An empirical study on how humans appreciate automated counterfactual explanations which embrace imprecise information.

• Design and evaluation of three methods for generation of counterfactual explanations. • Linguistic fuzzy counterfactual explanations embrace imprecise information. • Perceived explanation complexity can be automatically measured from data. • Explanation complexity correlates with informativeness, relevance, and readability. • Human evaluation should focus on explanation issues uncorrelated with complexity. The explanatory capacity of interpretable fuzzy rule-based classifiers is usually limited to offering explanations for the predicted class only. A lack of potentially useful explanations for non-predicted alternatives can be overcome by designing methods for the so-called counterfactual reasoning. Nevertheless, state-of-the-art methods for counterfactual explanation generation require special attention to human evaluation aspects, as the final decision upon the classification under consideration is left for the end user. In this paper, we first introduce novel methods for qualitative and quantitative counterfactual explanation generation. Then, we carry out a comparative analysis of qualitative explanation generation methods operating on (combinations of) linguistic terms as well as a quantitative method suggesting precise changes in feature values. Then, we propose a new metric for assessing the perceived complexity of the generated explanations. Further, we design and carry out two human evaluation experiments to assess the explanatory power of the aforementioned methods. As a major result, we show that the estimated explanation complexity correlates well with the informativeness, relevance, and readability of explanations perceived by the targeted study participants. This fact opens the door to using the new automatic complexity metric for guiding multi-objective evolutionary explainable fuzzy modeling in the near future. [ABSTRACT FROM AUTHOR]