Comparison and practical implementation of type-reduction algorithms for type-2 fuzzy sets and systems

Type-reduction algorithms are very important for type-2 fuzzy sets and systems. The earliest one, and also the most popular one, is the Karnik-Mendel Algorithm, which is iterative and computationally intensive. In the last a few years researchers have proposed several other more efficient type-reduction algorithms. In this paper we also propose a new algorithm which improves over the latest results. Experiments show that it is the most efficient one to use in practice. Particularly, when the number of elements in type-reduction is smaller than 100, which is true in most practical type-reduction computations, our proposed algorithm can save over 50% computational cost over the Karnik-Mendel Algorithms. We also give the Matlab implementation of our most efficient algorithm in the Appendix. It includes preprocessing steps to eliminate numerical problems, and also improved testing criteria to prevent possible infinite loops. This program will be very helpful in promoting the popularity of type-2 fuzzy sets and systems.