Ordering of fuzzy numbers through linguistic approximation based on Bonissone´s two step method

Linguistic approximation is a suitable way of transforming mathematical outputs into words that can be easily used and understood by laymen. The methods for linguistic approximation range from simple distance based ones to more complex methods aspiring on finding high semantic match between the approximated output and its linguistic label. This paper builds on Bonissone´s proposal of a two step method for linguistic approximation based on a pattern recognition approach. It suggests an algorithm for finding a partial ordering of fuzzy numbers utilizing the partial results from the two step method. As such it proposes a means of finding a partial ordering of fuzzy numbers through linguistic approximation. The proposed algorithm is showcased on several numerical examples and its performance is briefly discussed.