Abstract
Many authors have given the arithmetic form of triangular fuzzy numbers, especially for addition and subtraction; however, there is not much difference. The differences occur for multiplication, division, and inverse operations. Several authors define the inverse form of triangular fuzzy numbers in parametric form. However, it always does not obtain <img src=image/13429431_01.gif>, because we cannot uniquely determine the inverse that obtains the unique identity. We will not be able to directly determine the inverse of any matrix in the form of a triangular fuzzy number. Thus, all problems using the matrix <img src=image/13429431_02.gif> in the form of a triangular fuzzy number cannot be solved directly by determining <img src=image/13429431_03.gif>. In addition, there are various authors who, with various methods, try to determine <img src=image/13429431_03.gif> but still do not produce <img src=image/13429431_04.gif>. Consequently, the solution of a fully fuzzy linear system will produce an incompatible solution, which results in different authors obtaining different solutions for the same fully fuzzy linear system. This paper will promote an alternative method to determine the inverse of a fuzzy triangular number in parametric form. It begins with the construction of a midpoint <img src=image/13429431_05.gif> for any triangular fuzzy number <img src=image/13429431_06.gif>, or in parametric form <img src=image/13429431_07.gif>. Then the multiplication form will be constructed obtaining a unique inverse which produces <img src=image/13429431_08.gif>. The multiplication, division, and inverse forms will be proven to satisfy various algebraic properties. Therefore, if a triangular fuzzy number is used, and also a triangular fuzzy number matrix is used, it can be easily directly applied to produce a unique inverse. At the end of this paper, we will give an example of calculating the inverse of a parametric triangular fuzzy number for various cases. It is expected that the reader can easily develop it in the case of a fuzzy matrix in the form of a triangular fuzzy number.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
