An Investigation of Linear Diophantine Fuzzy Nonlinear Fractional Programming Problems

The linear Diophantine fuzzy set notion is the main foundation of the interactive method of tackling nonlinear fractional programming problems that is presented in this research. When the decision maker (DM) defines the degree a of a level sets, the max-min problem is solved in this interactive technique using Zimmermann's min operator method. By using the updating technique of degree a, we can solve DM from the set of a-cut optimal solutions based on the membership function and non-membership function. Fuzzy numbers based on a-cut analysis bestowing the degree a given by DM can first be used to classify fuzzy Diophantine inside the coefficients. After this, a crisp multi-objective non-linear fractional programming problem (MONLFPP) is created from a Diophantine fuzzy nonlinear programming problem (DFNLFPP). Additionally, the MONLFPP can be reduced to a single-objective nonlinear programming problem (NLPP) using the idea of fuzzy mathematical programming, which can then be solved using any suitable NLPP algorithm. The suggested approach is demonstrated using a numerical example.