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Solving fuzzy linear fractional set covering problem by a goal programming based solution approach

  • *Corresponding author: Harish Garg

    *Corresponding author: Harish Garg 
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  • In this paper, a fuzzy linear fractional set covering problem is solved. The non-linearity of the objective function of the problem as well as its fuzziness make it difficult and complex to be solved effectively. To overcome these difficulties, using the concepts of fuzzy theory and component-wise optimization, the problem is converted to a crisp multi-objective non-linear problem. In order to tackle the obtained multi-objective non-linear problem, a goal programming based solution approach is proposed for its Pareto-optimal solution. The non-linearity of the problem is linearized by applying some linearization techniques in the procedure of the goal programming approach. The obtained Pareto-optimal solution is also a solution of the initial fuzzy linear fractional set covering problem. As advantage, the proposed approach applies no ranking function of fuzzy numbers and its goal programming stage considers no preferences from decision maker. The computational experiments provided by some examples of the literature show the superiority of the proposed approach over the existing approaches of the literature.

    Mathematics Subject Classification: Primary: 68T35; 90B50; 62A86; 03E72.


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  • Figure 1.  The fuzzy objective function obtained by the proposed approach and the approach of Gupta and Saxena [14] for Example 1

    Figure 2.  The fuzzy objective function obtained by the proposed approach and the approach of Gupta and Saxena [14] for Example 2

    Table 1.  The goals obtained for Example 1 from Step 3 of the proposed approach

    $ X_1 $ $ X_2 $ $ X_3 $ function value
    Model (30) $ 1 $ $ 1 $ $ 0 $ $ Z^{1*}=0.622 $
    Model (31) $ 1 $ $ 1 $ $ 0 $ $ Z^{2*}=0.966 $
    Model (32) $ 1 $ $ 1 $ $ 0 $ $ Z^{3*}=1.034 $
    Model (33) $ 1 $ $ 1 $ $ 0 $ $ Z^{4*}=2.875 $
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