Highest Membership Degree Research Articles

DECISION METHOD FOR STATES VALIDATION IN DRINKING WATER PLANT MONITORING

Abstract This paper proposes a transitions validation method between system functional states in drinking water plant monitoring. The method is based in fuzzy entropy measure. The water plant is monitored by means of fuzzy classification method. The classification algorithm provides the membership degrees of the instant system data (individual) to all possible identified functional states (classes) of the water plant. Usually, the higher membership degree determines the recognized class. However, this criterion leads to uncertainty levels when decision is based on a bad conditioned fuzzy set due to similar membership degrees. The proposed method validates the recognized functional state in presence of uncertainty.

Interactive Fuzzy Linear Programming with Two-Phase Approach

This paper is for applying interactive fuzzy linear programming for the problem of product mix planning, which is one of the aggregate planning problem. We developed a modified algorithm, which has two-phase approach for interactive fuzzy linear programming to get a better solution. Adding two-phase method, we expect to obtain not only the highest membership degree, but also a better utilization of each constrained resource.

Classification of Remote Sensing Images From Urban Areas Using a Fuzzy Possibilistic Model

The classification of very high-resolution remotely sensed images from urban areas is addressed. Previous studies have shown the interest of exploiting the local geometrical information of each pixel to improve the classification. This is performed using the derivative morphological profile (DMP) obtained with a granulometric approach, using opening and closing operators. For each pixel, this DMP constitutes the feature vector on which the classification is based. In this letter, we present an interpretation of the DMP in terms of a fuzzy measurement of the characteristic size and contrast of each structure. This fuzzy measure can be compared to predefined possibility distributions to derive a membership degree for a set of given classes. The decision is taken by selecting the class with the highest membership degree. This model is illustrated and validated in a classification problem using IKONOS images.

Enumeration of All Possibly Optimal Vertices with Possible Optimality Degrees in Linear Programming Problems with a Possibilistic Objective Function

In this paper, we treat linear programming problems with fuzzy objective function coefficients. To such a problem, the possibly optimal solution set is defined as a fuzzy set. It is shown that any possibly optimal solution can be represented by a convex combination of possibly optimal vertices. A method to enumerate all possibly optimal vertices with their membership degrees is developed. It is shown that, given a possibly optimal extreme point with a higher membership degree, the membership degree of an adjacent extreme point is calculated by solving a linear programming problem and that all possibly optimal vertices are enumerated sequentially by tracing adjacent possibly optimal extreme points from a possibly optimal extreme point with the highest membership degree.

Feature selection based on a modified fuzzy C-means algorithm with supervision

In this paper we propose a new approach to feature selection based on a modified fuzzy C-means algorithm with supervision (MFCMS). MFCMS completes the unsupervised learning of classical fuzzy C-means with labeled patterns. The labeled patterns allow MFCMS to accurately model the shape of each cluster and consequently to highlight the features which result to be particularly effective to characterize a cluster. These features are distinguished by a low variance of their values for the patterns with a high membership degree to the cluster. If, with respect to these features, the distance between the prototype of the cluster and the prototypes of the other clusters is high, then these features have the property of discriminating between the cluster and the other clusters. To take these two aspects into account, for each cluster and each feature, we introduce a purposely defined index: the higher the value of the index, the higher the discrimination capability of the feature for the cluster. We execute MFCMS on the training set considering all patterns as labeled. Then, we retain the features which are associated, at least for one cluster, with an index larger than a threshold τ. We applied MFCMS to several real-world pattern classification benchmarks. We used the well-known k-nearest neighbors as learning algorithm. We show that feature selection performed by MFCMS achieved an improvement in generalization on all data sets.

Delineation and quantitation of brain lesions by fuzzy clustering in Positron Emission Tomography

In this study, we investigate the application of the fuzzy clustering to the anatomical localization and quantitation of brain lesions in Positron Emission Tomography (PET) images. The method is based on the Fuzzy C-Means (FCM) algorithm. The algorithm segments the PET image data points into a given number of clusters. Each cluster is an homogeneous region of the brain (e.g. tumor). A feature vector is assigned to a cluster which has the highest membership degree. Having the label affected by the FCM algorthm to a cluster, one may easily compute the corresponding spatial localization, area and perimeter. Studies concerning the evolution of a tumor after different treatments in two patients are presented.