Multiple attribute decision making problem using GRA method with incomplete weight information based on picture hesitant fuzzy setting

The main purpose of this study is to develop a way of solving multiattribute decision-making problems (MADM), where the value of an attribute appears as picture hesitant fuzzy number and the attribute weight information is not entirely known. So as to acquire attribute weight vector, we build up a model of optimization that relies on the basic ideal of the conventional grey relational analysis method, by which attribute weight can be resolved. We build up another model of optimization for the uncommon circumstance where the attribute weight information is totally unknown. By solving this model, we get a basic and definite equation which can be utilized to be determined attribute weight. The grey relation degree between each alternative and positive ideal solution (PIS) and negative ideal solution (NIS) are determined. At the same time, a degree of relative relational is defined to decide all alternative order of ranking by ascertaining the grey relation degree to both the PIS and NIS. To examine the produced approach and to show its effectiveness and applicability an illustrative examples are given. A comparative analysis with pre-existing MADM methods are considered to show the predominance of the proposed strategy.