To cope with awkward and unreliable information in daily life issues, the theory of interval-valued picture fuzzy set (IVPFS) is a useful idea to manage unpredictable and vague information. An IVPFS contains the degree of truth, abstinence, and falsity in the finite subset of a unit interval with a rule that is the sum of the upper parts of all degrees is cannot exceed from unit interval. In this study, to find the interrelationships among any number of IVPFSs, we examined the interval-valued picture fuzzy frank averaging operator, interval-valued picture fuzzy frank weighted averaging operator, interval-valued picture fuzzy frank weighted geometric operator and discussed their properties. Moreover, some special cases of the presented operators based on IVPFSs are also discovered. The analytic hierarchy process (AHP) by using the IVPFSs is also explored and discussed in their different aspects. Finally, a multiattribute decision-making procedure is investigated by using proposed operators based on IVPFSs. We illustrated some numerical examples based on explored frank aggregation operators and AHP methods to examine the feasibility and validity of the presented approaches. The comparative analysis, geometrical representations, advantages of the investigated approaches are also discussed.

中文翻译：

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基于区间值图像模糊集的弗兰克聚合算子和层次分析法及其应用

为了应对日常生活问题中的尴尬和不可靠信息，区间值图像模糊集（IVPFS）理论是管理不可预测和模糊信息的有用思想。IVPFS 包含单位区间的有限子集中的真实度、节制度和虚假度，其规则是所有度的上半部分之和不能超出单位区间。在这项研究中，为了找到任意数量的IVPFS之间的相互关系，我们研究了区间值图像模糊坦率平均算子、区间值图像模糊坦率加权平均算子、区间值图像模糊坦率加权几何算子并讨论了它们的性质。此外，还发现了基于 IVPFS 的所提出算子的一些特殊情况。还从不同方面探索和讨论了使用 IVPFS 的层次分析法 (AHP)。最后，通过使用基于 IVPFS 的建议算子研究了多属性决策过程。我们基于探索的坦率聚合算子和 AHP 方法说明了一些数值示例，以检查所提出方法的可行性和有效性。还讨论了所研究方法的比较分析、几何表示和优点。