Dear Sir/Madam,
How we calculate the following expression:
Suppose “A” is a triangular fuzzy number and “p” is crisp exponent over it such as Ap = [l, m, u]p
Example: calculate the value of [0.1,0.2,0.3]0.25 and [0.3,0.4,0.5]-0.25
Hello there
You can change this crisp number to (0.25,0.25,0.25) as a fuzzy number and then calculate other steps:
[(0.1)^0.25,(0.2)^0.25,(0.3)^0.25]
and
[(0.3)^(-0.25),(0.2)^(-0.25),(0.1)^(-0.25)]
The triangle fuzzy number (0.1,02.0.3) can be presented in a simplified, discrete form of pairs {(x, μ(x))} as {(0.1,0),(0.15,0.5),(0.2,1), 0.25,0.5),(0.3,0)}. To calculate the power 0.25 of this number replace values of x in the above notation by (x)0.25 and you will get the powered fuzzy number:
{(0.10 power,025,0),(0.15power0.25,0.5),(0.2,power0.25,1), (0.25,power0.25,0.5),(0.3,power0.25,0)}. To better understand this make a figure of the initial number and of the result.
Greetings for you!
According to the rules of fuzzy arithmetic, the following formula is used in the exponentiation:Ap =(mA(u))2/u. You have given a triangular number, that is, the type of the membership function is given, therefore, it is necessary to record the operation in the form of a functional dependency, in my opinion.
A0.25={(10u-1)0.25/u, (3-10u)0.25/u}
u=(0.1;0.3) is a continuous carrier of a fuzzy set !!!
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