Arrow categories have been shown to be a suitable categorical and algebraic framework for L-fuzzy relations. They axiomatize those relations and the usual relational operations such as meet, join, converse, and composition based on the operations given by the lattice of membership values L. However, an important tool when working with and applying fuzzy methods, are meet and composition operators that stem from a certain monoid operation on L (also called a t-norm on L). In this paper we investigate the relational properties of those operations in the abstract setting of arrow categories. In particular, we investigate properties similar to the well-known modular inclusion for regular composition.
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