## 7 Discussion
### Comparison of Computational Complexity  
The computational complexity of the proposed method is compared with the identification algorithms reviewed in Section 1.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Article** & **Relation to the Proposed Method** & **Contribution of the Proposed Method** \\ \hline
[4,5,27,28] & Implements T-S identification, uses unidimensional membership functions, generates rules that are outside the system’s area of influence. & Uses multidimensional membership functions to improve the accuracy of the fuzzy rule placement. \\ \hline
[35] & Uses genetic algorithms for the design of membership functions. The method is computationally intensive. & This method reduces computational overhead by ensuring that the rules and their centers of gravity are strategically placed within the data map, thereby avoiding unnecessary computations. \\ \hline
[36] & Designs multidimensional membership functions using radial basis function (RBF) networks, presenting high complexity in optimization and parameter selection. & Uses a physically-based approach (moments of inertia), facilitating model understanding and adjustment by engineers. \\ \hline
[37] & Designs membership functions based on Gaussian distributions, presenting a hierarchical approach to improve parameter estimation accuracy. & Our proposal is specifically designed for nonlinear multivariable systems, providing a robust formulation for these complex environments, whereas [37]’s approach focuses mainly on improving parameter accuracy in a more general context. \\ \hline
[38] & The design and tuning of RBF networks can be complex, especially for systems with highly dynamic and unpredictable behaviors. Adequate parameter selection for RBF networks is crucial and may require a laborious iterative process. & Uses moments of inertia to design membership functions, which is a more straightforward and less resource-intensive process. This reduces design complexity and facilitates implementation. \\ \hline
[39] & Designs multidimensional membership functions using interpolation methods and optimization techniques to improve nonlinear system control. Although it enhances nonlinear system control, it may not be as effective in reducing identification errors due to reliance on interpolation techniques. & Using moments of inertia to design membership functions provides a more effective reduction in identification distribution and dynamics. \\ \hline
[40] & Uses advanced interpolation and optimization techniques to design multidimensional membership functions. These techniques help better capture complex nonlinear relationships in the data. Although advanced interpolation and optimization techniques can improve accuracy, they may not ensure that rules are placed in the most appropriate intervals of the data space. \\ \hline \hline \end{tabular}
\end{table}
Table 9: Cited articles—contributions of the proposed method.  
From the computational complexity analysis in Table 10, it can be seen that the proposed method has certain advantages over the works cited in the Introduction Section 1. Some of these advantages stem from the use of solid mechanics concepts.