Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan.
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan.
Math Biosci Eng. 2023 Jan;20(2):3566-3593. doi: 10.3934/mbe.2023166. Epub 2022 Dec 6.
Aggregation is a very efficient indispensable tool in which several input values are transformed into a single output value that further supports dealing with different decision-making situations. Additionally, note that the theory of m-polar fuzzy (mF) sets is proposed to tackle multipolar information in decision-making problems. To date, several aggregation tools have been widely investigated to tackle multiple criteria decision-making (MCDM) problems in an m-polar fuzzy environment, including m-polar fuzzy Dombi and Hamacher aggregation operators (AOs). However, the aggregation tool to deal with m-polar information under Yager's operations (that is, Yager's t-norm and t-conorm) is missing in the literature. Due to these reasons, this study is devoted to investigating some novel averaging and geometric AOs in an mF information environment through the use of Yager's operations. Our proposed AOs are named as the mF Yager weighted averaging (mFYWA) operator, mF Yager ordered weighted averaging operator, mF Yager hybrid averaging operator, mF Yager weighted geometric (mFYWG) operator, mF Yager ordered weighted geometric operator and mF Yager hybrid geometric operator. The initiated averaging and geometric AOs are explained via illustrative examples and some of their basic properties, including boundedness, monotonicity, idempotency and commutativity are also studied. Further, to deal with different MCDM situations containing mF information, an innovative algorithm for MCDM is established under the under the condition of mFYWA and mFYWG operators. After that, a real-life application (that is, selecting a suitable site for an oil refinery) is explored under the conditions of developed AOs. Moreover, the initiated mF Yager AOs are compared with existing mF Hamacher and Dombi AOs through a numerical example. Finally, the effectiveness and reliability of the presented AOs are checked with the help of some existing validity tests.
聚集是一种非常有效的不可或缺的工具，它可以将多个输入值转换为单个输出值，进一步支持处理不同的决策情况。此外，请注意，m-极性模糊（mF）集的理论是为了解决决策问题中的多极信息而提出的。迄今为止，已经有几种聚合工具被广泛研究用于解决 m-极性模糊环境中的多准则决策（MCDM）问题，包括 m-极性模糊 Dombi 和 Hamacher 聚合算子（AOs）。然而，在 Yager 操作下处理 m-极性信息的聚合工具在文献中是缺失的。由于这些原因，本研究致力于通过使用 Yager 操作来研究 mF 信息环境中的一些新的平均和几何 AOs。我们提出的 AOs 被命名为 mF Yager 加权平均（mFYWA）算子、mF Yager 有序加权平均算子、mF Yager 混合平均算子、mF Yager 加权几何（mFYWG）算子、mF Yager 有序加权几何算子和 mF Yager 混合几何算子。通过示例解释了所提出的平均和几何 AOs，并研究了它们的一些基本属性，包括有界性、单调性、幂等性和交换性。此外，为了处理包含 mF 信息的不同 MCDM 情况，在 mFYWA 和 mFYWG 算子的条件下建立了一种用于 MCDM 的新算法。之后，在开发的 AOs 条件下，探讨了一个实际应用（即选择一个合适的炼油厂厂址）。此外，通过数值实例将所提出的 mF Yager AOs 与现有的 mF Hamacher 和 Dombi AOs 进行了比较。最后，借助一些现有的有效性检验来检验所提出的 AOs 的有效性和可靠性。
