Publications

We investigate essential relationships between generalization capabilities and fuzziness of fuzzy classifiers (viz., the classifiers whose outputs are vectors of membership grades of a pattern to the individual classes). The study makes a claim and offers sound evidence behind the observation that higher fuzziness of a fuzzy classifier may imply better generalization aspects of the classifier, especially for classification data exhibiting complex boundaries. This observation is not intuitive with a commonly accepted position in "traditional" pattern recognition. The relationship that obeys the conditional maximum entropy principle is experimentally confirmed. Furthermore, the relationship can be explained by the fact that samples located close to classification boundaries are more difficult to be correctly classified than the samples positioned far from the boundaries. This relationship is expected to provide some guidelines as to the improvement of generalization aspects of fuzzy classifiers.

Anomaly detection in time series is a popular topic focusing on a variety of applications, which achieves a wealth of results. However, there are many cases of missing anomaly and increased false alarm in most of the existing works. Inspired by the concept of interval-sets, this paper proposes an anomaly detection algorithm called a fuzzy interval-set and tries to detect the potential value of the time series from a new perspective. In the proposed algorithm, a time series will be divided into several subsequences. Each subsequence is regarded as an interval-set depending on its value space and boundary of the subsequence. The similarity measurements between interval sets adopt interval operations and point probability distributions of the interval bounds. In addition, an anomaly score is defined based on similarity results. The experimental results on synthetic and real data sets indicate that the proposed algorithm has better discriminative performance than the piecewise aggregate approximation method and reduces the false alarm rate significantly.

In this paper, a fuzzy c-means clustering algorithm based on interval-valued weights is proposed for improving clustering performance. In the proposed algorithm, the interval-valued weights are first constructed by synergy of the ReliefF algorithm and the analytic hierarchy process (AHP) method, and then they are transformed into a constraint condition associating with each weight variable in the weighted clustering objective function. In the sequence, the weighted clustering objective function is solved by combining the Lagrange multiplier method with the gradient-based iteration computation. In the whole process of algorithm iteration, a compulsion strategy with human–computer cooperation is adopted to ensure each weight variable satisfies interval constraint itself. Three well-known data set are used to perform profound experiments. Experimental results clearly show that the proposed algorithm has better clustering performance than other the weighted fuzzy c-means clustering algorithm.

This paper proposes a novel preference scale function based on the Poincare metric for decision-making with Intuitionistic Fuzzy Sets (IFSs). We first introduce a pair of two-dimensional vectors expressing the IFSs in multi-criteria decision-making problems, which satisfy the Poincare metric, and then construct a preference scale function based on it. The proposed scale function can address, without resorting to the accuracy function, the issue of the existing score function for IFSs returning zero scores when membership and non-membership degrees of an element are the same. The advantages of the proposed scale function over the existing ones are demonstrated through illustrative examples.