Optimal fuzzy solution for fully fuzzy quadratic fractional programming problems with decagonal membership function and ranking function technique

The fuzziness approach is useful when finding a solution to a programming problem with some element of uncertainty. Using standard programming techniques, an optimal value for coefficients may be difficult to compute. The quality of fuzziness makes the programming method especially useful in situations where the coefficients are fuzzy-shaped representations of real-world occurrences and cannot be determined accurately. There have been many attempts in recent years to solve the problem of fractional programming. But not be bounded that many papers or studies have been written about the fuzzy quadratic fractional programming problem. This paper first introduces a development method for solving quadratic fractional programming (QFP) problems depending on separating the quadratic objective function. Secondly, to solve a fully fuzzy quadratic fractional programming (FFQFP) problem in which all the variables and parameters of the problem are decagonal fuzzy numbers, we proposed a new nonlinear membership function of decagonal fuzzy numbers with a new ranking function technique to obtain the optimal fuzzy solution to the (FFQFP) problem as well as, development of the algorithm simplex method, in which the new data of tableau are made available with both to help of the new ranking function and the arithmetic’s decagonal operations to find the optimal decagonal fuzzy solution. Finally, the applied part of this paper includes an example that shows the steps to finding a fuzzy optimal solution to the presented problem.