scholarly journals Application of linear fractional programming problem with fuzzy nature in industry sector

Filomat ◽  
2020 ◽  
Vol 34 (15) ◽  
pp. 5073-5084
Author(s):  
Sapan Das ◽  
S.A. Edalatpanah ◽  
T. Mandal
Keyword(s):  
Fractional Programming ◽  
Simple Structure ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Linear Fractional Programming ◽  
Fuzzy Variables ◽  
Life Problems ◽  
Fuzzy Optimal Solution ◽  
Fuzzy Linear Fractional Programming

Several methods currently exist for solving fuzzy linear fractional programming problems under non negative fuzzy variables. However, due to the limitation of these methods, they cannot be applied for solving fully fuzzy linear fractional programming (FFLFP) problems where all the variables and parameters are fuzzy numbers. So, this paper is planning to fill in this gap and in order to obtain the fuzzy optimal solution we propose a new efficient method for FFLFP problems utilized in daily life circumstances. This proposed method is based on crisp linear fractional programming and has a simple structure. To show the efficiency of our proposed method some numerical and real life problems have been illustrated.

Fuzzy Numbers and Fractional Programming in Making Decisions

2020 ◽  
Vol 19 (04) ◽  
pp. 1123-1147
Author(s):  
Bogdana Stanojević ◽  
Simona Dzitac ◽  
Ioan Dzitac
Keyword(s):  
Fractional Programming ◽  
Fuzzy Numbers ◽  
Electrical Power ◽  
Real Life ◽  
Mathematical Optimization ◽  
Programming Models ◽  
Multi Criteria Decision Making ◽  
Wide Sense ◽  
Linear Fractional Programming ◽  
Life Problems

This study surveys the use of fuzzy numbers in classic optimization models, and its effects on making decisions. In a wide sense, mathematical programming is a collection of tools used in mathematical optimization to make good decisions. There are many sectors of economy that employ it. Finance and government, logistics and manufacturing, the distribution of the electrical power are worth to be first mentioned. When real life problems are modeled mathematically, there is always a trade-off between model’s accuracy and complexity. By this survey, we aim to present in a concise form some mathematical models from the literature together with the methods to solve them. We will focus mainly on fuzzy fractional programming problems. We will also refer to but not describe in detail the multi-criteria decision-making problems involving fuzzy numbers and linear fractional programming models.

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.

Methods for Solving Fully Fuzzy Transportation Problems Based on Classical Transportation Methods

2013 ◽  
pp. 328-347 ◽  
Author(s):  
Amit Kumar ◽  
Amarpreet Kaur
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Programming Formulation ◽  
Transportation Problems ◽  
Fuzzy Optimal Solution ◽  
Linear Programming Formulation ◽  
Fuzzy Transportation Problem

There are several methods, in literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, two new methods (based on fuzzy linear programming formulation and classical transportation methods) are proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as trapezoidal fuzzy numbers. The advantages of the proposed methods over existing methods are also discussed. To illustrate the proposed methods a fuzzy transportation problem (FTP) is solved by using the proposed methods and the obtained results are discussed. The proposed methods are easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

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 Fuzzy Hungarian Approach for Transportation Model

2013 ◽  
pp. 189-192
Author(s):  
Arun Patil ◽  
S. B. Chandgude
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Transportation Model ◽  
Trapezoidal Fuzzy Numbers ◽  
Fuzzy Optimal Solution ◽  
Transportation Models ◽  
Fuzzy Transportation Problem ◽  
The Cost

In this paper, a method is proposed to find the fuzzy optimal solution of fuzzy transportation model by representing all the parameters as trapezoidal fuzzy numbers. To illustrate the proposed method a fuzzy transportation problem is solved by using the proposed method and the results are obtained. The proposed method is easy to understand, and to apply for finding the fuzzy optimal solution of fuzzy transportation models in real life situations. However, we propose the method of fuzzy modified distribution for finding out the optimal solution for minimizing the cost of total fuzzy transportation. The advantages of the proposed method are also discussed.

scholarly journals Fuzzy solution of fully fuzzy multi-objective linear fractional programming problems

2021 ◽  
pp. 817-825
Author(s):  
Ganesan Kandasamy ◽  
T. Loganathan
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Optimal Solution ◽  
Linear Fractional Programming ◽  
Multi Objective ◽  
Fractional Programming Problem ◽  
Fuzzy Optimal Solution ◽  
Optimal Value ◽  
Novel Method ◽  
Linear Fractional Programming Problem

In this study, we present a novel method for solving fully fuzzy multi-objective linear fractional programming problems without transforming to equivalent crisp problems. First, we calculate the fuzzy optimal value for each fractional objective function and then we convert the fully fuzzy multi-objective linear fractional programming problem to a single objective fuzzy linear fractional programming problem and find its fuzzy optimal solution which inturn yields a fuzzy Pareto optimal solution for the given fully fuzzy multi-objective linear fractional programming problem. To demonstrate the proposed strategy, a numerical example is provided.

A Study of Fully Fuzzy Linear Fractional Programming Problems by Signed Distance Ranking Technique

2018 ◽  
pp. 73-115 ◽  
Author(s):  
Moumita Deb
Keyword(s):  
Linear Programming ◽  
Fractional Programming ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Linear Fractional Programming ◽  
Signed Distance ◽  
Decision Variables ◽  
Ranking Technique ◽  
Crisp Linear Programming ◽  
Fuzzy Linear Fractional Programming

The aim of this chapter is to study fully fuzzy linear fractional programming (FFLFP) problems where all coefficients of the decision variables and parameters are characterized by triangular fuzzy numbers. To deal with this, the authors have first to transform FFLFP problems to fuzzy linear programming (FLP) problems by using Charnes and Cooper method and then use signed distance ranking to convert fuzzy linear programming (FLP) problems to crisp linear programming (LP) problems. The proposed method is solved by using the simplex method to find the optimal solution of the problem. The authors have studied sensitivity analysis to determine changes in the optimal solution of the fully fuzzy linear fractional programming (FFLFP) problems resulting from changes in the parameters. To demonstrate the proposed method, one numerical example is solved.

Methods for Solving Fully Fuzzy Transportation Problems Based on Classical Transportation Methods

2011 ◽  
Vol 2 (4) ◽  
pp. 52-71 ◽  
Author(s):  
Amit Kumar ◽  
Amarpreet Kaur
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Transportation Problems ◽  
New Methods ◽  
Fuzzy Optimal Solution ◽  
Linear Programming Formulation ◽  
Fuzzy Transportation Problem

There are several methods, in literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, two new methods (based on fuzzy linear programming formulation and classical transportation methods) are proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as trapezoidal fuzzy numbers. The advantages of the proposed methods over existing methods are also discussed. To illustrate the proposed methods a fuzzy transportation problem (FTP) is solved by using the proposed methods and the obtained results are discussed. The proposed methods are easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

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