In this paper, a novel approach and framework based on interval-dependent degree and probability distribution for multi-criteria decision-making problems with multi-valued neutrosophic sets (MVNSs) is proposed. First, a simplified dependent function and distribution function are given and integrated into a concise formula, which is called the interval-dependent function and contains interval computing and probability distribution information in an interval. Then a transformation operator is defined and it is shown how to convert MVNSs into an interval set. Subsequently, the interval-dependent function with the probability distribution of MVNSs is deduced. Finally, an example and comparative analysis are provided to verify the feasibility and effectiveness of the proposed method. In addition, uncertainty analysis, which reflects the dynamic change of the ranking result with decision-makers’ preferences, is performed by setting different distribution functions, which increases the reliability and accuracy of the proposed method.

Machine learning and artificial intelligence based techniques have brought great convenience to human life but along with a series of algorithmic “black box”, discrimination and ethical issues. One of the solutions is to integrate human and machine like the expert evaluation based research of multi-attribute decision-making where “human brain intelligence” is used for the support of “artificial intelligence”. In this article, we proposed a new and effective method to evaluate and rank alternatives in multi-attribute decision-making. Different from many existing approaches, this proposed method employs both the projection lengths and the projection angles of alternatives to make decisions. It supports psychological desirableness of decision makers and uses a Relu function to further enhance the output qualities. This proposed method is very simple to construct and applicable for much wider situations than the existing similar methods.