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Solving Fully Fuzzy Multi-objective Linear Programming Problem Using Nearest Interval Approximation of Fuzzy Number and Interval Programming

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Abstract

This paper focuses on Fully Fuzzy Multi-Objective Linear Programming (FFMOLP) problem in which all the coefficients and decision variables are LR flat fuzzy numbers, the more generalized version of fuzzy numbers and all the constraints are fuzzy inequalities. A new algorithm is proposed for solving FFMOLP problem which first converts it into the Multi-Objective Interval Linear Programming (MOILP) problem. Further, taking the help of fuzzy slack variable, fuzzy surplus variables, nearest interval approximation of fuzzy numbers and scalarization technique, MOILP is then converted into the Crisp Linear Programming (CLP) problem. It is shown that the optimal solution of CLP problem is the fuzzy Pareto optimal solution of FFMOLP problem. The main advantage of the proposed algorithm is that it transforms FFMOLP problem into Crisp Linear Programming problem. Moreover, to apply algorithm, only the knowledge of arithmetic operations of LR flat fuzzy numbers, centre and width of the closed intervals are required. At the end, to illustrate the proposed method and its effectiveness over the existing method, numerical examples are solved and compared.

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Acknowledgements

The first author is thankful to the Council of Scientific and Industrial Research (CSIR), New Delhi, India, for the financial support (09/045(1153)/2012-EMR-I).

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, Delhi, 110007, India

    Uday Sharma

  2. Department of Mathematics, Miranda House, University of Delhi, Delhi, 110007, India

    Shashi Aggarwal

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  1. Uday Sharma
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  2. Shashi Aggarwal
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Correspondence to Uday Sharma.

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Sharma, U., Aggarwal, S. Solving Fully Fuzzy Multi-objective Linear Programming Problem Using Nearest Interval Approximation of Fuzzy Number and Interval Programming. Int. J. Fuzzy Syst. 20, 488–499 (2018). https://doi.org/10.1007/s40815-017-0336-8

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  • DOI: https://doi.org/10.1007/s40815-017-0336-8

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