Solution of linear and quadratic equations based on triangular linear Diophantine fuzzy numbers (Q823646)

Summary: 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 \(A+X=B\), \(A\cdot X+B=C\), and \(A\cdot X^2+B\cdot X+C=D\) where the elements \(A\), \(B\), \(C\), and \(D\) are TLDFNs. We provide a procedure for the solution of these equations using \((\langle\mathrm{s}, \mathrm{t}\rangle, \langle\mathrm{u}, \mathrm{v}\rangle)\)-cut and also provide the examples.