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Fuzzy Sets for Multicriteria Optimization

The Target Membership Functions

With a specific target for Y_i the MultiSimplex software uses a two-sided transformation to create membership functions expressed as:

Where

• Y_min is the low limit for acceptable values of Y_i.
• Y_max is the high limit for acceptable values of Y_i.
• C_i is the target value for Y_i.
• R is a constant that can take different values.

By changing the constant R it is also here possible to specify many different membership functions. Values of R above 1.0 will result in a slow increase from the unacceptable limits and fast near the target value. If the constant R has the value 1.0, the function will be strictly proportional between the limits and the target value. Values of R below 1.0 will result in a fast increase from the unacceptable limits and slow near the target value.

The shape of the target membership function with different values of the constant R.

1. Creating a Joint Response
2. Membership and Influence
3. The Maximization and Minimization Functions
4. The Aggregated Value of Membership

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