Open Conference Systems, CLADAG2023

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Fuzzy Functions with Elastic-net Estimators based on Possibilistic FCM
Nihat Tak

Last modified: 2023-06-12


Fuzzy functions (FFs) were introduced by Turksen [1] as non-rule based inference systems. The idea behind FFs is to cluster the observations by using Fuzzy c-means (FCM) algorithm. Thus, an object belongs to each cluster with some membership grade. Turksen claims that adding the membership grades into input matrix for each cluster as a new variable and combining the outcomes would improve the performance of the maximum likelihood estimator. Moreover, he also shows that adding different functions of membership grades into inputs improves the model performance even better. However, adding different functions of membership grades causes the multicollinearity problem. To overcome the problem, elastic-net estimators are adapted in fuzzy functions by Tak and ?nan [2]. They used FCM to cluster the inputs and obtain the membership grades. However, FCM calculates the centers of clusters by using all observations. Thus, FCM is very sensitive when there are outliers in the datasets. To deal with misspecification of the cluster centers, Possibilistic FCM (PFCM) is employed in fuzzy functions with elastic-net estimators. PFCM, detects an outlier in a dataset and omits its effect on the cluster centers. In this way, the cluster centers are calculated more correctly, thus, the membership grades. The proposed method is evaluated on three real world datasets. The results verified that the proposed method outperformed the other methods that are used in the study. Mean absolute percentage error and root mean squared error are used as the evaluation criteria.