Layered Concept Lattice Model and Its Application to Build Rapidly Concept Lattice

Algorithm 1

Roll-up building algorithm of layered concept lattice.

	Input: a lower concept lattice of layered formal context induced by formal context .
	Output: an upper concept lattice.
	Step 1. For , select all lower concepts containing layered attribute and form lower concept set to be rolled up.
	Step 2. The concepts in are sorted in ascending order according to the number of lower attributes contained within it. When the number of lower attributes is the same, the concepts containing fewer nonlower attributes are ranked ahead.
	Step 3. From top to bottom, roll up the lower concepts in . For the linear lower subconcepts under node concept in , the rolling-up method is as follows: combine the linear lower concepts containing into a new concept , where , , and insert to node below. If node concept contains subconcepts with nonlower attributes, then node is updated to be the common upper bound of and other concepts (excluding lower attributes in ) under node .
	Step 4. For the parallel lower subconcepts and lower subconcepts under node concept in , the rolling-up method is as follows: combine the parallel lower concepts containing into a new concept , where , , and insert to node below. If node concept contains subconcepts with nonlower attributes, then node is updated to be the common upper bound of and other concepts (excluding lower attributes in ) under node .
	Step 5. If the node concept has both the parallel lower subconcepts and the linear lower subconcepts, then linear lower subconcepts are fused firstly; the method of fusion is to replace the linear lower subconcepts with the minimum concept in these linear lower subconcepts and then roll up the parallel lower subconcepts by Step 4 secondly.
	Step 6. Update the subconcept , which is not rolled up from Step 3 to Step 5 but it contains the lower attribute of , to a new concept .
	Step 7. Repeat from Step 3 to Step 6 until the concept in does not contain the lower attribute of (namely, is an empty set).
	Step 8. Repeat from Step 1 to Step 7 until does not contain any layered attribute. Algorithm is completed.