The concept of information sets is inspired by the way we perceive information source values. However, they lack a provision to represent the hesitancy inevitably associated with the perceived values. To this end, recently the concept of hesitant information set (HIS) is proposed in the literature. In contrast to an information set that maps an information source value to a single perceived information value, HIS gives a set of multiple perceived information values for a single information source value. This paper explores HIS further for its properties. © 2018 Copyright is held by the owner/author(s).