Determining the General Inverse for Trapezoidal Fuzzy Numbers Matrix with Modification Elementary Row Operations

Until now, for trapezoidal fuzzy number (TrapFN), there have been very many algebra operations given by authors, in the algebraic operations given, specifically for several multiplication, addition, and subtraction 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 TrapFN 𝑝̃, it does not produce 𝑝̃⨂𝑝̃−1 = 𝑖, so for the Trapezoidal fuzzy Matrix’s (TrapFM) will not apply 𝑃̃⨂𝑃̃−1 = 𝐼̃, as a result various authors solve the TrapFN linear equation structure by decomposing the TrapFM in the form of a real number matrix, and some of them do not produce compatible solutions. According to that conditions, the author provides an alternative to the amplification, division and Operations on TrapFN in reverse which will produce 𝑝̃⨂𝑝̃−1 = 𝑖 . Furthermore, by modifying the elementary row operation, An algebraic alternative to TrapFN will be applied to determine the general inverse of TrapFM. At the end, an example of calculations for TrapFM of order 2x3 will be given.