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Regular version of the site

Article

On closure operators related to maximal tricliques in tripartite hypergraphs

Discrete Applied Mathematics. 2018. Vol. 249. P. 74-84.

Triadic Formal Concept Analysis (3FCA) was introduced by Lehman and
Wille almost two decades ago. Many researchers work in Data Mining and
Formal Concept Analysis using the notions of closed sets, Galois and closure
operators, and closure systems. However, a proper closure operator for enu-
meration of triconcepts, i.e. maximal triadic cliques of tripartite hypergraphs,
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 diffi-
culties 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.