General Approach to Triadic Concept Analysis

Triadic concept analysis (TCA) is an extension of formal concept analysis (dyadic case) which takes into account modi (e.g. time instances, conditions, etc.) in addition to objects and attributes. Thus instead of 2-dimensional binary tables TCA concerns with 3-dimensional binary tables. In our previous work we generalized TCA to work with grades instead of binary data; in the present paper we study TCA in even more general way. In order to cover up an analogy of isotone conceptforming operators (known from dyadic case in fuzzy setting) we developed an unifying framework in which both kinds of concept-forming operators are particular cases of more general operators. We describe the unifying framework, properties of the general concept-forming operators, show their relationship to those we used in our previous work.