Fuzzy relational compositions, dragonflies, undefined values, classification, partial fuzzy sets

Three-valued logic is an important topic in logic.This is due to its compatibility with the practical problems, where not all statements fall into True or False but rather ?Unknown?, ?Irrelevant?, ?Non-applicable?, or ?Indeterminable?. Their truthvalues were therefore modeled as undefined values. A generalization of such classical logic into the framework of fuzzy set theory has been successfully constructed and formed the so-called partialfuzzy logic. Distinct fuzzy logics employing the partiality were naturally based on extensions of standard three-valued logics (connectives) such as Bochvar, Soboci´ nski or Kleene ones, to themany-valued ones. However, most of the approaches focus rather on the errors coming from non-applicability or indeterminability than on the errors coming from unknown missing values. Andthe problem of missing values is equally important in computer science at the topic of three-valued logic. And, based on our experience with practical examples, this type of errors coming from missing values are much more frequently occurring morerelated to real applications. Therefore, in this paper, a new set of connectives based on the idea of lower estimation is proposed in order to serve to the problems coming from missing values. Somevalid properties of the newly proposed type of the connectives are investigated. The main focus is put on the application to the compositions of partial fuzzy relations and again, naturalproperties of such compositions are provided.