Towards comparing adaptive type-2 input based non-singleton type-2 FLS and non-singleton FLSs employing Gaussian inputs

Abstract

Fuzzy logic Systems (FLSs) are credited with providing very good performances which are able to handle the uncertainty and imprecision present in real-world environments and applications. Using type-2 FLSs can enable handling higher levels of uncertainty when compared to type-1 FLSs. The majority of the type-2 FLSs employ singleton type-2 FLSs which handle the encountered input uncertainty through fuzzy sets representing the linguistic labels in the antecedent fuzzy sets. However, singleton type-2 FLSs assume that the input signal is perfect and thus there is no provision for handling the uncertainties in the incoming input signals. Hence, there have been some efforts to investigate non-singleton type-2 FLS. However, the papers that employed non-singleton type-2 FLSs assumed that the fuzzy inputs are having a predefined shape (mostly Gaussian) which might not model the encountered uncertainty properly. In our previous works, we presented adaptive type-2 input based non-singleton type-2 FLS which employs dynamic inputs which are not assuming any specific shape. We have shown how the adaptive type-2 input based non-singleton type-2 FLS outperforms singleton (type-1 and type-2) FLSs. In this paper, we will compare the adaptive type-2 input based non-singleton type-2 FLS with other non-singleton (type-1 and type-2) FLSs which employ Gaussian fuzzy inputs. We will present real-world robot experiments showing how the adaptive type-2 input based non-singleton type-2 FLS outperforms the non-singleton FLSs which employ Gaussian fuzzy inputs when large amounts of uncertainty are encountered.