Résumé
Explainable Artificial Intelligence (XAI) is relatively new in offering the possibility for intelligent systems to give robust motivations for their decisions and behaviours. Since XAI is human-centred, it has strong connections with fuzzy systems. In this paper, we consider the local explanation of the output of a set of fuzzy linguistic rules from the contributions of the inputs to the output. The proposed contributions are defined from the average of the gradients on the line linking the start point to the end point. This approach ensures that the variation in the output is equal to the sum of the contributions of each input variable to the output. The considered application is based on avalanche expert knowledge expressed by a set of fuzzy rules that combines different physical variables to build an ordinal fuzzy scale of avalanche vigilance ("Relaxed", "Suspicious", "Alert", "Gamble"). The level of vigilance to be applied locally, along a mountain ski route, is explained in a way that is close to expert reasoning in order to decide modifications of the route.