Regaining Comprehensibility of Approximative Fuzzy Models via the Use of Linguistic Hedges

This chapter presents an effective and efficient approach for translating rules that use approximative sets to rules that use descriptive sets and linguistic hedges of predefined meaning. Following this approach, descriptive models can take advantage of any existing approach to approximative modelling which is generally efficient and accurate, whilst employing rules that are comprehensible to human users. This allows the comprehensibility of approximative models to be restored. Although trapezoidal fuzzy sets, including triangular ones, are most commonly used in fuzzy modelling for computational simplicity, applications of conventional linguistic hedges over such sets typically fail to result in significant changes of the sets definition. In particular, the full membership part of a trapezoid membership function does not change at all. This does not help in many modelling tasks as intended. Therefore, this chapter also presents an improved version of more effective hedges specifically devised for trapezoidal fuzzy sets, including three which do not appear in the literature. Simulation results are provided to demonstrate the advantages of utilising the revised and newly introduced hedges for assisting fuzzy modelling, in comparison to the use of conventional ones.