Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data

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,...

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Main Authors: Chen Li, Gong Zeng-tai, Duan Gang
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/542153
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author Chen Li
Gong Zeng-tai
Duan Gang
author_facet Chen Li
Gong Zeng-tai
Duan Gang
author_sort Chen Li
collection DOAJ
description 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 σ-λ rules. Furthermore we define and characterize the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on σ-λ rules. In addition, we design a special genetic algorithm to determine a type of general fuzzy measures from fuzzy data.
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issn 1110-757X
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publishDate 2013-01-01
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spelling doaj-art-c7cdd9ac17a0409395217866eae2d4522025-08-20T03:24:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/542153542153Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy DataChen Li0Gong Zeng-tai1Duan Gang2College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaSchool of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, ChinaFuzzy 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 σ-λ rules. Furthermore we define and characterize the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on σ-λ rules. In addition, we design a special genetic algorithm to determine a type of general fuzzy measures from fuzzy data.http://dx.doi.org/10.1155/2013/542153
spellingShingle Chen Li
Gong Zeng-tai
Duan Gang
Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data
Journal of Applied Mathematics
title Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data
title_full Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data
title_fullStr Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data
title_full_unstemmed Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data
title_short Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data
title_sort genetic algorithm optimization for determining fuzzy measures from fuzzy data
url http://dx.doi.org/10.1155/2013/542153
work_keys_str_mv AT chenli geneticalgorithmoptimizationfordeterminingfuzzymeasuresfromfuzzydata
AT gongzengtai geneticalgorithmoptimizationfordeterminingfuzzymeasuresfromfuzzydata
AT duangang geneticalgorithmoptimizationfordeterminingfuzzymeasuresfromfuzzydata