scholarly journals Ranking Function Application for Optimal Solution of Fractional programming problem

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Rasha Jalal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Ranking Function ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Linear Programming Problems

The aim of this paper is to suggest a solution procedure to fractional programming problem based on new ranking function (RF) with triangular fuzzy number (TFN) based on alpha cuts sets of fuzzy numbers. In the present procedure the linear fractional programming (LFP) problems is converted into linear programming problems. We concentrate on linear programming problem problems in which the coefficients of objective function are fuzzy numbers, the right- hand side are fuzzy numbers too, then solving these linear programming problems by using a new ranking function. The obtained linear programming problem can be solved using win QSB program (simplex method) which yields an optimal solution of the linear fractional programming problem. Illustrated examples and comparisons with previous approaches are included to evince the feasibility of the proposed approach.

scholarly journals A new Mean Deviation and Advanced Mean Deviation Techniques to Solve Multi-Objective Fractional Programming Problem Via Point-Slopes Formula

2021 ◽  
pp. 1051-1064
Author(s):  
Rebaz Mustafa ◽  
Nejmaddin A. Sulaiman
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Optimal Solution ◽  
Mean Deviation ◽  
New Techniques ◽  
Multi Objective ◽  
Fractional Programming Problem ◽  
A New Technique

In this paper, we have proposed a new technique to find an efficient solution to fractional programming problems (FPP). The multi-objective fractional programming problem (MOFPP) is converted into multi-objective linear programming (MOLPP) utilizing the point-slopes formula for a plane, which has equivalent weights to the MOFPP. The MOLPP is diminished to a single objective linear programming problem (SOLPP) through using two new techniques for the values of the objective function and suggesting an algorithm for its solution. Finally, we obtained the optimal solution for MOFPP by solving the consequent linear programming problem (LPP). The proposed practicability is confirmed with the existing approaches, with some numerical examples and we indicated comparison with other techniques. 

scholarly journals Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Aihong Ren
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Function Method ◽  
Optimal Solution ◽  
Ranking Function ◽  
Objective Functions ◽  
Bilevel Linear Programming ◽  
Fuzzy Optimal Solution ◽  
Deviation Degree

This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.

scholarly journals ON THE RATIO OF FUZZY NUMBERS – EXACT MEMBERSHIP FUNCTION COMPUTATION AND APPLICATIONS TO DECISION MAKING

2015 ◽  
Vol 21 (5) ◽  
pp. 815-832 ◽  
Author(s):  
Bogdana STANOJEVIĆ ◽  
Ioan DZIŢAC ◽  
Simona DZIŢAC
Keyword(s):  
Decision Making ◽  
Programming Problem ◽  
Membership Function ◽  
Fractional Programming ◽  
Fuzzy Numbers ◽  
Linear Constraints ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Fuzzy Linear Fractional Programming ◽  
Linear Fractional Programming Problem

In the present paper, we propose a new approach to solving the full fuzzy linear fractional programming problem. By this approach, we provide a tool for making good decisions in certain problems in which the goals may be modelled by linear fractional functions under linear constraints; and when only vague data are available. In order to evaluate the membership function of the fractional objective, we use the α-cut interval of a special class of fuzzy numbers, namely the fuzzy numbers obtained as sums of products of triangular fuzzy numbers with positive support. We derive the α-cut interval of the ratio of such fuzzy numbers, compute the exact membership function of the ratio, and introduce a way to evaluate the error that arises when the result is approximated by a triangular fuzzy number. We analyse the effect of this approximation on solving a full fuzzy linear fractional programming problem. We illustrate our approach by solving a special example – a decision-making problem in production planning.

scholarly journals Solving Linear Programming Problems with Grey Data

2018 ◽  
Vol 3 (1) ◽  
pp. 17-23 ◽  
Author(s):  
Michael Gr. Voskoglou
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Standard Method ◽  
Linear Programming Problem ◽  
Real Life ◽  
Optimal Solution ◽  
Real Numbers ◽  
Decision Variables ◽  
Linear Programming Problems

A Grey Linear Programming problem differs from an ordinary one to the fact that the coefficients of its objective function and / or the technological coefficients and constants of its constraints are grey instead of real numbers. In this work a new method is developed for solving such kind of problems by the whitenization of the grey numbers involved and the solution of the obtained in this way ordinary Linear Programming problem with a standard method. The values of the decision variables in the optimal solution may then be converted to grey numbers to facilitate a vague expression of it, but this must be strictly checked to avoid non creditable such expressions. Examples are also presented to illustrate the applicability of our method in real life applications.

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.

MULTI-OBJECTIVE FULLY FUZZIFIED LINEAR PROGAMMING

2001 ◽  
Vol 09 (05) ◽  
pp. 605-621 ◽  
Author(s):  
JAMES J. BUCKLEY ◽  
THOMAS FEURING ◽  
YOICHI HAYASHI
Keyword(s):  
Linear Programming ◽  
Evolutionary Algorithm ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Solution Procedure ◽  
Fuzzy Linear Programming ◽  
Multi Objective ◽  
Linear Programming Problems ◽  
Single Objective

In this paper we wish to solve multi-objective fully fuzzified linear programming problems which are multi-objective linear programming problems where all the parameters and variables are fuzzy numbers. We change this problem into a single objective fuzzy linear programming problem and then show that our solution procedure can be used to explore the whole undominated set. An evolutionary algorithm is then designed to generate undominated solutions. An example is presented showing our evolutionary algorithm solution.

scholarly journals An Equivalent Linear Programming Form of General Linear Fractional Programming: A Duality Approach

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1586
Author(s):  
Mehdi Toloo
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Functional Programming ◽  
General Linear ◽  
Data Envelopment ◽  
Linear Fractional Programming ◽  
Duality Approach ◽  
Fractional Functional

Linear fractional programming has been an important planning tool for the past four decades. The main contribution of this study is to show, under some assumptions, for a linear programming problem, that there are two different dual problems (one linear programming and one linear fractional functional programming) that are equivalent. In other words, we formulate a linear programming problem that is equivalent to the general linear fractional functional programming problem. These equivalent models have some interesting properties which help us to prove the related duality theorems in an easy manner. A traditional data envelopment analysis (DEA) model is taken, as an instance, to illustrate the applicability of the proposed approach.

scholarly journals Solution of Fully Bipolar Fuzzy Linear Programming Models

2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Muhammad Athar Mehmood ◽  
Muhammad Akram ◽  
Majed G. Alharbi ◽  
Shahida Bashir
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Equality Constraints ◽  
Fuzzy Linear Programming ◽  
Mathematical Tool ◽  
Decision Variables ◽  
Crisp Linear Programming

The Yin-Yang bipolar fuzzy set is a powerful mathematical tool for depicting fuzziness and vagueness. We first extend the concept of crisp linear programming problem in a bipolar fuzzy environment based on bipolar fuzzy numbers. We first define arithmetic operations of unrestricted bipolar fuzzy numbers and multiplication of an unrestricted trapezoidal bipolar fuzzy number (TrBFN) with non-negative TrBFN. We then propose a method for solving fully bipolar fuzzy linear programming problems (FBFLPPs) with equality constraints in which the coefficients are unrestricted triangular bipolar fuzzy numbers and decision variables are nonnegative triangular bipolar fuzzy numbers. Furthermore, we present a method for solving FBFLPPs with equality constraints in which the coefficients and decision variables are unrestricted TrBFNs. The FBFLPP is transformed into a crisp linear programming problem, and then, it is solved to achieve the exact bipolar fuzzy optimal solution. We illustrate the proposed methodologies with several numerical examples.

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