A method to solve linear programming problem with interval type-2 fuzzy parameters

2018 ◽  
Vol 18 (1) ◽  
pp. 103-130 ◽  
Author(s):  
Pradip Kundu ◽  
Saibal Majumder ◽  
Samarjit Kar ◽  
Manoranjan Maiti
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Interval Type ◽  
Fuzzy Parameters

Fuzzy Multi-objective Linear Programming Problem using DM's Perspective

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Linear Programming ◽  
Problem Solving ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Closed Interval ◽  
Programming Approach ◽  
Multi Objective ◽  
Mathematical Programming Approach ◽  
Interval Type

In this paper, a two-stage method has been proposed for solving Fuzzy Multi-objective Linear Programming Problem (FMOLPP) with Interval Type-2 Triangular Fuzzy Numbers (IT2TFNs) as its coefficients. In the first stage of problem solving, the imprecise nature of the problem has been handled. All technological coefficients given by IT2TFNs are first converted to a closed interval and then the objectives are made crisp by reducing a closed interval into a crisp number and constraints are made crisp by using the concept of acceptability index. The amount by which a specific constraint can be relaxed is decided by the decision maker and thus the problem reduces to a crisp multi-objective linear programming problem (MOLPP). In the second stage of problem solving, the multi-objective nature of the problem is handled by using fuzzy mathematical programming approach. In order to explain the methodology, two numerical examples of the proposed methodology in Production planning and Diet planning problems have also been worked out in this paper.

scholarly journals A METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS BASED ON MULTIOBJECTIVE LINEAR PROGRAMMING TECHNIQUE

2007 ◽  
Vol 24 (04) ◽  
pp. 557-573 ◽  
Author(s):  
M. ZANGIABADI ◽  
H. R. MALEKI
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Multiobjective Linear Programming ◽  
Programming Technique ◽  
Linear Programming Problems ◽  
Linear Programming Technique ◽  
Fuzzy Parameters

In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, we propose several theorems which are used to obtain optimal solutions of linear programming problems with fuzzy parameters. Finally some examples are given for illustrating the proposed method of solving linear programming problem with fuzzy parameters.

scholarly journals Fuzzy Linear Programming: Optimization of an Electric Circuit Model

2018 ◽  
Vol 18 (3) ◽  
pp. 419
Author(s):  
Ana Maria Amarillo Bertone ◽  
Rosana Sulei da Motta Jafelice ◽  
Marcos Antônio da Câmara
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Electric Circuit ◽  
Fuzzy Linear Programming ◽  
First Case

A problem of a voltage division circuit is modeled in order to determine the values of the resistors, centered in away that the impedance of the resistance voltage divider is minimal. This problem is equivalent to maximizing the admittance, associated to the resistance, which is defined as the quotient of the electric current and its voltage, measured in Siemens. Three cases are analyzed for the components of the linear programming: real numbers, fuzzy numbers of type-1, and fuzzy set of type-2. The first case is considered in order to validate the other two cases. The optimal solution in the fuzzy linear programming of type-1 is obtained through a total linear order defuzzification function, defined in the trapezoidal fuzzy numbers subspace of fuzzy numbers vector space, which allows to solve the corresponding linear programming problem with real components. A discussion upon the parameter for the linear defuzzification is establish to determined the best representative of the parameters family. The α−levels representation theorem is the method to obtain the optimal solution of type-2. For each α−level is solved a fuzzy linear programming problem of type-1, using the previous methodology. Numerical simulations illustrate the results in the three cases.

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