Actual existing multi-criteria decision-making (MCDM) methods yield results that may be questionable and unreliable. These methods very often ignore the issue of uncertainty and rank reversal paradox, which are fundamental and important challenges of MCDM methods. In response to these challenges, the Characteristic Objects Method (COMET) was developed. Despite it being immune to the rank reversal paradox, classical COMET is not designed for uncertain, decisional problems. In this paper, we propose to extend COMET using hesitant fuzzy set (HFS) theory. Hesitant fuzzy set theory is a powerful tool to express the uncertainty that derives from an expert comparing characteristic objects and identifying membership functions for each criterion domain. We present the theoretical foundations and principles of COMET, and we provide an illustrative example to show how COMET handles uncertain decision problems both practically and effectively.