On the Concept of Meaningfulness in Constrained Type-2 Fuzzy Sets
Pasquale D'Alterio, Jonathan M. Garibaldi, Robert John · 2019
Constrained type-2 fuzzy sets have been proposed as a tool to model type-2 fuzzy sets starting from a type-1 generator set with uncertainty. This constrained representation only defines as acceptable the embedded sets that have the same shape as the generator set in order to process only membership functions that are considered "meaningful" when using fuzzy operators such as centroid defuzzification. However, the idea of "meaningfulness" has never been clearly defined; at the same time there are some contexts in which a given concept (e.g. medium height) can be reasonably represented by multiple shapes, such as triangular and Gaussian. The aim of this paper is both to formally define the idea of meaningfulness of shapes and to extend the formal definitions of constrained interval type-2 fuzzy sets in order to allow the presence of multiple shapes among the acceptable embedded sets.