In my system i lost these datafiles.they no longer exist and database is in now unusable state. note that there are redo logs and temp files as well in this list

 /data04/TROY/TROY_INDEX10M01.dbf
 /data04/TROY/TROY_INDEX10M04.dbf
 /data04/TROY/TROY_INDEX10M07.dbf
 /data04/TROY/TROY_INDEX64K01.dbf
 /data06/TROY/oradata/TROY_PERFSTA02.dbf
 /data06/TROY/TROY_sysaux02.dbf
 /data04/TROY/TROY_system02.dbf
 /data04/TROY/TROY_temp01.dbf
 /data04/TROY/TROY_temp02.dbf
 /data04/TROY/TROY_undotbs04.dbf
 /data04/TROY/TROY_USERDATA10M01.dbf
 /data04/TROY/redo02b.log
 /data04/TROY/redo03a.log

To resolve this issue first i took these files offline as they no loger exist on my FS. If database still up and running then make them offline other wise start the databaase in mount state.

note that here system and sysaux datafiles are lost so anyways database is unusable. So in this case better shutdown the db (use shut abort if it hangs at shutdown immediate) and start it in mount state to perform restore and recover. If non system files are lost no need to shutdown db as it will be functional and you just take those files offline and perform restore and recovery

SQL > startup mount
ALTER DATABASE DATAFILE '/data04/TROY/TROY_INDEX10M01.dbf' OFFLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_INDEX10M04.dbf' OFFLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_INDEX10M07.dbf' OFFLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_INDEX64K01.dbf' OFFLINE;
ALTER DATABASE DATAFILE '/data06/TROY/TROY_sysaux02.dbf' OFFLINE;
ALTER DATABASE DATAFILE '/data06/TROY/oradata/TROY_PERFSTA02.dbf' OFFLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_temp01.dbf' OFFLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_temp02.dbf' OFFLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_undotbs04.dbf' OFFLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_system02.dbf' OFFLINE;

now go to rman and connect to catalog db and restore them. I have their backup avaialable on tape. exclude temp files as it can be added later

rman target / catalog CATUSR/rman@CAT_APP 
run {
SET AUTOLOCATE ON;
allocate channel C1 type 'SBT_TAPE';
allocate channel C2 type 'SBT_TAPE';
allocate channel C3 type 'SBT_TAPE';
allocate channel C4 type 'SBT_TAPE';
restore datafile '/data04/TROY/TROY_INDEX10M01.dbf';
restore datafile '/data04/TROY/TROY_INDEX10M04.dbf';
restore datafile '/data04/TROY/TROY_INDEX10M07.dbf';
restore datafile '/data04/TROY/TROY_INDEX64K01.dbf';
restore datafile '/data06/TROY/TROY_sysaux02.dbf';
restore datafile '/data06/TROY/oradata/TROY_PERFSTA02.dbf';
restore datafile '/data04/TROY/TROY_undotbs04.dbf';
restore datafile '/data04/TROY/TROY_system02.dbf';
}

redo02b.log and redo03a.log are multiplxed so copy redo02b.log from redo02a.log and redo03a.log from redo03b.log

now recover those restored datafiles

run {
SET AUTOLOCATE ON;
allocate channel C1 type 'SBT_TAPE';
allocate channel C2 type 'SBT_TAPE';
allocate channel C3 type 'SBT_TAPE';
allocate channel C4 type 'SBT_TAPE';
recover datafile '/data06/TROY/TROY_sysaux02.dbf';
recover datafile '/data04/TROY/TROY_INDEX10M01.dbf';
recover datafile '/data04/TROY/TROY_INDEX10M04.dbf';
recover datafile '/data04/TROY/TROY_INDEX10M07.dbf';
recover datafile '/data04/TROY/TROY_INDEX64K01.dbf';
recover datafile '/data06/TROY/oradata/TROY_PERFSTA02.dbf';
recover datafile '/data02/TROY/TROY/TROY_USERDATA10M01.dbf';
recover datafile '/data04/TROY/TROY_undotbs04.dbf';
recover datafile '/data04/TROY/TROY_system02.dbf';
}

use this command to check how many files still pending for recover. once alll files are recovered this command should retun no rows.here is the output when recover datafile was in progress.

note the recover column is YES for all files which needs recovery

select  file#,checkpoint_change#, status, recover from  v$datafile_header;


     FILE# NAME                                                                             CHECKPOINT_CHANGE# STATUS  REC
---------- -------------------------------------------------------------------------------- ------------------ ------- ---
        12 /data04/TROY/TROY_INDEX10M01.dbf                                             1.6024E+13 OFFLINE YES
        15 /data04/TROY/TROY_INDEX10M04.dbf                                             1.6024E+13 ONLINE  YES
        18 /data04/TROY/TROY_INDEX64K01.dbf                                             1.6024E+13 OFFLINE YES
        22 /data02/TROY/TROY/TROY_USERDATA10M01.dbf                                        1.6024E+13 OFFLINE YES
        27 /data04/TROY/TROY_undotbs04.dbf                                                    1.6024E+13 ONLINE  YES
        29 /data06/TROY/oradata/TROY_PERFSTA02.dbf                                            1.6024E+13 OFFLINE YES
        31 /data06/TROY/TROY_sysaux02.dbf                                                     1.6024E+13 OFFLINE YES
        38 /data04/TROY/TROY_INDEX10M07.dbf                                             1.6024E+13 OFFLINE YES

once all files are recovered check fuzzyness

select file#,name,checkpoint_change#,CHECKPOINT_TIME,fuzzy from v$datafile_header where fuzzy='YES';

go to sql prompt and to recover database to remove fuzzyness

SQL > recover database;

now fuzzy query should return no rows.

run again to verify

select file#,name,checkpoint_change#,CHECKPOINT_TIME,fuzzy from v$datafile_header where fuzzy='YES';

now open the database

SQL > alter database open;

make datafiles online

ALTER DATABASE DATAFILE '/data04/TROY/TROY_INDEX10M01.dbf' ONLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_INDEX10M04.dbf' ONLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_INDEX10M07.dbf' ONLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_INDEX64K01.dbf' ONLINE;
ALTER DATABASE DATAFILE '/data06/TROY/TROY_sysaux02.dbf' ONLINE;
ALTER DATABASE DATAFILE '/data06/TROY/oradata/TROY_PERFSTA02.dbf' ONLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_temp01.dbf' ONLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_temp02.dbf' ONLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_undotbs04.dbf' ONLINE;
ALTER DATABASE DATAFILE '/data04/TROY/TROY_system02.dbf' ONLINE;

use below query to verify that only ONLINE and SYSTEM status of all files.

SQL> select status,count(*) from v$datafile group by status;