Value
Instead of justification, the 7th edition of the PMBOK Guide talks about value (short for business value), and covers justification as a topic below it.
The best way of defining value in this context is the benefits-to-cost ratio. So, if you have two projects and they both benefit you by 1,000 units of money, but one costs you 100 units to do and the other 200, the first one is twice as valuable.
This definition is important because many use the word “value” to mean “benefit” in their day-to-day language, and, for example, talk about “value for money”, which doesn’t make sense if you consider value to be the benefits-to-cost ratio. Unfortunately, even some resources about project management mix these two definitions, which causes a lot of trouble.