# How do we decide which membership function to use?

In classical set theory, there are two options for an element. It is either a member of a set or not. But in fuzzy set theory, there are membership functions to define the "rate" of an element being a member of a set. In other words, classical logic says it is all black or white, but fuzzy logic offers that there is also grey which has shades between white and black.

Matlab Simulink Library is very easy to design and helpful in practice. And it has good examples on its own, like deciding about tips for a dinner looking at service and food quality. In the figure below, some various membership functions from Matlab's library are shown:

My question: How do we decide which membership function to use while designing a fuzzy controller system?

I mean, in general, not only in Matlab Simulink. I have seen Triangular and Gaussian functions are used mostly in practice, but how can we decide which function will give a better result for decision making? Do we need to train a neural network to decide which function is better depending on the problem and its rules? What are other solutions?

• Do you have data to start with? I would select the member functions to approximately match the data you try to model. The function will depend on the problem you are trying to solve. The simplest way would be to plot your data and select the best match. However, this won't work with complex data space. How complex is your problem? What is the dimensionality of your problem space? Feb 9, 2017 at 14:22
• @zlobi.wan.kenobi Thank you for kind comment, and sorry for being late to reply. I dont have a data set to start with. My question was a general one. I was confused about how to choose membership functions according to different problems. For example, it can be "disease decision" from blood examination, building self resulting system looking at different values. There is pure fuzzyness in this problem, since examination values have a wide scale. I understood about rule making, I just wondered if there is another way while choosing most suitable membership funtion, beside using neural networks? Feb 14, 2017 at 17:07
• You can do some research on Adaptive Neuro-Fuzzy Inference System! Jan 7, 2018 at 7:00