multi-objective linear programming problem

Considering multiple criteria and objectives simultaneously in a single real-world problem and the fuzzy nature of this type of problem is of particular importance and application. As a result,  multi-objective interval type-2 fuzzy linear programming problems have received much attention. However,  there are few and a limited number of methods available for solving multi-objective interval type-2 triangular fuzzy linear programming problems with ambiguity-type imprecision (interval type-2 triangular fuzzy numbers) in almost all of the problem parameters. This research first considers a multi-objective interval type-2 fuzzy linear programming problem with ambiguity in all coefficients,  in which,  all problem coefficients are interval triangular fuzzy numbers. In addition,  using the weighted sum method and the concept of nearest interval approximation,  the problem is solved,  and an example is provided.

In this article, we construct a new computational algorithm for solving multiobjective linear programming problem in  intuitionistic fuzzy environment. The resources and technological coefficients are taken to be intuitionistic fuzzy numbers. Here, the intuitionistic fuzzy multi-objective linear programming problem is transformed into an equivalent crisp multi-objective linear programming problem. By using fuzzy mathematical programming approach, the transformed multiobjective linear programming problem is reduced into a single objective nonlinear and non-convex programming problem. Stepwise algorithm is given for solving an intuitionistic fuzzy multiobjective linear programming problem and it is checked with a numerical example using intuitionistic fuzzy decisive set method.

In this paper fully fuzzy linear programming (FFLP) problem with both equality and inequality constraints is considered where all the parameters and decision variables are represented by non-negative trapezoidal fuzzy numbers. According to the current approach, the FFLP problem with equality constraints first is converted into a multi–objective linear programming (MOLP) problem with crisp constraints and then a lexicographic ordering method is used for solving the resulting MOLP problem. However, this approach cannot be used for finding the fuzzy optimal solution of FFLP problems with inequality constraints. The aim of this study is to point out and correct some errors in the definitions, notations operations and fuzzy ordering of the current approach for solving FFLP problems with fuzzy inequality constraints. Hence, a modified approach to obtain the fuzzy optimal solution of the FFLP problems with inequality constraints is proposed. Finally, several numerical examples are presented to illustrate the proposed approach.