Wen-Liang Hung

Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance

This paper presents a new method for similarity measures between intuitionistic fuzzy sets (IFSs). We will present a method to calculate the distance between IFSs on the basis of the Hausdorff distance. We will then use this distance to generate a new similarity measure to calculate the degree of similarity between IFSs. Finally we will prove some properties of the proposed similarity measure and use several examples to compare the proposed similarity measure with existing methods. Numerical results show that the proposed similarity measure is much simpler than existing methods and is well suited to use with linguistic variables.

Correlation of intuitionistic fuzzy sets by centroid method

Abstract In this paper, we propose a method to calculate the correlation coefficient of intuitionistic fuzzy sets by means of “centroid”. This value obtained from our formula tell us not only the strength of relationship between the intuitionistic fuzzy sets, but also whether the intuitionistic fuzzy sets are positively or negatively related. This approach looks better than previous methods which only evaluate the strength of the relation. Furthermore, we extend the “centroid” method to interval-valued intuitionistic fuzzy sets. The value of the correlation coefficient between interval-valued intuitionistic fuzzy sets lies in the interval [−1,1], as computed from our formula.

On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition

The importance of suitable distance measures between intuitionistic fuzzy sets (IFSs) arises because of the role they play in the inference problem. A concept closely related to one of distance measures is a divergence measure based on the idea of information-theoretic entropy that was first introduced in communication theory by Shannon (1949). It is known that J-divergence is an important family of divergences. In this paper, we construct J-divergence between IFSs. The proposed J-divergence can induce some useful distance and similarity measures between IFSs. Numerical examples demonstrate that the proposed measures perform well in clustering and pattern recognition.

Fuzzy entropy on intuitionistic fuzzy sets

In this article we exploit the concept of probability for defining the fuzzy entropy of intuitionistic fuzzy sets (IFSs). We then propose two families of entropy measures for IFSs and also construct the axiom definition and properties. Two definitions of entropy for IFSs proposed by Burillo and Bustince in 1996 and Szmidt and Kacprzyk in 2001 are used. The first one allows us to measure the degree of intuitionism of an IFS, whereas the second one is a nonprobabilistic‐type entropy measure with a geometric interpretation of IFSs used in comparison with our proposed entropy of IFSs in the numerical comparisons. The results show that the proposed entropy measures seem to be more reliable for presenting the degree of fuzziness of an IFS.

A similarity measure of intuitionistic fuzzy sets based on the Sugeno integral with its application to pattern recognition

Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although several similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, no one has considered the use of the Sugeno integral to define them. Since the Sugeno integral provides an expected-value-like operation, it can be a useful tool in defining the expected total similarity degree between two intuitionistic fuzzy sets. In this paper, we propose a new similarity measure formula for intuitionistic fuzzy sets induced by the Sugeno integral. Some examples are illustrated to compare the proposed method with several existing methods. Numerical results show that the proposed similarity measure is more reasonable than those existing methods. On the other hand, measuring the similarity between intuitionistic fuzzy sets is also important in pattern recognition. Finally, the proposed similarity measure uses a robust clustering method to recognize the patterns of intuitionistic fuzzy sets.

Parameter selection for suppressed fuzzy c-means with an application to MRI segmentation

This paper presents an algorithm, called the modified suppressed fuzzy c-means (MS-FCM), that simultaneously performs clustering and parameter selection for the suppressed fuzzy c-means (S-FCM) algorithm proposed by [Fan, J.L., Zhen, W.Z., Xie, W.X., 2003. Suppressed fuzzy c-means clustering algorithm. Pattern Recognition Lett. 24, 1607-1612]. The proposed algorithm is computationally simple, and is able to select the parameter @a in S-FCM with a prototype-driven learning. The parameter selection is based on the exponential separation strength between clusters. Numerical examples will serve to illustrate the effectiveness of the proposed MS-FCM algorithm. Finally, the S-FCM and MS-FCM algorithms are applied in the segmentation of the magnetic resonance image (MRI) of an ophthalmic patient. In our comparisons of S-FCM, MS-FCM, alternative FCM (AFCM) proposed by [Wu, K.L., Yang, M.S., 2002. Alternative c-means clustering algorithms. Pattern Recognition 35, 2267-2278] and similarity-based clustering method (SCM) proposed by [Yang, M.S., Wu, K.L., 2004. A similarity-based robust clustering method. IEEE Trans. Pattern Anal. Machine Intell. 26, 434-448] for these MRI segmentation results, we find that these four techniques provide useful information as an aid to diagnosis in ophthalmology. However, the MS-FCM provides better detection of abnormal tissue than S-FCM, AFCM and SCM when based on a window selection. Overall, the MS-FCM clustering algorithm is more efficient and is strongly recommended as an MRI segmentation technique.

