## 1 Introduction  
Rock slope failures are a typical type of geological hazard that feature large scale and serious damage, frequently occurring in mountainous regions. Rock slopes can be considered as a complex system that consists in random, discrete, and nonlinear information, such as the characteristics of geological structures, geographic types, and environmental impacts [1; 2; 3]. For the better protection of civil engineering, environmental conservation, and efficient operation, the assessment of rock slope stability has always been a challenging topic in the world. In the past several decades, different approaches have been developed to assess the stability of rock slopes, which can be primarily categorized into deterministic and probabilistic methods. Limit equilibrium and numerical analysis are the most common forms of deterministic method. The limit equilibrium method utilizes the static equilibrium principle to analyze the stress state under various failure modes of slopes [4], including Bishop's, Janbu's, Morgenstern-Price's and Fellenius' techniques, etc. [5; 6; 7]. Meanwhile, different numerical methods, such as finite element method, discrete element method, discontinuous deformation analysis, and numerical manifold method, have been employed in slope stability assessments and landslide evolution, which have achieved great success [8; 9; 10; 11; 12]. In engineering practices, the amount of available data for analysis is commonly limited. It has been realized that the deterministic approaches frequently fail to give reliable assessment when complex slope systems are encountered [13; 14], owing to the inadequacy of information regarding site characteristics as well as the inherent variability and measurement errors in geological and geotechnical parameters [15]. With the need to consider the risk and consequence of slope instability and parameter uncertainty, probabilistic approaches have been developed and applied to slope stability assessment. Different mathematics methods have been employed for rock slope engineering, such as the reliability theory, the fuzzy mathematics, the grey theory, and the artificial neural network (ANN). Early studies developed assessment models directly based on a single probabilistic method [16; 17; 18; 19; 20]. It has been realized later that the combination of different probabilistic methods can yield better assessments, such as the hybrid model of the projection pursuit (PP), particle swarm optimization (PSO), and the logistic curve function (LCF) [21]. The probabilistic methods have also been introduced into different failure criterions and verified against physical models to overcome the limitation of conventional methods without considering randomness and uncertainty of the slope status and mechanical parameters [22; 23; 24; 25; 26; 27; 28]. With the effort for probabilistic sensitivity analysis, more sophisticated models led to improved accuracy of assessment [29]; however, huge challenges remain in the high computational effort, complex modeling procedures, and the large amount of data required to yield results with acceptable accuracy. In recent years, the neutrosophic theory, as a new theory of uncertainty, has been accepted and rapidly applied to different fields, such as electrical engineering, medical diagnosis, and roughness estimation [30; 31; 32]. Neutrosophic number (NN) is a branch of neutrosophy that evolved from classic philosophy. [PERSON] [33; 34; 35] originally proposed the concept of neutrosophic number, which consists of both indeterminate and determinate information for a problem with uncertainty. [PERSON] [36; 37] developed three vector similarity measures, i.e., Jaccard, Dice, and cosine similarity measures, and incorporated them into the neutrosophic number to solve problems related to decision-making. [PERSON] [38] later combined possibility degree ranking method and ordered weighted aggregation operators of interval neutrosophic numbers to handle decision-making problems.