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Mathematical Model of Fuzzy Linear Programming

# Journal of Applied & Computational Mathematics

ISSN: 2168-9679

Open Access

Editorial - (2022) Volume 11, Issue 1

# Mathematical Model of Fuzzy Linear Programming

Eman Khorsheed*
*Correspondence: Eman Khorsheed, Department of Mathematics, College of Science, Bahrain, Email:
Department of Mathematics, College of Science, Bahrain

Received: 02-Jan-2022, Manuscript No. jacm-22-52790; Editor assigned: 04-Jan-2022, Pre QC No. P-52790; Reviewed: 16-Feb-2022, QC No. Q-52790; Revised: 21-Jan-2022, Manuscript No. R-52790; Published: 28-Jan-2022 , DOI: 10.37421/jacm.2022.11.451
Citation: Khorsheed, Eman. "Mathematical Model of Fuzzy Linear Programming."J Appl Computat Math 11 (2022): 451.
Copyright: © 2022 Khorsheed E. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

#### Editorial

Establishing a mathematical model of linear programming is to start from actual problems, grasp the main factors, determine the decision variables, find out the constraints, and establish a fuzzy linear programming model. Although many fuzzy linear programming models for economic problems have different characteristics, they all have the following three basic characteristics. Firstly, every seam economy problem uses a set of unknown variables (x1, x2, …, xn) to represent a certain planning plan, and a set of fixed values of this set of unknown variables represents a specific plan. Moreover, the variables in these economic problems often have non-negative requirements.

What is more, the research and resolution of these economic problems must meet certain conditions. For the fuzzy linear programming model problem, the selected conditions, namely the constraints, can be written in the form of linear equations and linear inequalities. Finally, there are often many different options for solving these economic problems, which means that there may be many options that meet the constraints. We ask them to choose an optimal solution from them. There is a question of measurement standards, that is, according to which quantitative standards to evaluate a plan is the best, we call this quantitative standard the objective function. The objective function is determined according to the nature and requirements of economic problems. According to different research questions, the objective function is often required to take the maximum or minimum value. The objective function and constraints of each problem are linear.

In the process of agricultural economic management, it has many advantages such as dynamic tracking, freedom from linear constraints, and easy adjustment of parameters. However, it is necessary to formulate a series of socio-economic development strategies and apply the fuzzy linear programming model to calculate the dynamic changes of each function value under different crop growth conditions. In addition, for multi objective variables of crops, the objective function and constraint conditions are fuzzy. That is, different membership functions are used to change within a certain range to make the target value rise and fall within a certain range. Fuzzy linear programming is to fuzzify the constraint conditions and the objective function and establish a new linear programming problem through the membership function, and its optimal solution is called the fuzzy optimal solution of the original problem. We should determine the constraints of the model, that is, the constraints that affect the final optimization goal. This requires full consideration of various restrictive factors that affect the realization of the ultimate optimization goal, and the main restrictive factors affecting the goal planning are expressed as a constraint relation [1-5].

The model established should take into account the protection of the ecological environment, economic development, and social harmony and stability in the project area. Therefore, it is necessary to establish an objective function based on the maximum economic benefit while taking into account ecological and social benefits and, finally, establish a fuzzy linear programming model. Use a two-stage solution method to solve: first, add artificial variables to the original linear programming problem, construct a fuzzy linear programming model, and then solve it; then use the simplex method to find the optimal solution of the original objective function, which is the original problem The fuzzy optimal solution of finally arrives at the optimal structural plan. Because of the uncertainty of crops in their growth and harvest, the concepts of motion and fuzziness should be introduced. Agricultural economic management should focus on the growth of crops and establish elastic constraints that change within a certain range. The constraints of linear programming are rigid and inelastic. If one constraint is not satisfied, the system will have no feasible solution. For example, if a certain constraint condition Fi(x) ≥ bi, according to the requirements of linear programming, the optimal solution with the lowest price can be calculated only if the constraint condition is satisfied, but it may also cause price rise or imbalance of crop development completely to meet the constraint condition Fi(x) ≥ bi. In this case, if the system can automatically relax the constraints, it is possible to export a balanced management method for economic development. Therefore, we use fuzzy logic methods to establish a fuzzy linear programming model for the optimization matrix of agricultural economic management.

#### References

1. Ilbahar, Esra, Cengiz Kahraman and Selcuk Cebi. "Location selection for waste-to-energy plants by using fuzzy linear programming." Energy 234 (2021): 121189.
2. Sahoo, D, A K Tripathy and J K Pati. "Study on multi-objective linear fractional programming problem involving pentagonal intuitionistic fuzzy number." RICO 6 (2022): 100091.
3. Fathy, E and A E Hassanien. "Fuzzy harmonic mean technique for solving fully fuzzy multilevel multiobjective linear programming problems." Alex Eng J 61 (2022): 8189-8205.
4. Liu, Ai-Hua, Shu-Ping Wan and Jiu-Ying Dong. "An axiomatic design-based mathematical programming method for heterogeneous multi-criteria group decision making with linguistic fuzzy truth degrees." Inf Sci 571 (2021): 649-675.
5. Truong, Hoa Quynh, and Chawalit Jeenanunta. "Fuzzy mixed integer linear programming model for national level monthly unit commitment underprice-based uncertainty: a case study in Thailand." Electr Power Syst Res 209 (2022): 107963.

#### Journal Highlights

###### Citations: 1282

Journal of Applied & Computational Mathematics received 1282 citations as per Google Scholar report