A Combination Algorithm of Multiple Lattice-Valued Concept Lattices

Abstract

With the rapid development of network technology, especially in the internet area, distributed computation and parallel processing of data are urgently needed. This paper studies the combination operation of the lattice-valued concept lattices to realize its distributed computation and parallel processing. The proposal of its corresponding combination algorithm is mainly according to the conjunction properties of incomparable attribute values. Firstly, we define a homotypic lattice-valued concept lattice and a combined concept lattice; secondly, we analyze some relations between the lattice-valued formal concepts under two conditions and prove the isomorphism of the combination theory; finally, we present the combination algorithm of multiple lattice-valued concept lattices and analyze the algorithm complexity and employ an example to show the application of this combination algorithm.

Keywords:

• Concept lattice
• Lattice-valued concept lattice
• Homotypic formal context
• Combination algorithm
• Parallel processing