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On solving Atanassov’s I-fuzzy linear programming problems: some variants of Angelov’s model

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Abstract

Angelov’s approach is the most common approach to solve Atanassov’s I-fuzzy linear programming problems. Here certain other variants of this basic model are studied. These variants are motivated by a recent study (Chandra and Aggarwal 2014) on fuzzy linear programming problems and follow very naturally from an associated bi-objective programming problem. This bi-objective programming problem aims to achieve a trade-off between the twin objectives of ‘meeting the aspiration level’ and ‘satisfaction of the given constraints’ which are defined in terms of their respective score functions. As an outcome of this study a new two phase approach to solve Atanassov’s I-fuzzy linear programming problems is obtained. Further, two additional formulations are also proposed on similar lines which also provide an efficient solution of the associated bi-objective optimization problem. These efficient solutions have a natural interpretation for the given I-fuzzy linear programming problem. A small numerical example is included as an illustration.

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Acknowledgments

The authors are thankful to the referees for their valuable suggestions and extensive comments which have helped to improve the paper. The authors are thankful to Professor Suresh Chandra and Professor Aparna Mehra, Department of Mathematics, IIT Delhi for their valuable suggestions and comments on this work.

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  1. University School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha University, Dwarka, Delhi, 110078, India

    A. Aggarwal & I. Khan

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  1. A. Aggarwal
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  2. I. Khan
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Correspondence to A. Aggarwal.

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Aggarwal, A., Khan, I. On solving Atanassov’s I-fuzzy linear programming problems: some variants of Angelov’s model. OPSEARCH 53, 375–389 (2016). https://doi.org/10.1007/s12597-015-0237-2

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