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Journal of Applied Mathematics
Volume 2013, Article ID 542153, 11 pages
http://dx.doi.org/10.1155/2013/542153
Research Article

Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data

1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2Department of Mathematics, Lanzhou City University, Lanzhou 730070, China
3School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China

Received 11 May 2013; Accepted 7 October 2013

Academic Editor: T. Warren Liao

Copyright © 2013 Chen Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Fuzzy measures and fuzzy integrals have been successfully used in many real applications. How to determine fuzzy measures is a very difficult problem in these applications. Though there have existed some methodologies for solving this problem, such as genetic algorithms, gradient descent algorithms, neural networks, and particle swarm algorithm, it is hard to say which one is more appropriate and more feasible. Each method has its advantages. Most of the existed works can only deal with the data consisting of classic numbers which may arise limitations in practical applications. It is not reasonable to assume that all data are real data before we elicit them from practical data. Sometimes, fuzzy data may exist, such as in pharmacological, financial and sociological applications. Thus, we make an attempt to determine a more generalized type of general fuzzy measures from fuzzy data by means of genetic algorithms and Choquet integrals. In this paper, we make the first effort to define the rules. Furthermore we define and characterize the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on rules. In addition, we design a special genetic algorithm to determine a type of general fuzzy measures from fuzzy data.