  Triadic Formal Concept Analysis (3FCA) was introduced by Lehman and Wille
almost two decades ago. And many researchers work in Data Mining and Formal
Concept Analysis using the notions of closed sets, Galois and closure
operators, closure systems, but up-to-date even though that different
researchers actively work on mining triadic and n-ary relations, a proper
closure operator for enumeration of triconcepts, i.e. maximal triadic cliques
of tripartite hypergaphs, was not introduced. In this paper we show that the
previously introduced operators for obtaining triconcepts and maximal connected
and complete sets (MCCSs) are not always consistent and provide the reader with
a definition of valid closure operator and associated set system. Moreover, we
study the difficulties of related problems from order-theoretic and
combinatorial point view as well as provide the reader with justifications of
the complexity classes of these problems.
