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Axioms 2013, 2(2), 208-223; doi:10.3390/axioms2020208

Using the Choquet Integral in the Fuzzy Reasoning Method of Fuzzy Rule-Based Classification Systems

Universidad Publica de Navarra, Campus Arrosadia 31006, Pamplona, Spain
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Received: 25 February 2013 / Revised: 21 March 2013 / Accepted: 3 April 2013 / Published: 23 April 2013
(This article belongs to the Special Issue Axiomatic Approach to Monotone Measures and Integrals)
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Abstract

In this paper we present a new fuzzy reasoning method in which the Choquet integral is used as aggregation function. In this manner, we can take into account the interaction among the rules of the system. For this reason, we consider several fuzzy measures, since it is a key point on the subsequent success of the Choquet integral, and we apply the new method with the same fuzzy measure for all the classes. However, the relationship among the set of rules of each class can be different and therefore the best fuzzy measure can change depending on the class. Consequently, we propose a learning method by means of a genetic algorithm in which the most suitable fuzzy measure for each class is computed. From the obtained results it is shown that our new proposal allows the performance of the classical fuzzy reasoning methods of the winning rule and additive combination to be enhanced whenever the fuzzy measure is appropriate for the tackled problem.
Keywords: fuzzy rule-based classification systems; Choquet integral; fuzzy measure; genetic algorithm fuzzy rule-based classification systems; Choquet integral; fuzzy measure; genetic algorithm
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Barrenechea, E.; Bustince, H.; Fernandez, J.; Paternain, D.; Sanz, J.A. Using the Choquet Integral in the Fuzzy Reasoning Method of Fuzzy Rule-Based Classification Systems. Axioms 2013, 2, 208-223.

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