FLC OF AN MDT TOOK OFF BELOW PUBLISHED WX MINIMUMS. (RVR IS CTLING.)

Narrative

ON FEB/XX/95; I WAS THE CAPT ON A PART 121 COMMERCIAL FLT FROM CORPUS CHRISTI TO DFW. AFTER A REDUCED REST OVERNIGHT; I DUTIED IN AT AM57 LCL TIME HAVING HAD LESS THAN 5 HRS SLEEP. AS WE TAXIED FOR TKOF; THE VISIBILITY WAS RPTED AS 1/4 MI AND PATCHY FOG WITH 1000 RVR ON RWY 13. AS WE REACHED THE DEP END OF THE RWY; THE TWR SAID THE VISIBILITY HAD DROPPED TO 1/8 MI AND 800 RVR; BUT THE CTLR SAID A NEW RPT WOULD COME OUT IN A FEW MIN. I ELECTED TO HOLD SHORT OF THE RWY AND WAIT FOR THE RPT. IN THE MEANTIME; I DOUBLE CHKED THE DEP MINIMUMS ON THE (COMMERCIAL) CHART WHICH SHOWED 2 PARAMETERS OF TKOF MINIMUMS -- 1 THAT SHOWED STANDARD 1 MI AND THE OTHER 1/4 MI OR 1600 RVR. I KNEW THAT MY COMPANY'S STANDARD PRACTICE OPS SPECS ALLOWED ME TO REDUCE MINIMUMS FROM THE STANDARD 1 MI WITH CERTAIN QUALIFYING CONDITIONS; HOWEVER; WHEN THE NEW WX RPT CAME OUT SHOWING 1/4 MI VISIBILITY AND 1000 RVR; I ASKED FOR AND RECEIVED CLRNC FOR TKOF. I MADE A NORMAL REDUCED VISIBILITY TKOF AND THE FLT PROCEEDED WITHOUT INCIDENT. I RELIED ON MY UNDERSTANDING OF MY COMPANY'S OPS SPECS REGARDING REDUCED VISIBILITY TKOFS RATHER THAN GETTING THE BOOK OUT AND MAKING ABSOLUTELY SURE I WAS IN FULL LEGAL COMPLIANCE BEFORE TAKING THE RWY. I FEEL THAT FATIGUE CLOUDED MY JUDGEMENT AND AFFECTED MY DECISION-MAKING ABILITY IN THIS SIT.