Centroid of a type-2 fuzzy set
Information Sciences: an International Journal
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Information Sciences: an International Journal
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Information Sciences: an International Journal
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Information Sciences: an International Journal
Information Sciences: an International Journal
Enhanced Karnik-Mendel algorithms
IEEE Transactions on Fuzzy Systems
Type-reduction of the discretised interval type-2 fuzzy set
FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
Interval type-2 fuzzy logic congestion control for video streaming across IP networks
IEEE Transactions on Fuzzy Systems
α-plane representation for type-2 fuzzy sets: theory and applications
IEEE Transactions on Fuzzy Systems
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Decision making with imprecise parameters
International Journal of Approximate Reasoning
Information Sciences: an International Journal
Interval Type-2 fuzzy voter design for fault tolerant systems
Information Sciences: an International Journal
International Journal of Approximate Reasoning
Study on enhanced Karnik-Mendel algorithms: Initialization explanations and computation improvements
Information Sciences: an International Journal
The sampling method of defuzzification for type-2 fuzzy sets: Experimental evaluation
Information Sciences: an International Journal
Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems
IEEE Transactions on Fuzzy Systems
Type-2 Fuzzistics for Symmetric Interval Type-2 Fuzzy Sets: Part 1, Forward Problems
IEEE Transactions on Fuzzy Systems
Interval Type-2 Fuzzy Logic Systems Made Simple
IEEE Transactions on Fuzzy Systems
Geometric Type-1 and Type-2 Fuzzy Logic Systems
IEEE Transactions on Fuzzy Systems
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IEEE Transactions on Fuzzy Systems
Exact inversion of decomposable interval type-2 fuzzy logic systems
International Journal of Approximate Reasoning
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In this study, a new centroid type reduction method is proposed for piecewise linear interval type-2 fuzzy sets based on geometrical approach. The main idea behind the proposed method relies on the assumption that the part of footprint of uncertainty (FOU) of an interval type-2 fuzzy set (IT2FS) has a constant width where the centroid is searched. This constant width assumption provides a way to calculate the centroid of an IT2FS in closed form by using derivative based optimization without any need of iterations. When the related part of FOU is originally constant width, the proposed method finds the accurate centroid of an IT2FS; otherwise, an enhancement can be performed in the algorithm in order to minimize the error between the accurate and the calculated centroids. Moreover, only analytical formulas are used in the proposed method utilizing geometry. This eliminates the need of using discretization of an IT2FS for the type reduction process which in return naturally improves the accuracy and the computation time. The proposed method is compared with Enhanced Karnik-Mendel Iterative Procedure (EKMIP) in terms of the accuracy and the computation time on seven test fuzzy sets. The results show that the proposed method provides more accurate results with shorter computation time than EKMIP.