Signomial Geometric Programming Approach to Solve Non-Linear Fractional Programming Problems

Nonlinear fuzzy fractional signomial programming problem: A fuzzy geometric programming solution approach

“…On varying 𝛼 ∈ [0, 1] due to proposed Method-2, the optimal range(lower and upper bounds) of the objective value is obtained as [−0.3717035, −0.2433155] in Tables 3 and 4. The following Figure 3 represents that the optimal objective value of the crisp NLFSPP obtained by Mishra and Ota [18] lies in the range of optimal objective values of fuzzy NLFFSPP obtained due to the proposed methods. In example 2, considering NLFFSPP as a crisp model the optimal solution is obtained as 𝑦 1 =0.5852915, 𝑦 2 =0.6997048, 𝑦 3 =0.5540157 and the corresponding optimal objective value is 𝑓 (𝑦) = −0.7102850.…”

“…In example 1, considering the crisp model of NLFFSPP in the numerical example, Mishra and Ota [18] obtained the optimal solution as 𝑦 1 =0.6461028, 𝑦 2 =0.7694510 and the corresponding optimal objective value is 𝑓 (𝑦) = −0.2433155. As this problem is a fuzzy optimization, using the proposed two solution approaches (Method-1 and Method-2) a set of solutions are obtained in Tables 1-4 for 𝑠 ∈ [0, 1] and 𝛼 ∈ [0, 1] respectively.…”

“…The crisp form of the following NLFFSPP was initially solved by Mishra and Ota [18] which is considered here in triangular fuzzy environment. min :…”

“…Jafarian et al [14] proposed a method to solve multi-objective nonlinear geometric programming problems by integrating the concept of intuitionistic fuzzy. Mishra and Ota [18] provided a novel way of addressing non-linear fractional programming problems based on the variable transformation method and signomial geometric programming technique. Maiti et al [17] suggested a way to solve multi-objective linear fractional programming problems with fuzzy coefficients and fuzzy variables using Taylor series approximation and a normalisation methodology.…”