Generalized exponential trapezoidal fuzzy numbers based on variance

Rezvani (Applied Mathematics and Computation, 262(2015), 191-198) derive Mellin transform for a generalized exponential trapezoidal fuzzy number A=(a,b,c,d)(E) in order to calculate the mean and variance of the probability density function. In future, other researchers may use those expressions for the mean and variance of the generalized exponential trapezoidal fuzzy number A =(a,b,c,d)(E), proposed by Rezvani, in their research work. In this note, it is shown that expression for Mellin transform M-x (t), the mean mu(A) (t) and sigma(2)(A) (t) are all not correct. It is also pointed out that the probability density function for any generalized exponential trapezoidal fuzzy number A=(a,b,c,d)(E) does not depend on w and as such cannot be used to rank generalized exponential trapezoidal fuzzy number A =(a,b,c,d)(E) as depicted in Table 1 in Rezvani [5]. Also, the correct expressions for M-x (t), the mean mu(A) (t) and sigma(2)(A) (t) are given along with some examples taken from Rezvani [5].