Additive consistent interval-valued Atanassov intuitionistic fuzzy preference relation and likelihood comparison algorithm based group decision making.

• The likelihood of interval-valued Atanassov intuitionistic fuzzy value.• Consistency of interval-valued Atanassov intuitionistic fuzzy preference relation.• Two special interval fuzzy preference relations are extracted.• Obtain the priority weights by a parametric linear program.• Construct an optimization model to derive decision makers' weights.