A mamdani-takagi-sugeno based linguistic neural-fuzzy inference system for improved interpretability-accuracy representation

Existing fuzzy and neural-fuzzy systems in the literature can be classified into three main categories, i.e. Mamdani, Takagi-Sugeno (T-S) or Tsukamoto systems based on their implemented fuzzy rule structures. Furthermore, depending on the intended modeling objective, there are two main approaches to fuzzy and neural-fuzzy modeling; namely: linguistic fuzzy modeling (LFM) and precise fuzzy modeling (PFM). In general, Mamdani fuzzy models are more interpretive but less accurate than T-S fuzzy models, and improving the output accuracy of Mamdani fuzzy models usually implies using a larger rule-base with increased complexity and reduced interpretability. This paper presents a linguistic neural-fuzzy architecture that combines the explanatory trait of Mamdani-typed fuzzy models with the output accuracy of T-S fuzzy systems in a hybrid approach referred to as Mamdani-Tagaki-Sugneo (MTS) fuzzy modeling. The resultant network is named the MTS linguistic neural-fuzzy inference system (MTS-LiNFIS). The improved trade-off between the interpretability and accuracy demands of Mamdani-based fuzzy approximation is demonstrated through the evaluation of the learning and modeling performances of MTS-LiNFIS using a simple benchmark application.