Efficient modeling and representation of agreement in interval-valued data

Recently, there has been much research into effective representation and analysis of uncertainty in human responses, with applications in cyber-security, forest and wildlife management, and product development, to name a few. Most of this research has focused on representing the response uncertainty as intervals, e.g., “I give the movie between 2 and 4 stars.” In this paper, we extend upon the model-based interval agreement approach (IAA) for combining interval data into fuzzy sets and propose the efficient IAA (eIAA) algorithm, which enables efficient representation of and operation on the fuzzy sets produced by IAA (and other interval-based approaches, for that matter). We develop methods for efficiently modeling, representing, and aggregating both crisp and uncertain interval data (where the interval endpoints are intervals themselves). These intervals are assumed to be collected from individual or multiple survey respondents over single or repeated surveys; although, without loss of generality, the approaches put forth in this paper could be used for any interval-based data where representation and analysis is desired. The proposed method is designed to minimize loss of information when transferring the interval-based data into fuzzy set models and then when projecting onto a compressed set of basis functions. We provide full details of eIAA and demonstrate it on real-world and synthetic data