All things are sorted or categorized in this world. We need to know the proper equation to find the solution to which set theory is best for our purpose.
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It develops the power to apply logic and logic is an intigral part of mathematics. More over application of venn diagrams helps to get solutions of complicated questions easily. Set theory is a combination of art, logic and calculations.
Why is it important to be able to identify sets and set theory as related to business operations?
The theory of numbers is based on the property of sets of different kinds of numbers.
Classical theory is a reference to established theory. Fuzzy set theory is a reference to theories that are not widely accepted.
Im not sure if there is any application of set notation and set theory, however set notation is important when you start learning about the domains and ranges of functions.