Lagrange-enhanced GRA framework for probabilistic simplified neutrosophic multiple-attributes decision-making and applications to painting teaching quality evaluation

Abstract

Universities are important talent training bases in China and the main driving force for achieving the strategic layout of “revitalizing the country through science and education” and “strengthening the country through talent". Oil painting is a global art with rich humanistic and artistic value. Most art colleges in China have set up oil painting courses. Analyze the current situation and value of oil painting course teaching in local art (teacher training) majors, and leverage the educational role of oil painting courses by enriching course offerings, emphasizing the integration of humanistic innovation, improving teacher literacy, and striving to further improve the quality and efficiency of oil painting course teaching. The quality evaluation of oil painting teaching in universities is viewed as multiple-attribute decision-making (MADM). The grey relational analysis (GRA) is a useful tool to cope with the MADM issue. The probabilistic simplified Neutrosophic set (PSNSs) is easy to characterize uncertain information during the quality evaluation of oil painting teaching in universities. In this paper, in order to obtain the weight information, an optimization model implemented to obtain a simple and exact formula which can be employed to derive the attribute weights values based on the Lagrange function and the probabilistic simplified neutrosophic number grey relational analysis (PSNN-GRA) technique is implemented for MADM to rank the alternatives. Finally, a numerical example for quality evaluation of oil painting teaching in universities is used to verify the practicability of the PSNN-GRA technique and compares it with other techniques.