Valued Hesitation in Intervals Comparison

The paper presents a valued extension of the recently introduced concept of PQI interval order. The main idea is that, while comparing objects represented by interval of values there is a zone of hesitation between strict difference and strict similarity which could be modelled through valued relations. The paper presents suitable definitions of such valued relations fulfilling a number of interesting properties. The use of such a tool in data analysis and rough sets theory is discussed in the paper.