Solution of Linear and Quadratic Equations Based on Triangular Linear Diophantine Fuzzy Numbers

Abstract

This paper is introducing a new concept of triangular linear Diophantine fuzzy numbers (TLDFNs) in a generic way. We first introduce the concept of TLDFNs and then study the arithmetic operations on these numbers. We find a method for the ranking of these TLDFNs. At the end, we formulate the linear and quadratic equations of the types $A+X=B,$ $A·X+B=C$ , and $A·X^2+B·X+C=D$ where the elements $A,B,C$ , and $D$ are TLDFNs. We provide a procedure for the solution of these equations using $\left(〈\text{s},\text{t}〉,〈\text{u},\text{v}〉\right)$ -cut and also provide the examples.