This article gathers several topics together, namely fuzzy relational compositions, partial fuzzy logics, generalized quantifiers and, finally, classification as a problem serving for the demonstrative purposes. Fuzzy relational compositions as one of the most fundamental areas from the fuzzy set theory are being extended and investigated from several perspectives in the last decades. One of such perspective was to employ generalized quantifiers replacing the original existential and universal quantifiers in the construction of the compositions. Recently, the compositions have been also re-designed to deal with undefined values and thus, the topic has been joined to the fuzzy partial logics. One of such approaches proposed a specific algebra for handling missing values. This article puts all the mentioned approaches together in order to design fuzzy relational compositions dealing with missing values with help of appropriate partial operations. After a brief investigation of properties of the proposed compositions, we provide readers with an example demonstrating that the construction allows to minimize negative impact of the missing values.

Fuzzy relational compositions based on fuzzy quantifiers naturally do not preserve all the properties that are preserved for “standard” fuzzy relational compositions and, in many cases, the property is preserved only in a weaker form. For example, the associativity, that is preserved in the standard case derived from the universal and the existential quantifiers, generally does not hold for the case of compositions based on fuzzy quantifiers. However, is it the case that only the standard quantifiers lead to the preservation of such properties? Without any restriction on the shape of the fuzzy relations, the answer is positive.