Efficient multi-stage reasoning with fuzzy words

Fuzzy systems are a natural choice for processing coarse granular information, but unfortunately, most fuzzy systems suffer from two drawbacks. Although knowledge is formulated at a coarse granular level using fuzzy sets, most information processing algorithms operate on the details at a fine granular level and are, therefore, computationally costly. Furthermore, the fuzzy results are not expressed with the predefined fuzzy sets that were used to describe fuzzy knowledge in a comprehensive way, and are therefore often difficult to understand. As a solution to these problems, we proposed a methodology in [1], [2] that represents and processes fuzzy information at the coarse granular level. Here, we show that even a chain of inferences, i.e., multi-stage reasoning can be processed entirely at the coarse granular level.