Fractional jet Captain reported ATC issuing a low altitude alert when the flight descended below a published altitude during a night IMC approach in an area of terrain. ATC issued a clearance to climb and the flight was vectored for another approach and landed safely.

Narrative

On arrival to AVL at night in IMC we were being vectored the ILS 17. Prior to commencing the approach we were given a heading to intercept the localizer inbound with an altitude. During the read back there was a distraction in the cockpit; and I queried the controller if we were cleared for the approach and was told to standby for approach clearance. The PIC (flying pilot) set 4000 ft. ; armed the localizer for capture and began descent. We were subsequently cleared for the approach. I noticed that we were outside of the approach fix WUGAG which has a crossing restriction of 5000 ft. or above and advised the flying pilot to shallow his descent rate. He stated No; we are cleared down to 4000 ft."; which I believed was our clearance as well. Soon after; while leveling at 4000 ft.; the controller asked us to state our altitude and asked if we had captured the glide slope. I replied with our altitude and that we had not captured the glide slope. The controller issued an altitude alert and instructions to climb while canceling the approach clearance. We were vectored for another approach and landed without incident. Both pilots believed that we had been cleared for an unrestricted descent to 4000 ft.; but in retrospect I believe that fatigue and distractions might have caused an error on our part.Suggestion: It was a long and fatiguing day with innumerable schedule changes and operational challenges; culminating in an approach at night to minimums (in fact we had to switch PIC designation prior to the last flight because I was the senior PIC but am still high mins and the weather would not allow for dispatch with me as PIC). As we know; errors rarely occur in a vacuum. Despite our best efforts at vigilance; I believe that scheduling practices predisposed us to make this sort of error. Even though we have the choice to label ourselves as fatigued and stop flying; it seems that one rarely knows one is fatigued until in a demanding flight environment. This segment of the aviation industry needs additional regulation and established best practices to mitigate the risk associated with the scheduling practices."