Examining the Fuzzy Inference on Mamdani Fuzzy Inference System and Takagi-Sugeno Fuzzy Model

Abstract

Fuzzy Inference Systems (FIS) have emerged as powerful tools for handling complex and uncertain systems in various domains. The two commonly used FIS models are the Mamdani Fuzzy Inference System (MFIS) and the Takagi-Sugeno Fuzzy Model (TSFM). This paper presents a comparative analysis of the fuzzy inference mechanisms employed in these two models. The Mamdani Fuzzy Inference System employs fuzzy rules to map input variables to output variables using linguistic variables and membership functions. It incorporates a fuzzy rule base, fuzzy logic operators, and defuzzification techniques to obtain crisp output values. The MFIS is particularly suitable for dealing with complex and nonlinear systems due to its ability to capture linguistic knowledge through rule-based modeling. On the other hand, the Takagi-Sugeno Fuzzy Model is a fuzzy rule-based model that approximates a system's behavior using a set of linear or nonlinear functions. Instead of employing linguistic variables, the TSFM uses input variables directly to formulate rule consequents. This model is known for its simplicity, interpretability, and computational efficiency. This paper investigates and compares the working principles, architecture, and key characteristics of the Mamdani Fuzzy Inference System and the Takagi-Sugeno Fuzzy Model. It discusses the rule inference process, membership functions, aggregation methods, and defuzzification techniques employed in each model. Additionally, it highlights the strengths and weaknesses of both models in terms of system modeling, interpretability, computational efficiency, and handling uncertainty.