A reconstruction decoder for computing with words

The Word decoder is a very important approach for decoding in the Perceptual Computer. It maps the computing with words (CWWs) engine output, which is a fuzzy set, into a word in a codebook so that it can be understood. However, the Word decoder suffers from significant information loss, i.e., the fuzzy set model of the mapped word may be quite different from the fuzzy set output by the CWW engine, especially when the codebook is small. In this paper we propose a Reconstruction decoder, which represents the CWW engine output as a combination of two successive codebook words with minimum information loss by solving a constrained optimization problem. The Reconstruction decoder preserves the shape information of the CWW engine output in a simple form without sacrificing much accuracy. It can be viewed as a generalized Word decoder and is also implicitly a Rank decoder. Moreover, it is equivalent to the 2-tuple representation under certain conditions. The effectiveness of the Reconstruction decoder is verified by three experiments.