Open set recognition (OSR) has been investigated for approximately 10 years. It can recognize samples from the known classes in the training dataset,whereas it rejects samples from the unknown classes not included in the training dataset. The current OSR schemes are mainly based on Support Vector Machine (SVM) and deep learning neural networks. These OSR schemes are mainly used in natural scenery images and are rarely used in spectral analysis. In this paper,the classical fuzzy reasoning classifier in the closed set is improved with application to tree class spectral classification in the open set. First, a Flame-NIR spectrometer picks up the wood near-infrared (NIR) spectral curve. After metric learning processing,the spectral 4-dimensional (4D) feature vector is used as a classification feature. Second,the fuzzy reasoning classifier is improved for its use in an open set scenario. A new generalized basic probability assignment (GBPA) is used based on the confidence value of a fuzzy rule and the product of membership degree probability in each dimension. The comparison experimental results on wood NIR datasets with different “Openness” values indicate that our proposed scheme (Fuzzy Reasoning Classifier in an Open Set,FRCOS) outperforms the state of the art OSR schemes based on machine learning and deep learning with good performance evaluation measures.