A PA31 PILOT ON AN IFR FLIGHT PLAN APPROACHING LAF EXPERIENCED AN AIRBORNE CONFLICT WITH ANOTHER AIRCRAFT. HE REPORTEDLY GOT AN ALERT FROM HIS TIS BUT NOT FROM THE CONTROLLER.

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ON VECTORS TO FINAL FOR THE ILS AT LAF; THE CTLR ASSIGNED 4000 FT AND AN INTERCEPT HDG. THE GNS 530 DISPLAYED A TFC AT 12 O'CLOCK POS 500 FT BELOW 2 NM OUT; I THOUGHT THE CTLR KNEW; I KEPT THE TFC PAGE ACTIVE I DID NOT SEE THE TFC; I HAD THE LIGHTS ON. DURING THE IN RANGE CHKLIST AND PREPARATION TO THE APCH THE DISPLAY ALARMED; AURALLY AND VISUALLY. I DISCONNECTED THE AUTOPLT AND MADE A 60 DEG TURN HARD BACK TO THE R AND CLBED; IN THE TURN I SAW THE TFC UNDERNEATH US IN THE GAP BTWN THE L ENG NACELLE AND THE AIRFRAME FOR A FRACTION OF A SECOND; VERY CLOSE; I COULD SEE WHAT APPEARED TO BE A TWIN WITH THE GEAR DOWN. AFTER LEVELING AT 5000 FT WE RETURNED TO OUR ASSIGNED HDG AND INITIATED A DSCNT BACK TO 4000 FT. WE MADE A CALL TO ZAU TO EXPLAIN OUR ALT AND HDG CHANGE; SHE DID NOT RESPOND; WE CALLED A 2ND TIME AND A 3RD TIME. IT SEEMED SHE WAS ON ANOTHER FREQ BECAUSE WHEN SHE MADE CALL TO OTHER ACFT WE COULD NOT HEAR THE REPLIES. SHE WAS NOT ATTENTIVE TO US AT ALL BECAUSE WE CALLED HER TO MAKE OUR TURN TO FINAL AFTER GETTING THE LOC NEEDLE MOVING WHEN WE WERE IN AN INTERCEPT HDG 110 DEGS OFF THE FINAL APCH COURSE. WE DID NOT WANT TO COMPLAIN BUT SHE STATED THAT SHE DID NOT HAVE RADAR COVERAGE BELOW 4000 FT. MY COMMENT IS THAT HOW CAN ANYBODY FEEL SAFE IF WE TRUST A RADAR SYS TO KEEP US FROM OTHER TFC AND IT DOES NOT HAPPEN; WE HAD NO SEPARATION SVC; NO TFC INFO FROM ATC AND WE HAD POOR TO NONE GUIDANCE FOR THE APCH. THE TIS SYS IS THE BEST INVESTMENT I HAD MADE ON MY ACFT AND I WILL UPGRADE TO A TCAS SYS SOON; I DO NOT TRUST THE ABILITY OF THE TFC CTL SYS TO KEEP ME AND MY FAMILY SAFE. I BELIEVE STRONGLY THAT THIS WAS A DISCRIMINATION CASE; THE CTLR DID NOT PAY ATTN TO US BECAUSE WE WERE A GA FLT; PERIOD. I CAN GUARANTEE THAT THIS WOULD NOT HAVE NEVER HAPPEN ON A PART 121 OP INTO LAF.