Connect Karnik-Mendel Algorithms to Root-Finding for Computing the Centroid of an Interval Type-2 Fuzzy Set

被引：65
|
作者：
Liu, Xinwang [1 ,2 ]
Mendel, Jerry M. [2 ]
机构：
[1] Southeast Univ, Sch Econ & Management, Nanjing 210096, Peoples R China
[2] Univ So Calif, Ming Hsieh Dept Elect Engn, Los Angeles, CA 90089 USA
来源：
IEEE TRANSACTIONS ON FUZZY SYSTEMS | 2011年 / 19卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Centroid computation; interval type-2 fuzzy set (IT2 FS); Karnik-Mendel (KM) algorithms; root-finding; WEIGHTED AVERAGE; LOGIC; DEFUZZIFICATION; SYSTEMS; DESIGN; WORDS;
D O I：
10.1109/TFUZZ.2011.2130528
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
Based on a new continuous Karnik-Mendel (KM) algorithm expression, this paper proves that the centroid computation of an interval type-2 fuzzy set using KM algorithms is equivalent to the Newton-Raphson method in root-finding, which reveals the mechanisms in KM algorithm computation. The theoretical results of KM algorithms are re-obtained. Different from current KM algorithms, centroid computation methods that use different root-finding routines are provided. Such centroid computation methods can obtain the exact solution and are different from the current approximate methods using sampled data. Further improvements and analysis of the centroid problem using root-finding and integral computation techniques are also possible.
引用
收藏
页码：652 / 665
页数：14
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