Abstract--- Fuzzy c-means clustering (FCM) with spatial constraints (FCM_S) is an effective algorithm suitable for image segmentation. Its effectiveness contributes not only to introduction of fuzziness for belongingness of each pixel but also to exploitation of spatial contextual information. Although the contextual information can raise its insensitivity to noise to some extent, FCM_S (1) still lacks enough robustness to noise and outliers and (2) is not suitable for revealing non-Euclidean structure of the input data due to the use of Euclidean distance (L2 norm). In this paper, to overcome the above problems, we first propose two variants, FCM_S1 and FCM_S2, of FCM_S to aim at simplifying its computation and then extend them, including

image segmentation

Abstract not found

Initially, an axiomatic approach to the definitions of fuzzy connectives are recalled. Based on these definitions several important fuzzy connectives and their properties are described. Then, the idea of approximate reasoning using generalized modus ponens and fuzzy implication are considered. After reviewing the well-known fuzzy systems, the artificial neural network based on logical interpretation of if-then rules is presented. The elimination of non-informative part of final fuzzy set before defuzzification plays the key role in this system. Then, new learning methods tolerant to imprecision are introduced and used to learning this system. The proposed learning methods make it possible to dispose an intrinsic inconsistency of neurofuzzy modeling, where zero-tolerance learning is used to obtain fuzzy model tolerant to imprecision. These new methods may be called #-insensitive learning, where, in order to fit the fuzzy model to real data, the weighted #-insensitive loss function is used. The #-insensitive learning leads to a fuzzy model with minimal Vapnik-Chervonenkis dimension, which results in an improved generalization ability of this system. Another advantage of the proposed learning methods is their outliers robustness. In this paper, two approaches to solving the #-insensitive learning problem are presented. The first approach leads to a quadratic programming problem with bound constraints and one linear equality constraint. The second approach leads to a problem of solving a system of linear inequalities. Three computationally efficient numerical methods for the #-insensitive learning are proposed. Finally, an example is given to demonstrate the validity of the introduced methods.

Weighted fuzzy clustering for capability-driven service aggregation

Abstract not found