Soft Computing and Its Applications, Volume One

Fuzzy Sets, Fuzzy Operators, and Fuzzy Relations 79

Now, expressing in terms of x and setting = 0 and in (2.61) we get

together with the domain of x,

, and

, which give,

=

.

EXPONENTIAL OF A FUZZY NUMBER

Let X= [a, b, c] >0 be a fuzzy number. Then is

the -cut of fuzzy numbers x. To calculate exponential of fuzzy number x we first take

the exponential of the -cut of X using interval arithmetic.

exp ( ) = exp ([b-a) + a,c – (c-b) ]) =

[ exp ((b – a) + a), exp (c-(c-b) ] (2.62)

To nd the membership function we equate to x both the rst and sec-

ond component in (2.62) which gives

x = exp ((b-a) +a) and

x = exp (c-(c-b) ...