Developing a Fuzzy Bicluster Regression to Estimate Heat Tolerance in Plants by Chlorophyll Fluorescence

Abstract

This paper presents a straightforward and useful fuzzy regression approach to estimate heat tolerance of plants by chlorophyll fluorescence measurement. The chlorophyll fluorescence measurement is an indicator of functional change of photosynthesis and is sensitive to temperature. Using the fluorescence-temperature curves, the experimenter may determine the heat tolerance ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Tc</i> ) of plants by intersections of two linear regression lines. However, as traditional statistical regression analysis shows, the experiment may contain uncertain factors or phenomena such as leaf nature and growth environment, which concludes that data may vary among individual plants and different species. This research presents a fuzzy bicluster regression (FBCR) analysis with genetic algorithms, which helps derive a fuzzy intersection set and fuzzy heat tolerance of plants, in addition to the traditional statistical regression analysis. A fuzzy clustering concept and simultaneously optimal determination of data clusters is also developed. Especially, when there are nonlinear inflections in data curves, due to the imperative use of linear regression models, the traditional regression analysis may become unable to sufficiently model the uncertainties exhibited. The FBCR analysis can resolve this problem effectively due to the nonlinear tolerance of the system, even in a linear model. To demonstrate the FBCR analysis, it was applied to estimate the heat tolerance of five plant species. The results derived appeared to be more suitable than that of the conventional method. The approach may provide a useful means for the experimenters to derive more credible results from their chlorophyll fluorescence-temperature data.