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In many domains of our daily life (e.g., agriculture, forestry, health, etc.), both laymen and experts need to classify entities into two binary classes (yes/no, good/bad, sufficient/insufficient, benign/malign, etc.). For many entities, this decision is difficult and we need another class called “maybe”, which contains a corresponding quantifiable tendency toward one of these two opposites. Human domain experts are often able to mark any entity, place it in a different class and adjust the position of the slope in the class. Moreover, they can often explain the classification space linguistically—depending on their individual domain experience and previous knowledge. We consider this human-in-the-loop extremely important and call our approach actionable explainable AI. Consequently, the parameters of the functions are adapted to these requirements and the solution is explained to the domain experts accordingly. Specifically, this paper contains three novelties going beyond the state-of-the-art: (1) A novel method for detecting the appropriate parameter range for the averaging function to treat the slope in the “maybe” class, along with a proposal for a better generalisation than the existing solution. (2) the insight that for a given problem, the family of t-norms and t-conorms covering the whole range of nilpotency is suitable because we need a clear “no” or “yes” not only for the borderline cases. Consequently, we adopted the Schweizer–Sklar family of t-norms or t-conorms in ordinal sums. (3) A new fuzzy quasi-dissimilarity function for classification into three classes: Main difference, irrelevant difference and partial difference. We conducted all of our experiments with real-world datasets.

Classification relies on the rules expressed by domain experts, or on the labeled attribute explaining the output classes. However, such information is not always available. In this work, we explore classification according to aggregation functions of mixed behaviour by the variability in ordinal sums of conjunctive and disjunctive functions. By this approach, entities are classified into three classes: yes, no and maybe including inclination to the classes yes and no. By the proposed approach, domain experts (or ordinal users) explain classification linguistically, without stating IF-THEN rules and labeled output. The applicability is illustrated by two examples. The discussion of the results and further research activities conclude the paper.

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