Parameter formulae for fundamental operations of weakly non-interactive fuzzy numbers

Abstract

D. Dubois and H. Prade (1981) introduced the concept of weakly noninteractive fuzzy numbers whose operations are based on the extension principle corresponding to each t-norm in place of the minimum operator. Some properties of weakly noninteractive fuzzy numbers and their practical method of calculation are investigated. Three parameters indicating the mean value and the left/right spreads of the fuzzy number are considered. Various parameter formulas for arithmetic operations and power function operation of certain kinds of weakly noninteractive fuzzy numbers involving no-interactive fuzzy numbers are presented. The formulas are applicable to both cases of the L-R fuzzy number of Dubois and Prade (1978) and an improved version of the calculation method using the digital representation. An attempt is made to classify general t-norms into the three classes from the viewpoint of the parameter formulas. The results of numerical experiments are shown for the formulas and the calculation method using the digital representation.<>