Footprint of uncertainty for type-2 fuzzy sets

Generalized type-2 fuzzy weight adjustment for backpropagation neural networks in time series prediction

“…6 and 7, we show the linguistic variables with generalized type-2 membership functions, where the value for the FOU is of 0.15 on the inputs and 0.00045 on the outputs for the GT2FIS in the hidden layer, and 0.15 on the inputs and 0.0015 on the outputs for the GT2FIS in the output layer [45]. These values are obtained considering 15% of the value of the range of each membership function, and this percentage is established empirically.…”

A Lyapunov stable type-2 fuzzy wavelet network controller design for a bilateral teleoperation system

“…In order to symbolically distinguish between a type-1 fuzzy set and a type-2 fuzzy set, a tilde symbol is put over the symbol for the fuzzy set; so, A ij denotes a type-1 fuzzy set, whereas ij à denotes the comparable type-2 fuzzy set. There are many methods that studied the construction of the membership functions [43,61].…”

Generalized Type-2 Fuzzy Systems for controlling a mobile robot and a performance comparison with Interval Type-2 and Type-1 Fuzzy Systems

“…In comparison with IT2FS, where the uncertainty is represented as an area, in GT2FS the uncertainty is depicted by a volume, and as such, are more capable of handling uncertainty. As GT2FS research is still fairly new, existing research is fairly limited, some examples of advancements are shown in computing the centroid by means of the centroid-flow algorithm (J M Mendel, 2011), similarity measures (Hao & Mendel, 2014), hierarchical collapsing method for direct defuzzification (Doostparast Torshizi & Fazel Zarandi, 2014), definition of footprint of uncertainty (Mo, Wang, Zhou, Li, & Xiao, 2014), a fast method for computing the centroid (H.-J. Wu, Su, & Lee, 2012), enhanced type-reduction (Yeh et al, 2011), monotone centroid flow algorithm for type-reduction (O. , conversion from IT2FS to GT2FS (Wagner, Miller, Garibaldi, Anderson, & Havens, 2014), computing with words for discrete GT2FS (Zhao, Li, & Li, 2013), matching GT2FS by comparing the vertical slices (Rizzi, Livi, Tahayori, & Sadeghian, 2013), and formation of GT2FS based on the information granule numerical evidence (Sanchez, Castro, & Castillo, 2013).…”