We present a TSK (Takagi-Sugeno-Kang)-based Linguistic Fuzzy Model (TSK-LFM) with uncertain model output. Based on the Linguistic Model (LM) proposed by Pedrycz, we develop a comprehensive design framework. The main design process is composed of the automatic generation of the contexts, fuzzy rule extraction by Context-based Fuzzy C-Means (CFCM) clustering, connection of bias term, and combination of TSK and linguistic context. Finally, we contrast the performance of the presented models with other models for coagulant dosing process in a water purification plant.

This paper first presents the performance analysis of the NACF algorithm. The results show the possibility of the degradation in the convergence speed. To improve the convergence speed, the bias term is introduced into the NACF algorithm and its efficiency is investigated through the computer simulations.