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

The aim of this paper is, first, to recall fuzzy relational compositions (products) and, to introduce an idea, how the so-called excluding symptoms could be incorporated into the theoretical background. Apart from rather natural definitions, we provide readers with a theoretical investigation that provides and answer to a rather natural question, under which conditions, in terms of the underlying algebraic structures, the proposed incorporation of excluding symptoms preserves the same properties as the incorporation in the classical relational compositions. The positive impact of the incorporation on reducing the suspicions provided by the basic ``circlet'' composition without losing the possibly correct suspicion, as in the case of the use of the Bandler-Kohout products, is demonstrated on an example.