The ordered weighted averaging (OWA) operator of Yager was introduced to provide a method for aggregating several inputs which lies between the Max and Min operators. The fundamental aspect of the OWA operator is a reordering step in which the input arguments are re-arranged according to their actual relative value. In this paper we describe a modified OWA operator in which the input arguments are not re-arranged according to their actual relative values but rather according to their estimated relative values. We describe an unusual application of this operator to lossless image compression.

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Robust signal processing algorithms rely on integer ordered statistics. This means that such algorithms cannot be used in a fuzzy environment where variables have fuzzy ranks. In this paper, we show how to calculate the kth order statistic for a set of arguments with fuzzy rank and thereby use classical robust signal processing algorithms in a fuzzy environment. The paper concludes with a simple application of using the fuzzy kth ordered statistic to filtering a noisy signal. ᮊ