Some Properties of Generalized Triangular Fuzzy Numbers and Generalized Trapezoidal Fuzzy Numbers in Terms of Cut Sets

In this paper, we give several properties of the generalized triangular fuzzy numbers and the generalized trapezoidal fuzzy numbers in terms of the cut sets. First, we present a characterization of all cut sets of a fuzzy set in R when this fuzzy set in R is a given generalized trapezoidal fuzzy number. Then we show that two generalized trapezoidal fuzzy numbers are equal if and only if there exist two distinct elements λ and τ of [0,1] such that the λ-cuts of these two generalized trapezoidal fuzzy numbers are equal and the τ-cuts of these two generalized trapezoidal fuzzy numbers are equal. As corollaries, we give corresponding conclusions of the above conclusions for the triangular fuzzy numbers, the trapezoidal fuzzy numbers, and the generalized triangular fuzzy numbers, respectively.