## 5 Conclusions  
We aimed here to address the general identification problem of the MCA model of Equation (2). This conceived using regression protocols and data pairs \((x,y)\) in order to unfold \(\alpha(x)\) and \(\beta(x)\) as independent functions granting highest reproducibility. This task was addressed here in two ways. A first one was through Weierstrass approximation theory that anticipated \(\alpha(x)\) and \(\beta(x)\) as determined by Equation (8) through Equation (10) and that epitomize by the \(\lambda_{m}(u)\) form in geometrical space. A second way to address the general identification problem relied on an ORBM slant. This conceived \(\alpha(x)\) and \(\beta(x)\) in the forms given by Equation (22) and Equation (23) respectively, and that engendered the \(\Omega_{BL}(u)\), \(\Omega_{ML}(u)\) and \(\Omega_{TSK}(u)\) protocols also intended to be fitted in geometrical space. This ORBM approach is also behind the adaptation of the form \(H_{TSK}(x)\) that takes advantage of the oustanding approximation capabilities of the general output of a first order TSK fuzzy model grants polyphasic interpolation of inherent MCA pattern in arithmetical scales. A consistent fit of the \(\lambda_{m}(u)\) arrangement could set up reliable reproducibility by direct retransformation to arithmetical scales. Moreover, this approach can also entail estimation of break point inherent to biphasic patterns. Concomitant broken line \(\Omega_{BL}(u)\) or weighted linear segment mixture \(\Omega_{ML}(u)\) regression could also offer reasonable MCA identification in many instances of allometric examination. Nevertheless, it is opportune to emphasize gains derived from adoption of a \(\Omega_{TSK}(u)\) approach. This construct bears a flexible computational assembly that allows intuitive and interactive integration of previous knowledge into the analysis [132]. This gives \(\Omega_{TSK}(u)\) a relative advantage over the conventional protocols addressed here. Moreover, analysis of model performance metrics show that the mean response function \(E_{\OmegaTSK}(y|x)\) brings about similar reproducibility strength as its \(E_{HTSK}(y|x)\) counterpart. Therefore, \(\Omega_{TSK}(u)\) could grant efficient identification of allometric proxies indistinctly of inherent complexity. This device also drives direct and intuitive identification of multiple break points for transition among successive growth phases comprising a PLA pattern. It is also worth highlighting that the extraordinary approximation capabilities of a first-order KSK fuzzy model that engenders \(\Omega_{TSK}(u)\) grant reliable identification of the scaling functions \(\alpha(x)\) and \(\beta(x)\) by retransforming fitted form of \(\Omega_{TSK}(u)\) to arithmetical scales. We can then consider that the essential aim of this contribution was fulfilled. The TSK arrangement also allows efficient implementation of the \(\kappa(x)\) criterion for curvature assessment. The identification schemes offered can be conveniently implemented on available data by using the codes provided. In summary, the presented MCA paradigm, along with identification schemes plus a suitable CF form could grant efficient projection of plant biomass units. This may well be also extended to the general settings of allometric examination. Nevertheless, we acknowledge that further substantiation is deemed necessary before proposed MCA could be adopted as a comprehensive tool for the analysis of allometric data. Meanwhile, present results endorse the relevance of the excerpt of [PERSON] and [PERSON] [81] on the hopelessness of a divergence between traditional logarithmic transformation and direct non-linear analysis slants in allometry. Surely, the efficiency of the proposed MCA arrangement can elucidate this glowing controversy. Conceptualization, H.E.-H.; Data curation, C.L.-R. Formal analysis, H.E.-H.; Methodology, H.E.-H., C.L.-R.; E.V.-D.; J.R.C.-R. Software, C.L.-R.; J.R.C.-R. Supervision, H.E.-H.; Validation, E.V.-D.; J.R.C.-R.