Fighter
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 6
Distraction; Situational Awareness
ATC Issue All Types; Airspace Violation All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Procedure; Human Factors
Multiple complex things were happening which led to me potentially violating an Minimum IFR Altitude (MIA) (I'm unsure as I couldn't tell if the was the warning stick of the actual MSAW alert).  During the lead up to the event there were multiple aircraft deviating for weather; a flight of Fighter jets had [requested priority handling]; and a C206 was having difficulty avoiding weather (as well as the pilot sounded spooked and afraid on frequency).  Aircraft X flight was returning to base from the military airspace and requested vectors for the TACAN14.  I vectored them Northwest outside of MUPEE descended them to 090 and gave them a turn to intercept the LMT314 radial.  During this time there was multiple pilot requests from other aircraft; NEXRAD weather to call; and several other things going on at the same time.  During the turn on; I believe the aircraft may have drifted; or may have gotten close to the 100 MIA just to the west of the LMT314 radial.During fighter missions to decrease sector pressure; Kingsley Approach could open up.  Also; while the approach quick cards on sector 10 are nice; trying to flip through the booklet and figure out which approach is which (they all look the same) was hard and became a distraction.  Maybe make the title of each approach reference card larger.  Also the MSAW warning vs alert looks the same (save for the warning stick.)  In this case; with tight quarters; NEXRAD weather overlaid; and multiple data-blocks; it was hard to decipher what exactly was happening.
A Seattle Center (ZSE) Controller reports of becoming busy and while vectoring an aircraft to final; the aircraft drifted close to a lower Minimum IFR Altitude (MIA).