A Novel Linguistic Relational Fuzzy C-Means

In real-world applications, sometimes there are uncertainties in the data sets whether from the collection process or from the natural languages. Moreover, the data may come in the form of fuzzy relation. To analyze data, one might use one of popular tools, i.e., a clustering method. There are several types of clustering including clustering on information from objects themselves or clustering on a relational data. Currently, there are few researches on a fuzzy data clustering and a fuzzy relational data clustering. However, those algorithms are either defuzzifying the data or the relation of the data before implementing the clustering Therefore, in this paper, we develop a linguistic relational fuzzy C-means (LRFCM) that works with fuzzy relation of vectors of fuzzy numbers directly. The algorithm is an extension of the regular relational fuzzy C-means (RFCM). The proposed algorithm does not defuzzify fuzzy attributes beforehand. We found that the results from the LRFCM are similar to that from the RFCM. However, the results from the LRFCM can provide information that contains all the uncertainties from the inputs while the RFCM cannot. We also compare the results with the fuzzy C-means clustering. These comparisons show that the LRFCM behaves the same way as the RFCM and the FCM in partitioning the input space into clusters.