## 7 Conclusions  
In this paper, an attractive extended TP combining with MTP and an improved PSO based on environmental factors and a crossover operator is constructed and proposed, referred to as ECPSO-MTP. The proposed ECPSO-MTP aims to establish a highly efficient P system for solving clustering problems that is integrated with the computing framework of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Image**} & \multirow{2}{*}{**Statistics**} & \multicolumn{4}{c}{**Comparative Approaches**} \\ \cline{3-6}  & & **K-Means** & **SC** & **PSO** & **ECPSO-MTP** \\ \hline \multirow{4}{*}{Castle} & Worst & 0.9302 & 0.9411 & 0.9327 & 0.9413 \\  & Best & 0.9377 & 0.9411 & 0.9377 & 0.9413 \\  & Mean & 0.9346 & 0.9411 & 0.9368 & 0.9413 \\  & S.D. & 0.0033 & \(3.36\times 10^{-16}\) & 0.0019 & \(4.49\times 10^{-16}\) \\  & Worst & 0.6930 & 0.8881 & 0.7669 & 0.7624 \\  & Best & 0.9248 & 0.8940 & 0.7820 & 0.9248 \\  & Mean & 0.7802 & 0.8882 & 0.7807 & 0.8978 \\  & S.D. & 0.0862 & 0.0008 & 0.0029 & 0.0558 \\  & Worst & 0.8205 & 0.9668 & 0.8318 & 0.8241 \\  & Best & 0.9730 & 0.9730 & 0.9730 & 0.9795 \\  & Mean & 0.9124 & 0.9676 & 0.9537 & 0.9696 \\  & S.D. & 0.0668 & 0.0027 & 0.0482 & 0.0671 \\  & Worst & 0.4805 & 0.5232 & 0.4910 & 0.5911 \\  & Best & 0.5860 & 0.7259 & 0.6287 & 0.8435 \\  & Mean & 0.5597 & 0.6233 & 0.5829 & 0.6344 \\  & S.D. & 0.0406 & 0.0620 & 0.0183 & 0.0639 \\  & Worst & 0.7200 & 0.7366 & 0.7497 & 0.7914 \\ Pyramid & Best & 0.7661 & 0.8394 & 0.7594 & 0.8410 \\  & Mean & 0.7533 & 0.7648 & 0.7551 & 0.8354 \\  & S.D. & 0.0157 & 0.0421 & 0.0038 & 0.0073 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Images**} & \multicolumn{4}{c}{**Comparative Approaches**} \\ \cline{2-5}  & **K-Means** & **SC** & **PSO** & **ECPSO-MTP** \\ \hline Lawn & 4 & 2 & 3 & 1 \\ Agar & 4 & 2 & 3 & 1 \\ Church & 4 & 2 & 3 & 1 \\ Castle & 4 & 2 & 3 & 1 \\ Elephants & 4 & 2 & 3 & 1 \\ Lane & 4 & 2 & 3 & 1 \\ Starfish & 4 & 2 & 3 & 1 \\ Pyramid & 4 & 2 & 3 & 1 \\ \hline Total Rank & 32 & 16 & 24 & 8 \\ Average Rank & 4 & 2 & 3 & 1 \\ Deviation & 1.5 & \(-\)0.5 & 0.5 & \(-\)1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Computation results of the Friedman test statistics (Mean). MTP and the evolutionism of PSO. Two types of evolution rules are defined and described in ECPSO-MTP, which are applied to different elementary membranes to evolve objects, including evolution rules with environmental factors and evolution rules with crossover operators. The environmental factor, which uses partitioning information, is randomly allocated to objects to replace global best and participate in the evolution process. The crossover operator is accomplished through the hybridization of the global best of elementary membranes to reject randomness. Information exchange and resource sharing between elementary membranes are accomplished by evolutional symport with promoters of MTP, including forward and backward communication rules. At last, comparison experiments are conducted on benchmark clustering and image segmentation datasets to validate the clustering efficiency of the proposed ECPSO-MTP. The distributed and parallel processing of P systems provides an efficient way for solving complex problems with polynomial or linear complexity. However, the application of P systems is limited by computational incompleteness and implementation difficulty. To address these limitations, many variations of P systems have been designed and developed, particularly extended P systems integrated with EC. The proposed ECPSO-MTP is an instance of such an extended P system. The monodirectional connection between elementary membranes in ECPSO-MTP is straightforward and simple to implement. Future studies will explore the combination of this novel variant of P systems with other SI approaches. In addition, reducing the complexity of this extended P system may become an important area of research in the future.