An Application of Fully Intuitionistic Fuzzy Multi-objective Linear Fractional Programming Problem in E-education System

This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore,...

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Veröffentlicht in:International journal of fuzzy systems Jg. 24; H. 8; S. 3544 - 3563
Hauptverfasser: Malik, Manisha, Gupta, S. K.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Heidelberg Springer Nature B.V 01.11.2022
Springer Berlin Heidelberg
Schlagworte:
Algorithms
Decision making
Distance learning
Education
Equivalence
Fuzzy logic
Fuzzy sets
Goal programming
Inventory
Linear programming
Mathematical functions
Mathematical programming
Monte Carlo simulation
Multiple objective analysis
Nonlinear programming
Optimization
Optimization models
Production planning
Variables
ISSN:1562-2479, 2199-3211
Online-Zugang:Volltext
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Abstract This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.
AbstractList This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.
Author Gupta, S. K.
Malik, Manisha
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Copyright Copyright Springer Nature B.V. Nov 2022
The Author(s) under exclusive licence to Taiwan Fuzzy Systems Association 2022
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  publication-title: Int. J. Appl. Eng. Res.
– volume: 6
  year: 2022
  ident: 1348_CR36
  publication-title: Results Control Optim.
  doi: 10.1016/j.rico.2021.100091
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Snippet This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving...
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SubjectTerms Algorithms
Decision making
Distance learning
Education
Equivalence
Fuzzy logic
Fuzzy sets
Goal programming
Inventory
Linear programming
Mathematical functions
Mathematical programming
Monte Carlo simulation
Multiple objective analysis
Nonlinear programming
Optimization
Optimization models
Production planning
Variables
Title An Application of Fully Intuitionistic Fuzzy Multi-objective Linear Fractional Programming Problem in E-education System
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https://pubmed.ncbi.nlm.nih.gov/PMC9415281
Volume 24
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