Fuzzy relational compositions; Fuzzy relational products; Bandler?Kohout products; Residuated algebraic structures; Medical diagnosis; Classification; Odonata

he aim of this paper is, first, to recall fuzzy relational compositions (products) and, to introduce an idea, how excluding features could be incorporated into the theoretical background. Apart from definitions, we provide readers with a theoretical investigation. This investigation addresses two natural questions. Firstly, under which conditions (in which underlying algebraic structures) the given three natural approaches to the incorporation of excluding symptoms coincide. And secondly, under which conditions, the proposed incorporation of excluding features preserves the same natural and desirable properties similar to those preserved by fuzzy relational compositions.The positive impact of the incorporation on reducing the suspicions provided by the basic ?circlet? composition without losing the possibly correct suspicion is demonstrated on a real taxonomic identification (classification) of Odonata. Here, we demonstrate how the proposed concept may eliminate the weaknesses provided by the classical fuzzy relational compositions and, at the same time, compete with powerful machine learning methods. The aim of the demonstration is not to show that proposed concept outperforms classical approaches, but to show, that its potential is strong enough in order to complete them or in order to be combined with them and to use its different nature.