Yager's OWA Research Articles

Bipolar ordered weighted averages: BIOWA operators

OWA operators were introduced by Yager and their Choquet integral-based representation was shown by Grabisch. Based on bi-capacities and related Choquet integral introduced by Grabisch and Labreuche, a new generalization of OWA operators, namely BIOWA operators are introduced. Our approach is exemplified by several examples. Bi-capacities leading to the standard Yager's OWA operators on real line are completely characterized. We introduce and exemplify quantifiers generating BIOWA operators with an arbitrary arity, and their orness. Finally, orness of BIOWA operators is also introduced and studied.

Fuzzy c-ordered-means clustering

Fuzzy clustering helps to find natural vague boundaries in data. The fuzzy c-means method is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantages of this method is its sensitivity to the presence of noise and outliers in data. This paper introduces a new robust fuzzy clustering method named Fuzzy C-Ordered-Means (FCOM) clustering. This method uses both the Huber's M-estimators and the Yager's OWA operators to obtain its robustness. The proposed method is compared to many other ones, e.g.: the Fuzzy C-Means (FCM), the Possibilistic Clustering (PC), the fuzzy Noise Clustering Method (NCM), the Lp norm clustering (Lp FCM) (0<p<1), the L1 norm clustering (L1 FCM), the Fuzzy Clustering with Polynomial Fuzzifier (PFCM) and the ε-insensitive Fuzzy C-Means (βFCM). To this end experiments on synthetic data with outliers have been performed as well as on data with heavy-tailed and overlapping groups of points in background noise.

On robust fuzzy c-regression models

One of the most popular clustering methods based on minimization of a criterion function is the fuzzy c-means one. Its generalization by application of hyperplane shaped prototypes of the clusters is known as the Fuzzy C-Regression Models (FCRM) method. Although with this generalization many new applications of clustering emerged, it appeared to be rather sensitive to poor initialization and to the presence of noise and outliers in data. In this paper we introduce a new objective function, using the Huber's M-estimators and the Yager's OWA operators to overcome the disadvantages of the approach considered. We derive and describe an algorithm for minimization of the objective function defined. We have called it the Fuzzy C-Ordered-Regression Models (FCORM) clustering algorithm. The algorithm is compared to a few other important reference ones. To this end experiments on synthetic data with various types of noise and different numbers of outliers are carried out. We investigate the methods performance in the conditions that can be encountered in signal analysis. Large-scale simulations demonstrate the competitiveness and usefulness of the method proposed.

Extending Yager's orness concept for the OWA aggregators to other mean operators

In this paper, we address the problem of defining the orness (closeness to the maximum) and andness (closeness to the minimum) of fuzzy aggregation operators. In particular, we center our study in fuzzy mean aggregators (as defined by Dubois, Prade and Yager). For this purpose, we propose the introduction of the orness distribution function, orness average value, orness extension measure and orness sequence, which we believe are valid concepts to characterize this type of aggregation operators. We study their application to several well-known mean operators, and prove as well that, in the case of Yager's OWA operators, the orness average value that we propose coincides with Yager's original orness definition. We also introduce a method for the construction of mean operators from a predefined orness distribution function and make some considerations about the extension of these concepts to the cases of weighted aggregations or aggregations based on fuzzy measures.

An analytic characterization of some aggregation operators

A class of aggregation operators that includes Yager's OWA operators is introduced. Both classes are completely characterized by means of their functional and analytic properties. The results are discussed from the point of view of representational measurement theory. © 1998 John Wiley & Sons, Inc.13: 59–68, 1998