Encoding words into interval type-2 fuzzy sets: The retained region approach

The first step of implementing computing with words using a perceptual computer is to establish an encoder to transform words into interval type-2 fuzzy sets. In this paper, a novel approach named the retained region approach is introduced for encoding words into interval type-2 fuzzy sets. In the retained region approach, the data part is redesigned relative to the existing approaches, and a new fuzzy set part is established in accordance with the principle of justifiable granularity. The different means and standard deviations of the embedded type-1 fuzzy sets associated with a word are recognized as the origins of its inter-uncertainty, and the relations between them are taken into account in the construction of interval type-2 fuzzy sets. Importantly, the retained region approach is a versatile approach that does not impose redundant constraints on the selection of embedded type-1 fuzzy sets, and the capacity of the retained region can be flexibly adjusted along the two dimensions of the mean and the standard deviation. Finally, the performance of the retained region approach is illustrated by several simulations and comparisons with existing approaches.