A direct solution approach to fuzzy mathematical programs with fuzzy decision variables

An analysis of fully fuzzy linear programming with fuzzy decision variables through logistics network design problem

“…The following fuzzy data are used for presenting the multi-echelon RL network design problem. Moreover, shipping cost ($) for one kg of recycled material from the recycling facilities to manufacturing plants are (5, 5.5, 6), (4.5, 5, 6.5), (5,6,7) and (4, 4.5, 5), respectively. Opening/operating costs and capacities of the facilities are also given in Table 10.…”

“…Then, an evolutionary algorithm was designed to find non-dominated solutions. Baykasoglu and Gocken [5] developed a direct solution approach for solving mathematical programming problems with fuzzy decision variables based on integrating a fuzzy ranking method into a meta-heuristic algorithm which aims to rank the objective function values and determine the feasibility degrees of the constraints. Mahdavi-Amiri and Nasseri [26] introduced a new dual algorithm for direct solution of the FLP problems with the help of the duality results and primal simplex tableau.…”

“…This constraint also presents a balance equation for the disposal sites. One can calculate the amounts of recycled materials (in kilograms) transported from the recycling facilities to manufacturing plants by using the constraint (5). In this constraint, in order to obtain the total amounts of the recycled materials in each recycling facility, the quantity of recyclable products is multiplied by the weight of the products, rate of contribution of material and the recycling fraction whose values are also defined as fuzzy numbers.…”

Fuzzy variable based fuzzy non-linear programming approach for optimization of complex system reliability

“…Qin et al [24] introduced the methods of critical value reduction for type-2 fuzzy variables and their applications. Baykasoglu [25] presented a direct solution approach to fuzzy mathematical programs with fuzzy decision variables. To the best of our knowledge, no mathematical model has been presented to consider fuzzy variable for NLP problem, in which the variables are considered as fuzzy number.…”

Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

“…Kaur and Kumar [26] studied the fully fuzzy linear programming problems based on trapezoidal fuzzy numbers. Baykasoglu and Gocken [27] used the particle swarm optimization method to solve the fuzzy mathematical programs with fuzzy decision variables in which only triangular fuzzy numbers were taken into account. The main reason for considering the triangular fuzzy numbers and trapezoidal fuzzy numbers is that they can be parametrically represented and formulated.…”