Frank Chung-Hoon Rhee

Uncertain Fuzzy Clustering: Interval Type-2 Fuzzy Approach to

In many pattern recognition applications, it may be impossible in most cases to obtain perfect knowledge or information for a given pattern set. Uncertain information can create imperfect expressions for pattern sets in various pattern recognition algorithms. Therefore, various types of uncertainty may be taken into account when performing several pattern recognition methods. When one performs clustering with fuzzy sets, fuzzy membership values express assignment availability of patterns for clusters. However, when one assigns fuzzy memberships to a pattern set, imperfect information for a pattern set involves uncertainty which exist in the various parameters that are used in fuzzy membership assignment. When one encounters fuzzy clustering, fuzzy membership design includes various uncertainties (e.g., distance measure, fuzzifier, prototypes, etc.). In this paper, we focus on the uncertainty associated with the fuzzifier parameter m that controls the amount of fuzziness of the final C-partition in the fuzzy C-means (FCM) algorithm. To design and manage uncertainty for fuzzifier m, we extend a pattern set to interval type-2 fuzzy sets using two fuzzifiers m1 and m2 which creates a footprint of uncertainty (FOU) for the fuzzifier m. Then, we incorporate this interval type-2 fuzzy set into FCM to observe the effect of managing uncertainty from the two fuzzifiers. We also provide some solutions to type-reduction and defuzzification (i.e., cluster center updating and hard-partitioning) in FCM. Several experimental results are given to show the validity of our method

C

Type-2 fuzzy sets (T2 FSs) have been shown to manage uncertainty more effectively than T1 fuzzy sets (T1 FSs) in several areas of engineering [4,6-12,15-18,21-27,30]. However, computing with T2 FSs can require undesirably large amount of computations since it involves numerous embedded T2 FSs. To reduce the complexity, interval type-2 fuzzy sets (IT2 FSs) can be used, since the secondary memberships are all equal to one [21]. In this paper, three novel interval type-2 fuzzy membership function (IT2 FMF) generation methods are proposed. The methods are based on heuristics, histograms, and interval type-2 fuzzy C-means. The performance of the methods is evaluated by applying them to back-propagation neural networks (BPNNs). Experimental results for several data sets are given to show the effectiveness of the proposed membership assignments.

-Means

Fuzzy logic has been applied in many engineering disciplines. The problem of fuzzy logic inference is investigated as a question of aggregation of evidence. A fixed network architecture employing general fuzzy unions and intersections is proposed as a mechanism to implement fuzzy logic inference. It is shown that these networks possess desirable theoretical properties. Networks based on parameterized families of operators (such as Yagers union and intersection) have extra predictable properties and admit a training algorithm which produces sharper inference results than were earlier obtained. Simulation studies corroborate the theoretical properties.

Interval type-2 fuzzy membership function generation methods for pattern recognition

In this paper, we introduce a new algorithm for clustering and aggregating relational data (CARD). We assume that data is available in a relational form, where we only have information about the degrees to which pairs of objects in the data set are related. Moreover, we assume that the relational information is represented by multiple dissimilarity matrices. These matrices could have been generated using different sensors, features, or mappings. CARD is designed to aggregate pairwise distances from multiple relational matrices, partition the data into clusters, and learn a relevance weight for each matrix in each cluster simultaneously. The cluster dependent relevance weights offer two advantages. First, they guide the clustering process to partition the data set into more meaningful clusters. Second, they can be used in subsequent steps of a learning system to improve its learning behavior. The performance of the proposed algorithm is illustrated by using it to categorize a collection of 500 color images. We represent the pairwise image dissimilarities by six different relational matrices that encode color, texture, and structure information.

Evidence aggregation networks for fuzzy logic inference

This paper presents a type-2 fuzzy C-means (FCM) algorithm that is an extension of the conventional fuzzy C-means algorithm. In our proposed method, the membership values for each pattern are extended as type-2 fuzzy memberships by assigning membership grades to the type-1 memberships. In doing so, cluster centers that are estimated by type-2 memberships may converge to a more desirable location than cluster centers obtained by a type-1 FCM method in the presence of noise. Experimental results are given to show the effectiveness of our method.

Clustering and aggregation of relational data with applications to image database categorization

This paper presents an interval type-2 fuzzy K-nearest neighbor (NN) algorithm that is an extension of the type-1 fuzzy K-NN algorithm proposed in. In our proposed method, the membership values for each pattern vector are extended as interval type-2 fuzzy memberships by assigning uncertainty to the type-1 memberships. By doing so, the classification result obtained by the interval type-2 fuzzy K-NN is found to be more reasonable than that of the crisp and type-1 fuzzy K-NN. Experimental results are given to show the effectiveness of our method.

A type-2 fuzzy C-means clustering algorithm

Abstract In many decision making systems involving multiple sources, the decisions made may be considered as the result of a rule-based system in which the decision rules are usually enumerated by experts or generated by a learning process. In this paper, we discuss the various issues involved in the generation of fuzzy rules automatically from training data for high-level computer vision. Features are treated as linguistic variables that appear in the antecedent clauses of the rules. We present methods to generate the corresponding linguistic labels (values) and their membership functions. Rules are generated by constructing a minimal approximate fuzzy aggregation network and then training the network using gradient descent methods. Several examples are given.

An interval type-2 fuzzy K-nearest neighbor

This paper presents an interval type-2 fuzzy C-spherical shells (FCSS) algorithm that is an extension of the type-1 FCSS algorithm proposed in. In our proposed method, the membership values for each pattern vector are extended as interval type-2 fuzzy memberships by assigning uncertainty to the type-1 memberships. By doing so, the cluster boundary obtained by the interval type-2 FCSS can be found to be more desirable than that of type-1 FCSS in the presence of noise. Experimental results are given to show the effectiveness of our method.

Fuzzy rule generation methods for high-level computer vision

This paper presents an interval type-2 fuzzy perceptron algorithm that is an extension of the type-1 fuzzy perceptron algorithm proposed by J. Keller et al. (1985). In our proposed method, the membership values for each pattern vector are extended as interval type-2 fuzzy memberships by assigning uncertainty to the type-1 memberships. By doing so, the decision boundary obtained by interval type-2 fuzzy memberships can converge to a more desirable location than the boundary obtained by crisp and type-1 fuzzy perceptron methods. Experimental results are given to show the effectiveness of our method.

An interval type-2 fuzzy C spherical shells algorithm

Type-2 fuzzy sets has been shown to manage uncertainty more effectively than type-1 fuzzy sets in several pattern recognition applications. However, computing with type-2 fuzzy sets can require high computational complexity since it involves numerous embedded type-2 fuzzy sets. To reduce the complexity, interval type-2 fuzzy sets can be used. In this paper, an interval type-2 fuzzy membership design method and its application to radial basis function (RBF) neural networks is proposed. Type-1 fuzzy memberships which are computed from the centroid of the interval type-2 fuzzy memberships are incorporated into the RBF neural network The proposed membership assignment is shown to improve the classification performance of the RBF neural network since the uncertainty of pattern data are desirably controlled by interval type-2 fuzzy memberships. Experimental results for several data sets are given.