The linear Diophantine fuzzy set (LDFS) has been proved to be an efficient tool in expressing decision maker (DM) evaluation values in multicriteria decision-making (MCDM) procedure. To more effectively represent DMs’ evaluation information in complicated MCDM process, this paper proposes a MCDM method based on proposed novel aggregation operators (AOs) under linear Diophantine fuzzy set (LDFS). A -Rung orthopair fuzzy set (-ROFS), Pythagorean fuzzy set (PFS), and intuitionistic fuzzy set (IFS) are rudimentary concepts in computational intelligence, which have diverse applications in modeling uncertainty and MCDM. Unfortunately, these theories have their own limitations related to the membership and nonmembership grades. The linear Diophantine fuzzy set (LDFS) is a new approach towards uncertainty which has the ability to relax the strict constraints of IFS, PFS, and –ROFS by considering reference/control parameters. LDFS provides an appropriate way to the decision experts (DEs) in order to deal with vague and uncertain information in a comprehensive way. Under these environments, we introduce several AOs named as linear Diophantine fuzzy Einstein weighted averaging (LDFEWA) operator, linear Diophantine fuzzy Einstein ordered weighted averaging (LDFEOWA) operator, linear Diophantine fuzzy Einstein weighted geometric (LDFEWG) operator, and linear Diophantine fuzzy Einstein ordered weighted geometric (LDFEOWG) operator. We investigate certain characteristics and operational laws with some illustrations. Ultimately, an innovative approach for MCDM under the linear Diophantine fuzzy information is examined by implementing suggested aggregation operators. A useful example related to a country’s national health administration (NHA) to create a fully developed postacute care (PAC) model network for the health recovery of patients suffering from cerebrovascular diseases (CVDs) is exhibited to specify the practicability and efficacy of the intended approach.

中文翻译：

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多准则决策问题的线性丢番图模糊爱因斯坦聚合算子

线性丢番图模糊集 (LDFS) 已被证明是在多标准决策 (MCDM) 过程中表达决策者 (DM) 评估值的有效工具。为了在复杂的 MCDM 过程中更有效地表示 DM 的评价信息，本文提出了一种基于线性丢番图模糊集 (LDFS) 下提出的新型聚合算子 (AO) 的 MCDM 方法。A -梯级正交对模糊集（-ROFS)、勾股模糊集 (PFS) 和直觉模糊集 (IFS) 是计算智能中的基本概念，它们在不确定性建模和 MCDM 中有多种应用。不幸的是，这些理论在会员和非会员等级方面有其自身的局限性。线性丢番图模糊集 (LDFS) 是一种解决不确定性的新方法，它能够放松 IFS、PFS 和–ROFS 通过考虑参考/控制参数。LDFS 为决策专家 (DE) 提供了一种适当的方法，以便以全面的方式处理模糊和不确定的信息。在这些环境下，我们引入了几种AO，称为线性丢番图模糊爱因斯坦加权平均（LDFEWA）算子、线性丢番图模糊爱因斯坦有序加权平均（LDFEOW​​A）算子、线性丢番图模糊爱因斯坦加权几何（LDFEWG）算子和线性丢番图模糊爱因斯坦有序加权平均（LDFEOW​​A）算子。加权几何 (LDFEOW​​G) 算子。我们通过一些插图研究了某些特性和运行规律。最后，通过实施建议的聚合算子来检查线性丢番图模糊信息下 MCDM 的创新方法。