I don't know if SPECIAL has any relationship with weapons, so I'll work on the assumption that they don't.

My idea then is to do just that, along with some new weapons:

1) new weapons- melee weapons, large and small; knives and bumper swords, for example. These already exist in the game- people in the Diner room can be seen using knives, and Raiders sometimes carry swords.

Melee weapons naturally require the carrier to be closer to the enemy, which may be disadvantageous, ie Deathclaws or Radroaches.

2) In regards to SPECIAL stats and weapons here are my ideas

Strength: improves damage with heavy melee weapons

Perception: improves damage with rifles

Endurance: improves damage with handguns

Charisma: improves damage with fists

Intelligence: improves damage with energy weapons

Agility: improves damage with knives

Luck: chance for "critical hit" with all weapons

3) Weapon types:

a) shotguns are better against melee enemies, but unlike melee weapons are still an option for ranged combat

melee weapons have a chance to stun targets for a second, preventing the target from moving or fighting

c) rifles encourage the carrier to fight at a distance, useful for the weaker dwellers that cannot sustain much damage/ low on health

d) energy weapons can weaken targets they hit, making them more vulnerable to things like stun and critical hits.

Another idea is that they die in a pile of goo, which causes other hostile targes in the same room a stun, OR they cause your other fighting dwellers to fight harder for a duration (comon, seeing a Deathclaw vaporize can be lifting to morale!).

e) handguns are your default control group weapon- no particular enefits, but more plentiful

4) Armour types: Raiders, Deathclaws, Molerats and Radroachs have diferent types of armour. Radroaches are light, whereas Deathclaws are heavy. Radiers come in all possible types depending on what they spawn as.

5) Ammo types: a new UI feature that outiks your entire vault's armed dwellers with some specific bouses. These act as a secondary resource- use up a particulary ammo type and you canno use more until you gain more. Ammo types can be found by exploring.

a) Hollow Point: more damage to unarmoured targets (ie Radroaches); common

Armour Picering: more damage to armoured targets (re Deathclaws); rare

c) Explosive: damage multiple targets close together; uncommon

6) More enemies:

a) Enclave: slow moving, heavy armour and with energy weapons.

Super Mutants w/ Centaurs: slower, moderate armour and with more powerful melee/ ranged weapons than Raiders

c) Savage Dogs: they do not attack your Vault per se by entering the elavators, rather they loiter outside and prevent new dwellers from coming and attack exploring dwellers. You can attack them via guards assigned to the entrance but they will enter and fight your guards.

7) Allies:

Mercenares: they appear as a button when Radiers/ Deathclaws come to attack- they spawn outside and run into yor Valt and automaticlly chase the attackers. Disadvantages is that your dwellers do not gain XP after the incident, and they are pricey. THese can have a cooldown timer, so that they cannot be spammed.

Brotherhood of Steel: they will appear like Radiers, but instead of an alarm they will enter your Vault and loiter at the entrance. Unlike mercenaries, they do not cost caps but instead induce a significant resource drain, to simulate your accomodating them. Any incidents that occur like Radiers they will assist. They will leave after a Raider/ Deathclaw attack, or you can dismiss them before that time, but like Raiders their apperance is random.

Traders: they will appear like Raiders, and rarer than BoS. You can choose to pay them for an increase in happiness and a chance to buy some common items, or accomodate them for increased resource drain for a longer happiness increase. Traders will flee lke pregnant women if incidents occur.

Yea I've covered that idea http://www.gamesas.com/topic/1534394-improvements-to-fos-forward-looking-to-fos-2/.

The only issue with this idea (and it has less to do with the idea, but rather the other ingame designs that nullify this idea) is that training rooms literally render it null. All dwellers can get 10 in every stat so to correspond a weapon type with the quantity of a stat would just be pointless.

Now if you take the dweller creation idea I state in the linked post above (first point near the top) and also remove training rooms (to leave room for other rooms that carry more gameplay value even pass end game) then you can make the above suggestions.

To add to that, I do like what you said about positioning vs weapons. Such as shotguns are good vs melee weapons. A bonus in positioning should be given though it shouldn't just be weapon vs weapon but rather weapon in reference to target's relative position.