A Type-2 Nonsingleton Type-2 Fuzzy Logic System to Handle Linguistic and Numerical Uncertainties in Real World Environments

Real world environments are characterized by high levels of linguistic and numerical uncertainties. Recently, interval type-2 Fuzzy Logic Systems (FLSs) appeared as an attractive mechanism to handle the high levels of uncertainty available in real world applications. However, the majority of the type-2 FLSs handle the linguistic and numerical uncertainties using singleton interval type-2 FLSs that mix the numerical and linguistic uncertainties to be handled only by the linguistic labels type-2 fuzzy sets. However, this seems paradoxical as this ignores the fact that if numerical uncertainties were present they should affect the incoming inputs to the FLS and hence we cannot treat the incoming FLS inputs as perfect signals as in the case of singleton FLSs. Even in papers that employed nonsingleton type-2 FLSs, the input signals were having a predefined shape (mostly Gaussian or triangular) which might not reflect the real uncertainty distribution associated with the given sensor. This work presents an interval type-2 FLS approach where the numerical uncertainties will be modelled and handled by nonsingleton type-2 fuzzy inputs and the linguistic uncertainties will be handled by interval type-2 fuzzy sets to represent the antecedents' linguistic labels. The nonsingleton type-2 fuzzy inputs are dynamic and they are automatically generated from data and they do not assume a specific shape about the distribution associated with the given sensor. The paper will present the system description and we will present an example, which employs real-world data to clarify the presented approach.