On Solutions of Fully Fuzzy Linear Fractional Programming Problems Using Close Interval Approximation for Normalized Heptagonal Fuzzy Numbers

2021 ◽  
Vol 15 (4) ◽  
pp. 471-477
Keyword(s):  
Fractional Programming ◽  
Fuzzy Numbers ◽  
Linear Fractional Programming ◽  
Close Interval ◽  
Interval Approximation ◽  
Fuzzy Linear Fractional Programming

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 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.

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.

Solving Discounting Problem Using Piece-Wise Quadratic Fuzzy Numbers

2021 ◽  
Vol 10 (4) ◽  
pp. 1-13
Author(s):  
Hemiden Abd El-Wahed Khalifa ◽  
Pavan Kumar
Keyword(s):  
Portfolio Selection ◽  
Fuzzy Numbers ◽  
Interval Number ◽  
Fuzzy Arithmetic ◽  
Investment Portfolio ◽  
Numerical Example ◽  
Research Article ◽  
Close Interval ◽  
Interval Approximation

The discounting problem is one of the important aspects in investment, portfolio selection, purchasing with credit, and many other financial operations. In this paper, a discounting problem using piecewise quadratic fuzzy numbers is proposed. The implementation of piecewise quadratic fuzzy numbers is described based on such operations. Fuzzy arithmetic and interval number arithmetic are used for computation. The close interval approximation of piecewise quadratic fuzzy numbers is used for solving the proposed discounting problem. This research article addresses the discounted investment for Year 1, Year 2, and Year 3. Additionally, the authors determine the cumulative discounted investment for different values of the parameter α ranging from 0 to 1. A discounting problem using piecewise quadratic fuzzy numbers is solved as a numerical example to illustrate the proposed procedure.

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.

Sign in / Sign up

Export Citation Format

Share Document