Combining fuzzy words

Dealing with coarse granular information is very attractive for several reasons: 1. The number of details in an application might be so large that processing is not feasible without abstracting from details. 2. As we see, e.g., in spoken languages, coarse granular information is often easier to understand than lots of details. 3. Detailed information is not always available. Since coarse granular information is often fuzzy, fuzzy systems are a natural choice for its processing. Unfortunately, most fuzzy systems suffer from two drawbacks: Although knowledge is formulated on a coarse granular level using fuzzy sets, the number of calculations for processing fuzzy knowledge depends on the number of details and not just on the number of fuzzy sets. Furthermore, the fuzzy results cannot be expressed with the predefined fuzzy sets that we used to describe fuzzy knowledge in a comprehensive way, and are therefore often difficult to understand. As a solution to these problems, we propose a methodology that represents fuzzy information generally by a combination of predefined fuzzy sets (fuzzy words). In this way, processing can be based on the small number of fuzzy words and the results are easy to understand. In this article, we focus on the mathematical basics for combining fuzzy words.