We consider the task of selecting an optimal sub-model among a collection of fuzzy linear regression models. The Akaike criterion, also known as AIC, is a well-established measure for assessing competing models. Using the extension principle of Zadeh, we develop a simple procedure that involves sampling crisp data from fuzzy numbers to construct fuzzy AICs. We advocate a non-parametric approach, based on the empirical likelihood concept, to compute the likelihood function. Indeed, the fuzzy distribution of the stochastic part of the fuzzy regression model is not easily trackable, and no a priori distribution is theoretically justified. An empirical application shows the practicality of the method. Indeed, according to their fuzzy AIC, a collection of sub-models could be easily ordered by a proper distance measure. Although other ranking methods could also be applied, we advocate the use of the Generalised Signed Distance measure. Our contribution is to demonstrate how to derive and compute fuzzy AICs based on empirical likelihood, and to utilise them for ranking fuzzy regression models.

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Selection of Fuzzy Regression Models by AIC

  • Julien Rosset,
  • Laurent Donzé

摘要

We consider the task of selecting an optimal sub-model among a collection of fuzzy linear regression models. The Akaike criterion, also known as AIC, is a well-established measure for assessing competing models. Using the extension principle of Zadeh, we develop a simple procedure that involves sampling crisp data from fuzzy numbers to construct fuzzy AICs. We advocate a non-parametric approach, based on the empirical likelihood concept, to compute the likelihood function. Indeed, the fuzzy distribution of the stochastic part of the fuzzy regression model is not easily trackable, and no a priori distribution is theoretically justified. An empirical application shows the practicality of the method. Indeed, according to their fuzzy AIC, a collection of sub-models could be easily ordered by a proper distance measure. Although other ranking methods could also be applied, we advocate the use of the Generalised Signed Distance measure. Our contribution is to demonstrate how to derive and compute fuzzy AICs based on empirical likelihood, and to utilise them for ranking fuzzy regression models.