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On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts

机译：在决策上下文中将广义Bonferroni手段扩展到Atanassov邻对

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摘要

Extensions of aggregation functions to Atanassov orthopairs (often referred to as intuitionistic fuzzy sets or AIFS) usually involve replacing the standard arithmetic operations with those defined for the membership and non-membership orthopairs. One problem with such constructions is that the usual choice of operations has led to formulas which do not generalize the aggregation of ordinary fuzzy sets (where the membership and non-membership values add to 1). Previous extensions of the weighted arithmetic mean and ordered weighted averaging operator also have the absorbent element (1,0). which becomes particularly problematic in the case of the Bonferroni mean, whose generalizations are useful for modeling mandatory requirements. As well as considering the consistency and interpretability of the operations used for their construction, we hold that it is also important for aggregation functions over higher order fuzzy sets to exhibit analogous behavior to their standard definitions. After highlighting the main drawbacks of existing Bonferroni means defined for Atanassov orthopairs and interval data, we present two alternative methods for extending the generalized Bonferroni mean. Both lead to functions with properties more consistent with the original Bonferroni mean, and which coincide in the case of ordinary fuzzy values.
机译：将聚合函数扩展到Atanassov正交对（通常称为直觉模糊集或AIFS）通常涉及用为成员和非成员正交对定义的标准算术运算替换标准算术运算。这种结构的一个问题是，通常的运算选择导致公式不能概括普通模糊集的聚合（隶属度和非隶属度值加1）。加权算术平均值和有序加权平均算子的先前扩展也具有吸收性元件（1,0）。在Bonferroni均值的情况下，这尤其成问题，其泛化对于建模强制性需求很有用。除了考虑用于其构造的操作的一致性和可解释性之外，我们认为对于高阶模糊集的聚合函数表现出与其标准定义相似的行为也很重要。在强调了为Atanassov邻对和区间数据定义的现有Bonferroni均值的主要缺点之后，我们提出了两种扩展广义Bonferroni均值的替代方法。两者都导致函数具有与原始Bonferroni均值更一致的属性，并且在普通模糊值的情况下一致。

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