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

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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.

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Abbreviations

LFP:

Linear fractional programming

MOLFP:

Multi-objective linear fractional programming

DM:

Decision-maker

IF:

Intuitionistic fuzzy

IF-LFP:

Intuitionistic fuzzy linear fractional programming

IF-MO-LFP:

Intuitionistic fuzzy multi-objective linear fractional programming

IFN:

Intuitionistic fuzzy number

TIFN:

Triangular intuitionistic fuzzy number

s. t.:

Subject to

ELC:

E-learning centre

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Acknowledgements

The authors are deeply thankful to the Editor and the anonymous referees for their fruitful comments which helped us to improve the overall quality of the manuscript. Moreover, the first author is grateful to the Ministry of Human Resource Development, India, for financial support, to carry out this research work. The second author would like to acknowledge the Uttarakhand State Council for Science and Technology, Dehradun, India to provide financial support to carry out this work under the Project No. UCS &T/R7D-19/20-21/19222/1.

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  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247 667, India

    Manisha Malik & S. K. Gupta

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  1. Manisha Malik
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Correspondence to S. K. Gupta.

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Malik, M., Gupta, S.K. An Application of Fully Intuitionistic Fuzzy Multi-objective Linear Fractional Programming Problem in E-education System. Int. J. Fuzzy Syst. 24, 3544–3563 (2022). https://doi.org/10.1007/s40815-022-01348-2

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