An approach for solving linear programming problem with intuitionistic fuzzy objective coefficient

Nasseri, Seyed Hadi; Goli, M.; Bavandi, Salim

doi:10.1109/cfis.2018.8336644

Cited by 4 publications

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…After defining a ranking function and arithmetic operations on these numbers, they solved the intuitionistic FLP problems without converting these problems into the crisp linear programming problem. Nasseri et al [38] proposed an approach for solving FLP problems based on comparison of IFNs by the help of linear accuracy function. They define an auxiliary problem, having only triangular intuitionistic fuzzy cost coefficients, and then study the relationships between these problems leading to a solution for the primary problem.…”

Section: Introductionmentioning

confidence: 99%

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

Goli

Nasseri

2020

Fuzzy Information and Engineering

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Goli

Nasseri

2020

Fuzzy Information and Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

Kumar

2024

Int J Syst Assur Eng Manag

View full text Add to dashboard Cite

A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem

Singh

Sharma

Chakraborty

et al. 2022

Complex Intell. Syst.

View full text Add to dashboard Cite

This paper presents an optimization method to solve a multi-objective model of a bi-level linear programming problem with intuitionistic fuzzy coefficients. The idea is based on TOPSIS (technique for order preference by similarity to ideal solution) method. TOPSIS method is a multiple criteria method that identifies a satisfactory solution from a given set of alternatives based on the minimization of distance from an ideal point and maximization of distance from the nadir point simultaneously. A new model of multi-objective bi-level programming problem in an intuitionistic fuzzy environment has been considered. The problem is first reduced to a conventional multi-objective bi-level linear programming problem using accuracy function. Then the modified TOPSIS method is proposed to solve the problem at both the leader and the follower level where various linear/non-linear membership functions are used to represent the flexibility in the approach of decision-makers (DMs). The problem is solved hierarchically, i.e., first the problem at the leader level is solved and then the feasible region is extended by relaxing the decision variables controlled by the leader. The feasible region is extended to obtain a satisfactory solution for the DMs at both levels. Finally, the application of the proposed approach in the production planning of a company has been presented. An illustrative numerical example is also given to explain the methodology defined in this paper.

show abstract

An approach for solving linear programming problem with intuitionistic fuzzy objective coefficient

Cited by 4 publications

References 10 publications

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

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

An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem

Contact Info

Product

Resources

About