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

1
Department of Business Administration, Chung Yuan Christian University, Taoyuan 32023, Taiwan
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Department of Computer Science & Information Management, SooChow University, No.56 Kueiyang Street, Section 1, Taipei 100, Taiwan
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1155; https://doi.org/10.3390/math7121155
Received: 14 October 2019 / Revised: 18 November 2019 / Accepted: 23 November 2019 / Published: 1 December 2019
: 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. View Full-Text
Keywords: fuzzy measure; hierarchical Choquet integral; genetic algorithm; heuristic least mean-squares algorithm (HLMS) fuzzy measure; hierarchical Choquet integral; genetic algorithm; heuristic least mean-squares algorithm (HLMS)
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Chen, C.-Y.; Huang, J.-J. Forming a Hierarchical Choquet Integral with a GA-Based Heuristic Least Square Method. Mathematics 2019, 7, 1155.

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