I have been playing with the idea of writing a short introduction to fuzzy set theory for a while now. Today I finally had time to start writing the first entry to this series, an introduction to vagueness. The posts will be mainly adaptations and excerpts from my thesis and other articles I’ve written, if you’re interested in learning the basics and philosophy that define fuzzy set theory I hope this is a good starting point. Also I hope it will generate some exposure for fuzzy set theory in general (looking at visitor counts of this website I doubt it but you never know).
The first time I came in to contact with fuzzy sets was during my Bachelor’s degree in Electrical Engineering. As part of the curriculum of a Control Systems course it was decided to add one class on fuzzy control systems. This however was way too brief for me to develop a good understanding or to spark some interest in this subject in the first place. I just couldn’t understand why it would make sense to introduce constructs like fuzziness into the “perfect” world of mathematics where everything is crisp, sound and nicely structured (this is what every mathematician or engineer likes right).
This view changed during my Master’s degree when I had the honor to have my thesis supervised by Uzay Kaymak and Rui de Almeida at the Eindhoven University of Technology, both experts in fuzzy set theory. Their passion and knowledge on the subject inspired me to specialize in fuzzy sets. For me it helped to understand the broader philosophical concepts first before looking at fuzzy sets itself (it helps to put things in perspective I think) . That is why this series will start with a short philosophical review of fuzziness and vagueness in the broadest sense. After this I will touch upon the mathematics behind fuzzy set theory and fuzzy logic. This will be followed by a brief introduction on evolving fuzzy Takagi-Sugeno algorithms, the implementation I’ve written in R is based on this theorem.