Efficient General Type-2 Fuzzy Computation
AuthorHaas, Benjamin David
AdvisorFadali, M. Sami
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This thesis presents new implementations of the meet and join operations to support the use of general type-2 fuzzy sets and systems. The implementations use interval based secondary membership functions instead of the more common representation of secondary membership functions. The details of the changes to meet and join to account for these changes in structure are presented.Typically, the computational complexity for a general type-2 fuzzy set operation given n discretized points in the fuzzy set is O(n^4 ) . However, we show that using interval based secondary membership functions reduces the computational complexity of operations on the general type-2 fuzzy sets to O(n^2*m) where m is the number of alpha -cuts and is typically much less than n. If m = 1, then this is the same for interval type-2 fuzzy sets. The reduction in computation time occurs in all aspects of the general type-2 sets and systems including set operations, inferencing, and type reduction, making general type-2 fuzzy sets more attractive in applications where interval type-2 fuzzy sets do not provideadequate models.We implemented the new algorithms in a computer program package to provide a tool for the use of general type-2 fuzzy sets and systems. The program includes the operations necessary for general type-2 sets and systems as well as interval type-2 sets and systems and allows the user to choose which type to use. Examples using the program package are also provided to demonstrate its usefulness.