance between the true result of the operation and its approximation. The monotonic functions are then used to define a parametric representation of a large class of fuzzy numbers having general shapes of the membership function and a simple and accurate procedure is introduced for the fuzzy arithmetic. Several computational experiments are given to show the good performance of the proposed procedure.
Approximate Fuzzy Arithmetic Operations Using Monotonic Interpolations / M.L.Guerra; L.Stefanini. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - STAMPA. - 150/1:(2005), pp. 5-33.
Approximate Fuzzy Arithmetic Operations Using Monotonic Interpolations
GUERRA, MARIA LETIZIA;
2005
Abstract
We suggest the use of piecewise monotonic interpolations to approximate and represent a fuzzy number (or interval) and to derive a procedure to control the absolute error associated to the arithmetic operations (+,-,⋅,:) between fuzzy numbers, in order to reduce the distance between the true result of the operation and its approximation. The monotonic functions are then used to define a parametric representation of a large class of fuzzy numbers having general shapes of the membership function and a simple and accurate procedure is introduced for the fuzzy arithmetic. Several computational experiments are given to show the good performance of the proposed procedure.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
