## 1 Introduction  
Extensive advances in Machine Learning (ML) have demonstrated its potential in successfully addressing complex problems in safety-critical areas, such as in healthcare [1, 2, 3], aerospace [4, 5, 6], driver distraction [7, 8, 9], civil engineering [10, 11], and manufacturing [12, 13]. Historically, however, many ML models, especially those involving neural networks, are viewed as 'black boxes', where little is known about the decision-making process. The lack of adequate interpretability and verification of ML models [14, 15] has therefore prevented an even wider adoption and integration of those approaches in high-integrity systems. For domains where mistakes are unacceptable due to the safety, security, and financial issues that they may cause, the need to accurately interpret the predictions and inference of ML models becomes imperative. The recent rise in complexity of ML architectures has made it more difficult to explain their outputs. Although there is an overall agreement about the safety and ethical needs for interpreting ML outputs [15; 16], there is however no consensus on how this challenge can be addressed. On the one hand, there are advocates for the development of models that are themselves interpretable rather than putting the effort later into making black-box models explainable [17]. The argument is that, for critical decision-making, explanations of the black-box models are often unreliable and can be misleading and unsafe. Conversely, other researchers have focused their efforts on explaining complex ML models, and significant advances have been achieved [18; 19; 20]. An important approach to ML output elucidation adopting post-training explanations is given by feature importance estimates [21; 22]. There are multiple methods for calculating feature importance, and they do not necessarily agree on how a feature relevance is quantified. Therefore, it is not easy to validate estimated feature importance unless the ground truth is known. Furthermore, there is no consensus regarding the best metric for feature importance calculation. The lack of consensus of current approaches in determining the importance of data attributes for ML decision making is a problem for safety-critical systems, as the explanation offered for the outcomes obtained is likely to be unreliable. Therefore, there is the need for more reliable and accurate ways of establishing feature importance. One possible strategy is to combine the results of multiple feature importance quantifiers as a way to reduce the variance in estimates, leading to a more robust and trustworthy interpretation of the contribution of each feature to the final ML model prediction. In this paper, we propose a general, adaptable, and extensible framework, which we named Multi-Method Ensemble (MME) for feature importance fusion with the objective of reducing the variance in current feature importance estimates. The MME Framework is divided into four main parts:  
1. The application of traditional data pre-processing and preparation approaches for computational modelling;
2. Predictive modelling using ML approaches, such as random forest (RF), gradient-boosted trees (GBT), support vector machines (SVM), and deep neural networks (DNN);
3. Feature importance calculation for the ML models adopted, including values obtained from Permutation Importance (PI) [23], SHapley Additive exPlanations (SHAP) [24], and Integrated Gradient (IG) [25]; and
4. Feature importance fusion strategy using ensembles. The framework as well as the ensemble strategies are tested on datasets considering different noise levels, number of important features, and number of total features. In order to make sure our results are reliable, we conduct our experiments on synthetic data, where we determine the features and their importance beforehand. We compare the performance of our framework to the more common method that uses a single feature importance method with multiple ML models, which we named Single Method Ensemble (SME).