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Title: Analysis and Applications of the Km Algorithm in Type-2 Fuzzy Logic Control and Decision Making
Keywords: Type-2 fuzzy logic, Interval type-2 fuzzy set, Karnik-Mendel algorithm, Control , Decision making
Issue Date: 19-Aug-2011
Source: NIE MAOWEN (2011-08-19). Analysis and Applications of the Km Algorithm in Type-2 Fuzzy Logic Control and Decision Making. ScholarBank@NUS Repository.
Abstract: Interval type-2 (IT2) fuzzy logic controller (FLC) is an extension of type-1 (T1) FLC. A large number of experiments have demonstrated that the IT2 FLC can produce more satisfactory performance. However, there has been no rigorous theoretical analysis studying the potential advantage of the IT2 FLC. The challenge that impedes its theoretical study is the Karnik-Mendel / enhanced Karnik-Mendel (KM / EKM) iterative algorithm for type-reduction. To perform theoretical study of the IT2 FLC, the mathematical input-output relationship of a class of symmetric IT2 fuzzy PD/PI controller was established. By comparing the derived expressions with its T1 counterpart, four interesting characteristics of symmetric IT2 FLC were identified. These characteristics provide insights into why an IT2 FLC is better able to balance the amount of the compromise between faster response and smaller overshoot. As an extension of the study of symmetric IT2 FLC, a class of non-symmetric IT2 FLC was considered. By comparing the expressions of the non-symmetric and symmetric IT2 FLCs, the similarities and differences in the characteristics of both IT2 FLCs were established. The unique characteristics provide insights into why the non-symmetric IT2 fuzzy controller can better balance the conflicting aims of fast transient response and small overshoot. Another application of the KM iterative algorithm is the computation of fuzzy weighted average (FWA) and linguistic weighted average (LWA). Three algorithms that further reduce the computational burden needed to calculate FWA and LWA were presented. Among the three proposed algorithms, the one which requires the least computational overhead can achieve an approximately 60% reduction in the computational time of the KM iterative algorithm and an approximately 40% reduction of the EKM iterative algorithm.
Appears in Collections:Ph.D Theses (Open)

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