SIMILARITY MEASURES BETWEEN TYPE-2 FUZZY SETS

In this paper, we give similarity measures between type-2 fuzzy sets and provide the axiom definition and properties of these measures. For practical use, we show how to compute the similarities between Gaussian type-2 fuzzy sets. Yang and Shihs [22] algorithm, a clustering method based on fuzzy relations by beginning with a similarity matrix, is applied to these Gaussian type-2 fuzzy sets by beginning with these similarities. The clustering results are reasonable consisting of a hierarchical tree according to different levels.

Fuzzy clustering on LR-type fuzzy numbers with an application in Taiwanese tea evaluation

This paper presents a fuzzy clustering algorithm, called the alternative fuzzy c-numbers (AFCN) clustering algorithm, for LR-type fuzzy numbers based on an exponential-type distance function. On the basis of the gross error sensitivity and influence function, this exponential-type distance is claimed to be robust with respect to noise and outliers. Hence, the AFCN clustering algorithm is more robust than the fuzzy c-numbers (FCN) clustering algorithm presented by Yang and Ko (Fuzzy Sets and Systems 84 (1996) 49). Some numerical experiments were performed to assess the performance of FCN and AFCN. Numerical results clearly indicate AFCN to be superior in performance to FCN. Finally, we apply the FCN and AFCN algorithms to real data. The experimental results show the superiority of AFCN in Taiwanese tea evaluation.

Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets

In this paper, we propose a method to calculate the correlation coefficient of intuitionistic fuzzy sets by means of mathematical statistics. This value obtained from our formula tell us not only the strength of relationship between the intuitionistic fuzzy sets, but also whether the intuitionistic fuzzy sets are positively or negatively related. This approach looks better than previous methods which only evaluate the strength of the relation. Furthermore, we extend the proposed method to interval-valued intuitionistic fuzzy sets. The value of the correlation coefficient between interval-valued intuitionistic fuzzy sets lies in the interval [-1, 1], as computed from our formula.

Bootstrapping approach to feature-weight selection in fuzzy c-means algorithms with an application in color image segmentation

The fuzzy c-means (FCM) algorithm is a popular fuzzy clustering method. It is known that an appropriate assignment to feature weights can improve the performance of FCM. In this paper, we use the bootstrap method proposed by Efron [Efron, B., 1979. Bootstrap methods: Another look at the jackknife. Ann. Statist. 7, 1-26] to select feature weights based on statistical variations in the data. It is simple to compute and interpret for feature-weights selection. Compared with the feature weights proposed by Wang et al. [Wang, X.Z., Wang, Y.D., Wang, L.J., 2004. Improving fuzzy c-means clustering based on feature-weight learning. Pattern Recognition Lett. 25, 1123-1132], Modha and Spangler [Modha, D.S., Spangler, W.S., 2003. Feature weighting in k-means clustering. Machine Learn. 52, 217-237], Pal et al. [Pal, S.K., De, R.K., Basak, J., 2000. Unsupervised feature evaluation: A neuro-fuzzy approach. IEEE Trans. Neural Networks 11, 366-376] and Basak et al. [Basak, J., De, R.K., Pal, S.K., 1998. Unsupervised feature selection using a neuro-fuzzy approach. Pattern Recognition Lett. 19, 997-1006] we find that the proposed method provides a better clustering performance for Iris data and several simulated datasets based on error rate criterion and also performs well in color image segmentation according to Liu and Yangs [Liu, J., Yang, Y.H., 1994. Multiresolution color image segmentation technique. IEEE Trans. Pattern Anal. Machine Intell. 16, 689-700] evaluation function.