An -polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The -polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the -polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi -norm and -conorm to handle uncertainty in -polar fuzzy (, henceforth) information, which are Dombi weighted averaging () operator, Dombi ordered weighted averaging () operator, Dombi hybrid averaging () operator, Dombi weighted geometric () operator, Dombi weighted ordered geometric operator, and Dombi hybrid geometric () operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve information with and operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with -ELECTRE-I approach (Akram et al. 2019) and Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.

中文翻译：

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极性模糊信息下决策的Dombi集合算子的扩展

一个-极模糊集是分析多极，多属性，多指标数据的功能强大的数学模型。本-极模糊集已经出现作为一个有用的工具，在多属性决策刻画的不确定性。这篇文章的目的是分析下集结算子-与Dombi规范操作的帮助极模糊的环境。在这篇文章中，我们开发了一些平均和几何集成使用Dombi运营商-规范和-余模在处理不确定性-极模糊（，从今以后）的信息，这是Dombi加权平均（）操作，Dombi有序加权平均（）运算符，Dombi混合平均（）运算符，Dombi加权几何（）运算符，Dombi加权有序几何运算符和Dombi混合几何（）运算符。我们研究提议的算子的性质，即幂等，单调性和有界性。此外，我们给出了一种算法来解决涉及和操作员信息的多准则决策问题。为了证明所提出模型的有效性和可行性，我们用所提出的模型解决了两个数值示例，并与-ELECTRE-I方法（Akram等人2019）和Hamacher聚合算子（Waseem等人2019）。最后，我们通过有效性测试来检查发达运营商的有效性。