Unspecified Consequences for the Center
The definition of the continuous central function and the study of each are provided by Mendel and Liu (2007). Theoretical work can be justified for a discrete central function. In connection with this fact, Mendel and Liu showed several interesting properties of the continuous center function. It can be summed up that some of these properties have a decrease in central function or there is an appetizing spot to the left of the minimum value, and an increased or an appetizing spot to the right of this value. Also, this function has a global minimum when k=L. The right-center function yr has similar properties because when k=R, this function has a global maximum. Therefore, it increases to the left of the maximum value and decreases to the right.
Generalization Center for Interval Type 2 Fuzzy Set
Calculating the generalized centroid of the interval type 2 fuzzy set (IT2 FS) is an important step in the operation of the IT2 FLS. Several algorithms have been proposed to calculate this, but the KM algorithm is the most used method in type 2 fuzzy logic applications. The computational properties of the KM algorithm have been improved from, resulting in a new version with the enhanced Karnik-Mendel (EKM) algorithm tab. Another iterative algorithm is proposed for calculating the generalized centroid of IT2 FS. Experimental traces show that this algorithm is faster than the original KM algorithm. However, there is no computational comparison between it and the EKM algorithm. The algorithm is really simple. By running an exhaustive search over the non-shortened central function to find the min and max, you can reduce search time by introducing conditions that stop the algorithm when the minimum or maximum value is reached. The discrete centroid function is not convex, but has well-defined properties, which helps to set the required stopping conditions. This work here introduces a new version of the tabbed algorithm to the iterative algorithm with stop conditions (IASCO) and compares it with the EKM algorithm in terms of computation time and arithmetic precision.
