In this study, Dombi operations are introduced on two m-polar fuzzy sets (mFSs). Here, Dombi operation on m-polar fuzzy numbers (mFNs), some new averaging and geometric averaging operators, namely mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid weighted averaging (mFDHWA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi ordered weighted geometric (mFDOWG) operator, and mF Dombi hybrid weighted geometric (mFDHWGA) operator, have been proposed. Further, some properties like idempotency, boundedness, monotonicity, and commutativity are established. Next, a multi-attribute decision-making (MADM) method in mFNs environment based on mFDWA and mFDWG operators is constructed. Finally, an application of the present MADM method for selecting the best location for the construction of thermal power stations is presented. The present approach with the existing procedure is also compared and a sensitivity analysis of the proposed plan is given.

在这项研究中，在两个m极模糊集（mFS）上引入了Dombi运算。在这里，m上的Dombi运算极模糊数（mFNs），一些新的平均和几何平均算子，即mF Dombi加权平均（mFDWA）算子，mF Dombi有序加权平均（mFDOWA）算子，mF Dombi混合加权平均（mFDHWA）算子，mF Dombi加权几何算子已经提出了（mFDWG）运算符，mF Dombi有序加权几何（mFDOWG）运算符和mF Dombi混合加权几何（mFDHWGA）运算符。此外，建立了一些特性，如幂等性，有界性，单调性和可交换性。接下来，构建了基于mFDWA和mFDWG运算符的mFNs环境中的多属性决策（MADM）方法。最后，提出了本MADM方法在选择最佳位置建造火力发电厂中的应用。