In this article we used picture linguistic fuzzy Choquet integral weighted averaging (PLFCIWA) operator for multi-attribute group decision making problem, where the attribute weight information are completely unknown. Firstly, we utilized the PLFCIWA operator to aggregate the total preference value of each alternative by decision makers. An optimization model are used to obtain the weighting vector of the criteria, using the basic ideal of traditional grey relational analysis (GRA) method. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution is computed. Then, a relative relational degree is defined to find the ranking order of all alternatives by calculating the degree of grey relation to both the positive-ideal solution (PIS) and negative ideal solution (NIS) simultaneously. Finally, a descriptive example is solved to satisfy effectiveness and practicality of the proposed techniques.