Ranking nonnormal p-norm trapezoidal fuzzy numbers with integral value

This paper considers the ranking fuzzy numbers with integral value, proposed by Liou and Wang, for the nonnormal pp-norm trapezoidal fuzzy numbers. Two interesting special cases of pp-norm trapezoidal fuzzy numbers are the well-known triangular and trapezoidal fuzzy numbers. For the nonnormal fuzzy numbers, the differences exist among the membership functions for the triangular, trapezoidal and pp-norm trapezoidal fuzzy numbers. These differences can affect their left, right and total integral values, so we establish the relationship between these three types of fuzzy numbers.