An algebraic method and a genetic algorithm to the identification of fuzzy measures based on Choquet integrals

2014 ◽  
Vol 26 (3) ◽  
pp. 1393-1400 ◽  
Author(s):  
Naomi Kochi ◽  
Zhenyuan Wang
Keyword(s):  
Genetic Algorithm ◽  
Algebraic Method ◽  
Fuzzy Measures ◽  
Choquet Integrals

scholarly journals Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chen Li ◽  
Gong Zeng-tai ◽  
Duan Gang
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Real Data ◽  
Difficult Problem ◽  
Particle Swarm Algorithm ◽  
Fuzzy Data ◽  
Algorithm Optimization ◽  
Practical Applications ◽  
Fuzzy Measures ◽  
Choquet Integrals

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 theσ-λrules. Furthermore we define and characterize the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based onσ-λrules. In addition, we design a special genetic algorithm to determine a type of general fuzzy measures from fuzzy data.

Fuzzy Measures and Choquet Integrals based on Fuzzy Covering Rough Sets

2021 ◽  
pp. 1-1
Author(s):  
Xiaohong Zhang ◽  
Jingqian Wang ◽  
Jianming Zhan ◽  
Jianhua Dai
Keyword(s):  
Rough Sets ◽  
Fuzzy Measures ◽  
Choquet Integrals

Multi-Attribution Classification Based on Lower Integral with Genetic Algorithm

2014 ◽  
Vol 668-669 ◽  
pp. 1090-1093
Author(s):  
Ai Xia Chen ◽  
Jun Hua Li
Keyword(s):  
Genetic Algorithm ◽  
Linear Programming ◽  
Linear Programming Problem ◽  
Fuzzy Integral ◽  
Data Sets ◽  
Fuzzy Measures ◽  
Benchmark Data ◽  
Minimum Potential ◽  
And Performance ◽  
Set Function

Fuzzy integral has been widely used in multi-attribution classification when the interactions exist between the attributions. Because the fuzzy measure defined on the attributions represents the weights of all the attributions and the interactions between them. The lower integral is a type of fuzzy integral with respect to fuzzy measures, which represents the minimum potential of efficiency for a group of attributions with interaction. The value of lower integrals can be evaluated through solving a linear programming problem. Considering the lower integral as a classifier, this paper investigates its implementation and performance. The difficult step in the implementation is how to learn the non-additive set function used in lower integrals. And Genetic algorithm is used to solve the problem. Finally, numerical simulations on some benchmark data sets are given.

scholarly journals Choquet Integral of Fuzzy-Number-Valued Functions: The Differentiability of the Primitive with respect to Fuzzy Measures and Choquet Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Zengtai Gong ◽  
Li Chen ◽  
Gang Duan
Keyword(s):  
Integral Equations ◽  
Real Line ◽  
Fuzzy Number ◽  
Laplace Transformation ◽  
Choquet Integral ◽  
Fuzzy Measures ◽  
Nonadditive Measure ◽  
Choquet Integrals ◽  
Lebesgue Measures ◽  
Interval Valued

This paper deals with the Choquet integral of fuzzy-number-valued functions based on the nonnegative real line. We firstly give the definitions and the characterizations of the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on the nonadditive measure. Furthermore, the operational schemes of above several classes of integrals on a discrete set are investigated which enable us to calculate Choquet integrals in some applications. Secondly, we give a representation of the Choquet integral of a nonnegative, continuous, and increasing fuzzy-number-valued function with respect to a fuzzy measure. In addition, in order to solve Choquet integral equations of fuzzy-number-valued functions, a concept of the Laplace transformation for the fuzzy-number-valued functions in the sense of Choquet integral is introduced. For distorted Lebesgue measures, it is shown that Choquet integral equations of fuzzy-number-valued functions can be solved by the Laplace transformation. Finally, an example is given to illustrate the main results at the end of the paper.

scholarly journals Forming a Hierarchical Choquet Integral with a GA-Based Heuristic Least Square Method

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1155
Author(s):  
Chen ◽  
Huang
Keyword(s):  
Choquet Integral ◽  
Least Square Method ◽  
Least Square ◽  
Integral Model ◽  
Fuzzy Measures ◽  
Proposed Model ◽  
Choquet Integrals ◽  
The Mean ◽  
Input Variables ◽  
Least Mean Squares Algorithm

: Identifying the fuzzy measures of the Choquet integral model is an important component in resolving complicated multi-criteria decision-making (MCDM) problems. Previous papers solved the above problem by using various mathematical programming models and regression-based methods. However, when considering complicated MCDM problems (e.g., 10 criteria), the presence of too many parameters might result in unavailable or inconsistent solutions. While k-additive or p-symmetric measures are provided to reduce the number of fuzzy measures, they cannot prevent the problem of identifying the fuzzy measures in a high-dimension situation. Therefore, Sugeno and his colleagues proposed a hierarchical Choquet integral model to overcome the problem, but it required the partition information of the criteria, which usually cannot be obtained in practice. In this paper, we proposed a GA-based heuristic least mean-squares algorithm (HLMS) to construct the hierarchical Choquet integral and overcame the above problems. The genetic algorithm (GA) was used here to determine the input variables of the sub-Choquet integrals automatically, according to the objective of the mean square error (MSE), and calculated the fuzzy measures with the HLMS. Then, we summed these sub-Choquet integrals into the final Choquet integral for the purpose of regression or classification. In addition, we tested our method with four datasets and compared these results with the conventional Choquet integral, logit model, and neural network. On the basis of the results, the proposed model was competitive with respect to other models.

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