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Fuzzy Sets for Multicriteria Optimization

Membership and Influence

In fuzzy set theory the term "target" can be represented with a characteristic function varying with the response variable. This function, varying between 0 and 1, is the membership function of the variable in question. "Close to the target" can for example be represented by all values above 0.7.

Example of membership function for the fuzzy set "target".

The membership functions will of course vary significantly in shape depending on the characteristic you want to describe. The basic idea is however the same: To translate, or transform, different response variables into a measure that can be adequately compared and combined with others.

In the MultiSimplex software, it is possible to define three types of optimization objectives, with accompanying membership functions. Derringer and Suich first suggested these functions in 1980.

The relative importance of individual response variables can also vary. One may be very important, while another may be only moderately important. In the MultiSimplex software it is called influence, and also expressed with a number between 0 and 1.

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

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