Improvement in the infrared band division method for foreign fibers based on interval-valued linear Diophantine fuzzy decision theory

Abstract

Foreign fibers are the main factors affecting cotton quality, and different types of foreign fibers can form different spectral characteristics in collecting spectra. This study focuses on identifying the optimal reflectance region to accommodate multiple foreign fiber types by optimizing waveband selection under consistent detection conditions. Traditional waveband division relies on a single evaluation index and overlooks interactions among spectral attributes. Therefore, this paper proposes a multi-attribute group decision-making (MAGDM) method based on interval-valued linear Diophantine fuzzy set (IVLDFS) information to optimize waveband division for foreign fiber detection by quantitatively analyzing spectral parameter interactions. First, considering that the power average operator might negate the influence of unreasonable parameters on decision-making results and combine with the Heronian mean operator to assess interrelationships between parameters thoroughly, the interval-valued linear Diophantine fuzzy power Heronian aggregation (IVLDFPHA) and interval-valued linear Diophantine fuzzy weighted power Heronian aggregation (IVLDFPWHA) operators are deduced. The entropy weight method is then used for calculating the weight vector of the decision set, and a MAGDM method is proposed within the fuzzy environment of the IVLDFS. The method is applied to the selection of optimal bands for foreign fibers, and compared with the interclass separability banding method and adaptive band selection method to analyze the effects of different band delineation methods on the results. Results confirm that the near-infrared band W₃ ∼ 780–1100 nm is the best detection band.