Type-2 Fuzzy Granular Models by Mauricio A. Sanchez, Oscar Castillo, Juan R. Castro
By Mauricio A. Sanchez, Oscar Castillo, Juan R. Castro
In this booklet, a chain of granular algorithms are proposed. A nature encouraged granular set of rules in accordance with Newtonian gravitational forces is proposed. a sequence of tools for the formation of higher-type details granules represented via period Type-2 Fuzzy units also are proven, through a number of ways, akin to Coefficient of edition, precept of justifiable granularity, uncertainty-based info inspiration, and numerical proof dependent. And a fuzzy granular program comparability is given as to illustrate the diversities in how uncertainty impacts the functionality of fuzzy details granules.
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Extra resources for Type-2 Fuzzy Granular Models
9 shows the complete system used for simulation the robot controller. Results for the simulation were performed using various external perturbations: band-limited white noise, pulse generated noise, and uniform random number noise. 1; for pulse generated noise, the amplitude was 1, the period was set to 1, the pulse width (%) was set to 1, and the phase delay was set to 0; and for the uniform random number noise, the limits where set to [−1, 1]. The test criterions chosen to compare the performance of T1, IT2 and GT2 FSs are ISE, IAE, ITSE, and ITAE, shown in Eqs.
The individual acceleration factors are ﬁxed, this causes the PSO to search more slowly inside the conﬁned space, otherwise the spread signiﬁcantly increases and that is not a desirable behavior. The rest of the parameters are set to typical recommended parameter values. The objective function for the PSO is another very important topic that must be addressed in order to obtain the best possible solution. Shown in Eq. 28) is the manually adjusted objective function. Where h is the RMSE of the output coverage, and # is the RMSE of the size of the Footprint Of Uncertainty.
8. 9. 10. LOOP foreach i in xi IF min( xi , x j ) < radius THEN; verify if there are points which can interact and join together, where i ≠ j INTERACTIONS_EXIST=TRUE; indicate that another iteration can be done mi ∪ m j ; join the mass of x j unto xi ⎛ mj ⎞ ⎟ xi , x j ρbarycenter = ⎜⎜ ⎟ ⎝ mi + m j ⎠ ; calculate the barycenter distance between xi and x j ρbarycenter ; calculate a scaling factor λ xi , x j 11. λ= 12. xi = xi + λ(x j − xi ) ; update de position of xi to its new location, based on λ 13.