A fuzzy logic based estimator for respondent driven sampling of complex networks

Respondent Driven Sampling (RDS) is a popular network-based method for sampling from hidden population. This method is a type of chain referral (or snowball) sampling in which an estimator is used to infer the proportion of the population with that property. Existing RDS estimators are asymptotically unbiased based on various underlying assumptions. However, these assumptions are often violated in practice, and little attention has been given to violation of one of these assumptions on accurately reporting the degree by all nodes. In this paper, we address the violation of this assumption and propose a new estimator based on fuzzy computing. In particular, the number of an individual's contacts can be a fuzzy concept. Using fuzzy functions, we transform the reported degrees to fuzzy numbers and estimate the infection prevalence in the hidden population by the proposed estimator. We simulate RDS method under the condition that all assumptions are satisfied except the one for the degree, and then evaluate the proposed estimator in synthetic and real datasets. Our results show that the fuzzy-based estimator can reduce the sampling bias in average 54% as compared to the existing methods.