Abstract

Recently, research into the analysis of large-scale, complex data has been progressing in the fields of artificial intelligence and computational intelligence. In machine learning, methods of clustering and classification are gaining importance. Conventional clustering methods rely on exclusive classification, which determines whether an object belongs to a cluster. However, these methods are not always effective for large-scale, complex data. The main reason for this is that extreme summarization can result in the loss of information present in the complex data. On the other hand, achieving more complex structures requires computational effort and lacks robustness. Therefore, clustering methods that recognize uncertainty in cluster boundaries and consider the degree to which objects belong to a cluster have attracted attention. Fuzzy clustering, a clustering method based on fuzzy theory which is a component of computational intelligence, a branch of artificial intelligence, is characterized by its ability to obtain results that are closer to real-world data and superior robustness and tractability by determining cluster boundaries using fuzzy measures rather than probabilistic measures. Furthermore, it is possible to flexibly determine the degree of uncertainty at cluster boundaries depending on the data structure. This is a crucial difference from conventional statistical classification methods, which assume probabilistic and statistical uncertainty at cluster boundaries. This allows fuzzy clustering to extract classification structures that adapt to dynamic changes in the classification structure of data.
However, dynamically changing clustering results can be complex, making them difficult to interpret. Therefore, this study proposes a method that takes dynamic changes in uncertainty into account and estimates the degree of reliability in clustering results using a measure derived from the classification structure obtained by fuzzy clustering. This method uses T-norm and asymmetric aggregation operators defined in statistical measure spaces as aggregation functions for clustering results and their reliability. This allows for adjustment of the emphasis placed on clustering results or reliability. Furthermore, we introduce a new weight for the classification structure of objects, which allows the degree of uncertainty at fuzzy clustering cluster boundaries to be adjusted depending on the classification structure of the data. This weight can estimate the reliability in the classification structure of the data depending on the uncertainty of the boundaries of the fuzzy clustering of objects. In other words, if a clear result is obtained even when the uncertainty is set large in fuzzy clustering, there is high reliability that the true data structure is clear. Conversely, if the classification result is ambiguous even with small uncertainty set in fuzzy clustering, there is high reliability that the data structure is truly ambiguous. By utilizing this property, we define a high reliability degree in generalization performance that can be changed depending on the data structure. We demonstrate the effectiveness of this method through several education based numerical examples.