scholarly journals Penalty method for fuzzy linear programming with trapezoidal numbers

2009 ◽  
Vol 19 (1) ◽  
pp. 149-156 ◽  
Author(s):  
Bogdana Stanojevic ◽  
Milan Stanojevic
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Fuzzy Number ◽  
Penalty Method ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Constraint Violation ◽  
Deterministic Problem ◽  
Multi Objective Programming ◽  
Linear Programming Problems

In this paper we shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a penalty method. We will transform the problem of maximizing a function having trapezoidal fuzzy number values under some constraints into a deterministic multi-objective programming problem by penalizing the objective function for possible constraint violation. Furthermore, the obtained deterministic problem will have only unavoidable inequalities between trapezoidal fuzzy numbers parameters as constraints.

scholarly journals Comparing different ranking functions for solving fuzzy linear programming problems with fuzzy cost coefficients

2021 ◽  
Vol 4 (2) ◽  
pp. 3-17
Author(s):  
Betsabé Pérez Garrido ◽  
Szabolcs Szilárd Sebrek ◽  
Viktoriia Semenova
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Ranking Functions ◽  
Statistical Software ◽  
Linear Programming Problems ◽  
Fuzzy Cost ◽  
The Cost ◽  
Cost Vector

In many applications of linear programming, the lack of exact information results in various problems. Nevertheless, these types of problems can be handled using fuzzy linear programming. This study aims to compare different ranking functions for solving fuzzy linear programming problems in which the coefficients of the objective function (the cost vector) are fuzzy numbers. A numerical example is introduced from the field of tourism and then solved using five ranking functions. Computations were carried out using the FuzzyLP package implemented in the statistical software R.

scholarly journals PENDEKATAN ALGORITMA GENETIKA DALAM MENYELESAIKAN PERMASALAHAN FUZZY LINEAR PROGRAMMING

2011 ◽  
Vol 5 (3) ◽  
pp. 36
Author(s):  
Siska Dewi Lestari ◽  
Subanar Subanar
Keyword(s):  
Genetic Algorithm ◽  
Linear Programming ◽  
Objective Function ◽  
Fuzzy Number ◽  
Fitness Function ◽  
Fuzzy Linear Programming ◽  
Right Hand ◽  
Fuzzy Constraint ◽  
Linear Programming Problems ◽  
Genetic Algorithm Approach

Fuzzy linear programming is one of the linear programming developments which able to accommodate uncertainty in the real world. Genetic algorithm approach in solving linear programming problems with fuzzy constraints has been introduced by Lin (2008) by providing a case which consists of two decision variables and three constraint functions. Other linear programming problem arise with the presence of some coefficients which are fuzzy in linear programming problems, such as the coefficient of the objective function, the coefficient of constraint functions, and right-hand side coefficients constraint functions. In this study, the problem studied is to explain the genetic algorithm approach to solve linear programming problems where the objective function coefficients and right-hand sides are fuzzy constraint functions.PT Dakota Furniture study case provides a linear programming formulation with a given objective function coefficients and right-hand side coefficients are fuzzy constraint functions. This study describes the use of genetic algorithm approach to solve the problem of linear programming of PT Dakota to maximize the mean income. The genetic algorithm approach is done by simulate every fuzzy number and each fuzzy numbers by distributing them on certain partition points. Then genetic algorithm is used to evaluate the value for each partition point. As a result, the Final Value represents the coefficient of fuzzy number.  Fitness function is done by calculating the value of the objective function of linear programming problems. Empirical results indicated that the genetic algorithm approach can provide a very good solution by giving some limitations on each fuzzy coefficient.Genetic algorithm approach can be extended not only to resolve the case of PT Dakota Furniture, but can also be used to solve other linear programming case with some coefficients in the objective function and constraint functions are fuzzy.Keywords : Genetic Algorithm, Fuzzy Linear Programming, Linear Programming, Two-Phase Simplex Method

NEW IMPROVED METHOD FOR SOLVING THE FUZZY LINEAR PROGRAMMING PROBLEMS WITH VARIABLES GIVEN AS FUZZY NUMBERS

2021 ◽  
Vol 10 (12) ◽  
pp. 3699-3723
Author(s):  
L. Kané ◽  
M. Konaté ◽  
L. Diabaté ◽  
M. Diakité ◽  
H. Bado
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Interval Linear Programming ◽  
Interval Numbers ◽  
Programming Technique ◽  
Solution Approach ◽  
Interval Linear ◽  
Linear Programming Problems

The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fuzzy linear programming problem with variables given as fuzzy numbers with minimum uncertainty. In this paper, the fuzzy linear programming problems with variables given as fuzzy numbers is transformed into equivalent interval linear programming problems with variables given as interval numbers. The solutions to these interval linear programming problems with variables given as interval numbers are then obtained with the help of linear programming technique. A set of six random numerical examples has been solved using the proposed approach.

scholarly journals Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 569
Author(s):  
Wu
Keyword(s):  
Linear Programming ◽  
Numerical Method ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Optimal Solutions ◽  
Membership Functions ◽  
Fuzzy Decision ◽  
Existence Of Optimal Solutions ◽  
Decision Variables ◽  
Linear Programming Problems

The numerical method for solving the fuzzy linear programming problems with fuzzydecision variables is proposed in this paper. The difficulty for solving this kind of problem is thatthe decision variables are assumed to be nonnegative fuzzy numbers instead of nonnegative realnumbers. In other words, the decision variables are assumed to be membership functions. One of thepurposes of this paper is to derive the analytic formula of error estimation regarding the approximateoptimal solution. On the other hand, the existence of optimal solutions is also studied in this paper.Finally we present two numerical examples to demonstrate the usefulness of the numerical method.

scholarly journals A Novel Approach to Solve Fully Fuzzy Linear Programming Problems with Modified Triangular Fuzzy Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2937
Author(s):  
Saeid Jafarzadeh Ghoushchi ◽  
Elnaz Osgooei ◽  
Gholamreza Haseli ◽  
Hana Tomaskova
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Fuzzy Linear Programming ◽  
Fuzzy Decision ◽  
Triangular Fuzzy Numbers ◽  
Novel Approach ◽  
Decision Variables ◽  
Linear Programming Problems ◽  
Fuzzy Solution

Recently, new methods have been recommended to solve fully fuzzy linear programming (FFLP) issues. Likewise, the present study examines a new approach to solve FFLP issues through fuzzy decision parameters and variables using triangular fuzzy numbers. The strategy, which is based on alpha-cut theory and modified triangular fuzzy numbers, is suggested to obtain the optimal fully fuzzy solution for real-world problems. In this method, the problem is considered as a fully fuzzy problem and then is solved by applying the new definition presented for the triangular fuzzy number to optimize decision variables and the objective function. Several numerical examples are solved to illustrate the above method.

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