Abstract
As a tool of qualitative representation, conditional preference network (CP-net) has recently become a hot research topic in the field of artificial intelligence. The semantics of CP-nets does not restrict the generation of cycles, but the existence of the cycles would affect the property of CP-nets such as satisfaction and consistency. This paper attempts to use the feedback set problem theory including feedback vertex set (FVS) and feedback arc set (FAS) to cut cycles in CP-nets. Because of great time complexity of the problem in general, this paper defines a class of the parent vertices in a ring CP-nets firstly and then gives corresponding algorithm, respectively, based on FVS and FAS. Finally, the experiment shows that the running time and the expressive ability of the two methods are compared.
Highlights
The evil of graph exists in cycles [1,2,3]
For cutting the cycles of conditional preference network (CP-net), two methods are presented based on feedback vertex set (FVS) and feedback arc set (FAS)
For the length of all arcs are equal in CP-nets [22, 23], breadth-first search algorithm is the optimal solution, that is, the first solution it finds from the root of a certain minimum number of arcs; but for general figure
Summary
The evil of graph exists in cycles [1,2,3]. Several famous problems in computer science just like satisfiability, knapsack, and graph three-colorability problem are all related to cycles. A conditional preference network [1], abbreviated as a CP-net, is a simple and intuitive tool of graph model [6], which can represent preferences of agent, so do learning and aggregation and suits for describing qualitative multiattribute decision-making preference with dependencies. It can be converted into a weighted directed graph under usual conditions. For cutting the cycles of CP-nets, two methods are presented based on feedback vertex set (FVS) and feedback arc set (FAS).
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