A Takagi–Sugeno-Kang Fuzzy Model Formalization of Eelgrass Leaf Biomass Allometry with Application to the Estimation of Average Biomass of Leaves in Shoots: Comparing the Reproducibility Strength of the Present Fuzzy and Related Crisp Proxies

Abstract

The identification of the functional relationship that regulates the variation of individual leaf biomass in terms of related area in eelgrass, allows the derivation of convenient proxies for a nondestructive estimation of the average biomass of the leaves in shoots. The concourse of these assessment methods is fundamental for assessing the performance of restoration efforts for this species that are based on transplanting techniques. Prior developments proposed proxies for a nondestructive estimation of aforementioned average biomass of leaves in shoots derived from allometric models for the dependence of leaf biomass in terms of linked area. The reproducibility power of these methods is highly dependent on analysis method and data quality. Indeed, previous results show that allometric proxies for average biomass of leaves in shoots produced by parameter estimates fitted from quality controlled data via nonlinear regression yield the highest reproducibility strength. Nevertheless, the use of data processing entails subtleties mainly related to the subjectivity of the criteria for the rejection of inconsistent replicates in raw data. Here we introduce efficient- data quality control- free surrogates derived from a first order Takagi-Sugeno-Kang fuzzy model aimed to approximate the mean response of eelgrass leaf biomass depending on associated area. A comparison of the performances of the allometric and the fuzzy model constructs identified using available raw data shows that the Takagi-Sugeno-Kang paradigm for individual leaf biomass in terms of related area produced the most precise proxies for observed average biomass of leaves in shoots. The present results show how gains derived from the outstanding approximation capabilities of the first order Takagi-Sugeno-Kang fuzzy model for the nonlinear dynamics can be extended to the realm of eelgrass allometry.