Fuzzy and Multi-Level Decision Making: Soft Computing Approaches by Chi-Bin Cheng & Hsu-Shih Shih & E. Stanley Lee

Author:Chi-Bin Cheng & Hsu-Shih Shih & E. Stanley Lee
Language: eng
Format: epub
ISBN: 9783319925257
Publisher: Springer International Publishing

where X represents the original crisp constraint set.

Now, the corresponding compensatory formulation for the bi-level problem in Example 5.1 is:

where represents the degree of compensation.

This compensatory formulation can be solved by any linear programming code. The compromise solution is , with a total degree of satisfaction at . Compared to the solution obtained in Chap. 6, where with the same objective function and decision values, the degree of satisfaction has been improved due to the use of better aggregation operator. To investigate the effect of compensation in more detail, 11 different cases with varies from 0 to 1.0 were solved and the results are listed in Table 5.2. The value of µand varies within a range from 0.69 to 0.78 and remains at 0.69, except at , where .Table 5.2Results of Example 5.1

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