ALTERNATIF PROSES DIAGONALISASI MATRIKS BILANGAN FUZZY TRIANGULAR

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).