# From Expert Words Directly to Numerical Simulations: Group-Theoretic Approach to Computing with Words in Information/Intelligent Systems

## Abstract

In many real-life situations, e.g., when making an environmental decision, it is important to be able to predict long-term consequences of different decisions. Very often, these predictions must be done in the situation where the only available information consists of expert rules, which are formulated by words from natural language. One possible way to transform these expert words into numerical simulation (leading to prediction) is to use the fuzzy control methodology. However, there is a problem with using this methodology: it invokes replacing each word by a membership function, and this replacement drastically increases the required computer space (and thus, increases the computation time), i.e., it “de-granulates” the original compact description. It is, therefore, desirable to get from the original words directly to numerical simulations, thus avoiding this de-granulation.

In seeking this direct transformation, we will use the experience of modern physics, where symmetry groups are a tool that enables to compress complicated differential equations into compact form. In our previous papers, we have shown that the symmetry group approach can be used to find optimal membership functions, optimal t-norms and t-conorms, and optimal defuzzification procedures. In this paper, we show that the same approach can also be used to combine these steps and produce an (optimal) direct transformation from words to numerical results.

## Keywords

Membership Function Fuzzy System Optimality Criterion Fuzzy Control Direct Transformation## Preview

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