FUZZY SETS, FUZZY ARITHMETIC AND DEFUZZIFICATION - Modelling Uncertainty in Flood Forecasting Systems - page 144

(I.14)

Division

Let Then

(I.15)

(I.16)

Multiplication of a fuzzy number by a crisp number
The multiplication between fuzzy-fuzzy numbers (Eqs. (I.13) and (I.14)) can be extended

to the multiplication between a crisp number and a fuzzy number. Let in
is a crisp number whose value is x * , that is = X = x * . Which means that

(I.17)

This then follows in Equations (I.13) and (I.14) that

(I.18)

Substituting Equation (I.18) into Equations (I.13) and (I.14) we obtain

(I.19)

(I.20)