This is actually taken from a well-accepted concept in modern psychology. It's called the SUDS, or Subjective Units of Distress Scale. Because emotions can vary greatly from person to person, there is no "standard" way to measure them, which is what makes them subjective.
However, you yourself know how intense an emotion such as fear feels to you, and that's how you assign it a degree of intensity using the 0-10 scale.