Relationship Between Triadic Concept Reducts and Concept Reducts

Triadic concept analysis is an extension of formal concept analysis,and the ternary relation reflected in the triadic context corresponds to the binary relation based on the condition,so there is a close connection between the concept reduction that keeps the binary relation unchanged and the triadic concept reduction that keeps the ternary relation unchanged.Based on this,the relationship between concept reducts and triadic concept reducts is investigated.Firstly,the data under each condition in the tri-adic context is regarded as a formal context,and according to the relationship between formal concepts and triadic concepts,it is proved that the sets formed by the concept reducts of all conditionally determined formal contexts can generate triadic concept consistent sets.Secondly,using the set formed by triadic concepts according to the same conditions can get the set of concepts under the corresponding conditions.It is further proved that the concept consistent sets of formal contexts determined by all conditions can be generated from triadic concept reducts,and the equivalent proposition that triadic concept reducts and concept reducts are generated by each other is given.Finally,the relationship between the three types of formal concepts and the three types of triadic concepts is discussed with respect to the three types of concepts that play different roles in concept reducts and triadic concept reducts.