A cubic m-polar fuzzy set (CmPFS) is a new hybrid extension of cubic set (CS) and m-polar fuzzy set (mPFS). A CS comprises two parts; one part consists of a fuzzy interval (may sometimes be a fuzzy number) acting as membership grade (MG), and the second part consists of a fuzzy number acting as non-membership grade (NMG). An mPFS assigns m number of MGs against each alternative in the universe of discourse. A CmPFS deals with single as well as multi-polar information in the cubic environment. In this article, we explore some new aspects and consequences of the CmPFS. We define score and accuracy functions to find the priorities of alternatives/objects in multi-criteria decision-making (MCDM). For this objective, some new operations, like addition, scalar/usual multiplication, and power, are defined under Dombi’s t-norm and t-conorm. We develop several new aggregation operators (AOs) using cubic m-polar fuzzy Dombi’s t-norm and t-conorm. We present certain properties of suggested operators like monotonicity, commutativity, idempotency, and boundedness. Additionally, to discuss the application of these AOs, we present an advanced superiority and inferiority ranking (SIR) technique to deal with the problem of conversion from a linear economy to a circular economy. Moreover, a comparison analysis of proposed methodology with some other existing methods is also given.

中文翻译：

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具有Dombi的T-范数和T-conorm的三次M极模糊混合算子及其应用

立方m极模糊集（CmPFS）是立方集（CS）和m极模糊集（mPFS）的新混合扩展。CS包括两部分：一部分由充当成员资格等级（MG）的模糊区间（有时可能是模糊数）组成，第二部分由充当非成员等级（NMG）的模糊数组成。一个mPFS分配m在话语领域反对每种选择的MG数量。CmPFS处理立方环境中的单极和多极信息。在本文中，我们探讨了CmPFS的一些新方面和后果。我们定义得分和准确性函数，以在多标准决策（MCDM）中找到替代方案/目标的优先级。为此，在Dombi的t-范数和t-conorm下定义了一些新的运算，例如加法，标量/常规乘法和幂。我们使用立方m极模糊Dombi的t-范数和t-conorm开发了几个新的聚合算子（AO）。我们介绍了建议的算子的某些性质，如单调性，可交换性，幂等性和有界性。此外，要讨论这些AO的应用，我们提出了一种先进的优劣排行（SIR）技术来处理从线性经济向循环经济的转化问题。此外，还对提议的方法与其他一些现有方法进行了比较分析。