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Zbl 1217.90162
Tan, Qing; He, Qing; Zhao, Weizhong; Shi, Zhongzhi; Lee, E.S.
An improved FCMBP fuzzy clustering method based on evolutionary programming. (English)
[J] Comput. Math. Appl. 61, No. 4, 1129-1144 (2011). ISSN 0898-1221

Summary: In current PC computing environment, the fuzzy clustering method based on perturbation (FCMBP) is failed when dealing with similar matrices whose orders are higher than tens. The reason is that the traversal process adopted in FCMBP is exponential complexity. This paper treated the process of finding fuzzy equivalent matrices with smallest error from an optimization point of view and proposed an improved FCMBP fuzzy clustering method based on evolutionary programming. The method seeks the optimal fuzzy equivalent matrix which is nearest to the given fuzzy similar matrix by evolving a population of candidate solutions over a number of generations. A new population is formed from an existing population through the use of a mutation operator. Better solutions survive into next generation and finally the globally optimal fuzzy equivalent matrix could be obtained or approximately obtained. Compared with FCMBP, the improved method has the following advantages: (1) Traversal searching is avoided by introducing an evolutionary programming based optimization technique. (2) For low-order matrices, the method has much better efficiency in finding the globally optimal fuzzy equivalent matrix. (3) Matrices with hundreds of orders could be managed. The method could quickly get a more accurate solution than that obtained by the transitive closure method and higher precision requirement could be achieved by further iterations. And the method is adaptable for matrices of higher order. (4) The method is robust and not sensitive to parameters.

MSC 2000:: *90C70 Fuzzy programming
90C59 Approximation methods and heuristics

Keywords: fuzzy clustering; FCMBP fuzzy clustering; optimal fuzzy equivalent matrix; evolutionary programming

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Zentralblatt MATH Berlin [Germany]