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.

中文翻译：

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基于图片犹豫模糊设置的权重信息不完全的GRA方法多属性决策问题

本研究的主要目的是开发一种解决多属性决策问题（MADM）的方法，其中属性值表现为图片犹豫模糊数，并且属性权重信息不完全已知。为了获得属性权重向量，我们建立了一个依赖于常规灰色关联分析方法的基本思想的优化模型，通过该模型可以求解属性权重。我们为属性权重信息完全未知的罕见情况建立了另一种优化模型。通过求解该模型，我们得到一个基本的、确定的方程，可以用来确定属性权重。确定每个备选方案与正理想解（PIS）和负理想解（NIS）之间的灰色关联度。同时，通过确定与 PIS 和 NIS 的灰色关联度，定义了一个相对关联度来决定所有替代的排序顺序。为了检查产生的方法并显示其有效性和适用性，给出了一个说明性示例。与现有 MADM 方法的比较分析被认为显示了所提出策略的优势。