Extension of Duality Results and a Dual Simplex Method for Linear Programming Problems With Intuitionistic Fuzzy Variables

Abstract

The aim of this paper is to introduce a formulation of linear programming problems involving intuitionistic fuzzy variables. Here, we will focus on duality and a simplex-based algorithm for these problems. We classify these problems into two main different categories: linear programming with intuitionistic fuzzy numbers problems and linear programming with intuitionistic fuzzy variables problems. The linear programming with intuitionistic fuzzy numbers problem had been solved in the previous literature, based on this fact we offer a procedure for solving the linear programming with intuitionistic fuzzy variables problems. In methods based on the simplex algorithm, it is not easy to obtain a primal basic feasible solution to the minimization linear programming with intuitionistic fuzzy variables problem with equality constraints and nonnegative variables. Therefore, we propose a dual simplex algorithm to solve these problems. Some fundamental concepts and theoretical results such as basic solution, optimality condition and etc., for linear programming with intuitionistic fuzzy variables problems, are established so far. Moreover, the weak and strong duality theorems for linear programming with intuitionistic fuzzy variables problems are proved. In the end, the computational procedure of the suggested approach is shown by numerical examples.

Fuzzy linear programming with the intuitionistic polygonal fuzzy numbers

“…We call this problem the ranked linear programming (RLP) problem. It is clear that the values of the variables in the optimal solution of problem (18) equal the ranking values of the fuzzy variables in the optimal solution of problem (9). Moreover, the steps of solving the original problem are equivalent to the steps of solving the corresponding RLP problem in number and order, which means that the fuzzy simplex method proposed in this paper terminates in a finite number of iterations.…”

“…On the other hand, a single step algorithm that directly solves the problem without converting it to crisp was also suggested by Nagoorgani and Ponnalagu [17]. Discussion of duality of the IFLP problem can also be found in [14], and a dual simplex method was proposed by Goli and Nasseri [18]. A fully fuzzy IFLP with unconstrained LR-type of intuitionistic fuzzy numbers was introduced by Singh and Yadav [19].…”

Solving Goal Programming by Alternative Simplex Method

“…An Easy Simplex (AHA Simplex) algorithm was studied by Ansari [1] in 2019. Extensions of Duality Results and a Dual Simplex Method for Linear Programming Problems have been recommended by Goli and Nasseri [5] in 2020.…”