Fighting-type Pokémon take double damage from Flying and Psychic-type attacks. However, they only take half damage from Bug, Rock, and Dark-type attacks. They take normal damage from all other attack types.
Fighting-type moves do double damage to Normal, Ice, Rock, Dark, and Steel-type Pokémon. However, they only do half damage to Poison, Flying, Psychic, and Bug-type Pokémon and they don't affect Ghost-type Pokémon. They do normal damage to all other Pokémon types.