Abstract:
This article discusses the alternative diagonalization process on the triangular fuzzy
number matrix of size n×n in parametric form. Many forms of arithmetic operations
have been given by the author, especially triangular fuzzy numbers. For addition,
subtraction and scalar multiplication operations there is not much difference while
for multiplication, division and inverse there are many ways. However, the algebraic
operations offered have some drawbacks for example, for any triangular fuzzy number
˜p = (p, α, β), does not necessarily apply ˜p(r) ⊗
1
˜p(r)
= ˜i(r) . In this article, an
alternative arithmetic operation will be used for the multiplication, division and
inverse operations of triangular fuzzy numbers by using the midpoint concept. This
midpoint concept is then used to determine the eigenvalues and eigenvectors as well
as the inverse matrix of triangular fuzzy numbers. Meanwhile, to determine the
cofactor of the triangular fuzzy number matrix using ˜ Cij(r) = [−1,−1]i+j ⊗ ˜Mij(r).