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Generalized ordered modular averaging operator and its application to group decision making

机译：广义有序模块化平均算子及其在群体决策中的应用

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In this paper, we propose a new class of operators called the ordered quasi-modular averaging (OQMA) operators based on the ordered modular averaging (OMA) operators. It is shown that the OQMA operators are monotonic, bounded, idempotent, commutative and quasi-comonotone modular. Moreover, we introduce the generalized ordered modular averaging (GOMA) operator, which is a special case of the OQMA operator. Some special cases of the GOMA operator are discussed. An orness measure to reflect the or-like degree of the GOMA operator is proposed. We further extend the GOMA operator to the generalized ordered hybrid modular (GOHM) operator, which focuses not only on the degree of importance with respect to input arguments but also their serial positions. Finally, a new method based on the GOHM operator for multi-attribute group decision making is presented and a numerical example shows that the developed approach is feasible. (C) 2015 Elsevier B.V. All rights reserved.
机译：在本文中，我们提出了一种基于有序模数平均（OMA）运算符的新型运算符，称为有序拟模平均（OQMA）运算符。结果表明，OQMA算子是单调的，有界的，幂等的，可交换的和拟共单调模块。此外，我们介绍了广义有序模块化平均（GOMA）运算符，这是OQMA运算符的特例。讨论了GOMA运算符的一些特殊情况。提出了一种反映GOMA算子的似然度的orness度量。我们进一步将GOMA运算符扩展到广义有序混合模块化（GOHM）运算符，该运算符不仅关注输入自变量的重要性程度，还关注它们的串行位置。最后，提出了一种基于GOHM算子的多属性群决策方法，并通过数值算例表明了该方法的可行性。 （C）2015 Elsevier B.V.保留所有权利。

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