Solution of Linear Diophantine Fuzzy Linear Programming Problems by Separation and Addition Method

Solution of LDF LP Problems by Separation and Addition Method

Resumen

There are many real-world applications for the widely used concepts of intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PFSs), and q-rung orthopair fuzzy sets (q-ROFSs). Unfortunately, these theories have limitations of their own regarding membership and non-membership grades. We present the novel idea of a linear Diophantine fuzzy set (LDFS) with the addition of reference parameters to get rid of these limitations. The decision maker (DM) can freely select the grades without any restrictions due to this concept, which eliminates the limitations of existing methodologies. By modifying the physical meaning of reference parameters, this structure also categorises the problem.To address triangular fully linear Diophantine fuzzy linear programming (TFLDFLP) problem, we developed a technique separation and addition approach. The main advantage of ranking functions is that the linear Diophantine variables nature was not altered to become crisp. It is divided into linear programming (LP) strategies by using arithmetic operations and ordering relations. Numerical examples are presented in detail to illustrate the suggested methodology.