  As from time to time it is impractical to ask agents to provide linear orders
over all alternatives, for these partial rankings it is necessary to conduct
preference completion. Specifically, the personalized preference of each agent
over all the alternatives can be estimated with partial rankings from
neighboring agents over subsets of alternatives. However, since the agents'
rankings are nondeterministic, where they may provide rankings with noise, it
is necessary and important to conduct the trustworthy preference completion.
Hence, in this paper firstly, a trust-based anchor-kNN algorithm is proposed to
find $k$-nearest trustworthy neighbors of the agent with trust-oriented
Kendall-Tau distances, which will handle the cases when an agent exhibits
irrational behaviors or provides only noisy rankings. Then, for alternative
pairs, a bijection can be built from the ranking space to the preference space,
and its certainty and conflict can be evaluated based on a well-built
statistical measurement Probability-Certainty Density Function. Therefore, a
certain common voting rule for the first $k$ trustworthy neighboring agents
based on certainty and conflict can be taken to conduct the trustworthy
preference completion. The properties of the proposed certainty and conflict
have been studied empirically, and the proposed approach has been
experimentally validated compared to state-of-arts approaches with several data
sets.
