The recent information set theory provides a useful mechanism to represent an agent’s perceived information values. However, often a decision-maker (DM) considers multiple evaluations for the same information source value. To this end, we extend the recent information set as hesitant information set (HIS). It gives the multiple perceived information values, corresponding to an information source value. In the context of multi-attribute decision making, HIS represents a set of different possible subjective utilities that an agent may perceive as an evaluation of an alternative-attribute pair. The basic operations, and properties of HIS are investigated. A few information measures based on HIS are presented. Besides many illustrative examples, a real application in group multi attribute decision making problem is included.