Determining the General Inverse for Trapezoidal Fuzzy Numbers Matrix with Modification Elementary Row Operations
Mashadi, Weni Gustiana, Sri Gemawati

University of Riau

Abstract

Abstract. Until now, for trapezoidal fuzzy numbers, there have been very many algebra operations given by various authors, in the algebraic operations given, specifically for addition, subtraction, and scalar multiplication operations there is not much difference given by the various authors. However, for multiplication, division, or inverse operations, there are many differences. Not only that for any trapezoidal fuzzy number \widetilde{u}, but it also does not produce \widetilde{u}\bigotimes{\widetilde{u}}^{-1}=\widetilde{i}, so the trapezoidal fuzzy number matrix will not apply \widetilde{U}\bigotimes{\widetilde{U}}^{-1}=\widetilde{I}, as a result, various authors solve the trapezoidal fuzzy number linear equation system by decomposing the trapezoidal fuzzy number matrix in the form of a real number matrix, and some of them do not produce compatible solutions. Based on these conditions, the author provides an alternative to the multiplication, division, and inverse operations of trapezoidal fuzzy numbers which will produce \widetilde{u}\bigotimes{\widetilde{u}}^{-1}=\widetilde{i}. Furthermore, by modifying the elementary row operation, our alternative trapezoidal fuzzy number algebra operation will be applied to determine the general inverse of any trapezoidal fuzzy number matrix. Finally, an example will be given for a 2x3 trapezoidal fuzzy number matrix.

Keywords: Trapezoidal fuzzy numbers, Modification of elementary row operations, General inverse

Topic: Mathematics and Its Applications