No. In Duel types resistances and weaknesses cancel each-other out. Also resistances stack and weaknesses stack. Immunities are unaffected even if the other type is weak to it. So if one type is weak to fighting and the other is resistant to fighting(like in an Ice-Flying type), the Pokemon takes neutral damage from fighting. If both Types are resistant to Fighting(like in a Psychic-Flying type) then the Pokemon is x4 resistant to Fighting. If both Types are weak to Fighting(like in an Ice-Dark type) then the Pokemon is x4 Weak to Fighting. If one type is Weak/Neutral/Resistant Fighting and the other type is Immune to Fighting then the Pokemon is Immune.