The intuitionistic fuzzy numbers (IFNs) have been extensively studied in recent years. However, the traditional operational rules (ORs) of the IFNs still have some drawbacks in solving the practical decision-making problems. Einstein t-conorm and t-norm (TAT) are an important and typical class of the TAT, but the ORs for the IFNs based on the Einstein TAT (ETAT) cannot consider the interaction between the membership degree (MD) and the non-membership degree (N-MD), they may get the unreasonable evaluation results in some realistic decision-making situations. So this paper proposes some new Einstein interactive ORs for the IFNs, then, it further presents the intuitionistic fuzzy Einstein interactive weighted averaging (IFEIWA) operator to overcome above existing drawbacks, and some properties of this operator are proved. Simultaneously, in order to eliminate the effects of the existing biases of some decision experts in the process of evaluating attributes, this paper proposes the intuitionistic fuzzy Einstein interactive power averaging (IFEIPA) operator and the intuitionistic fuzzy Einstein interactive weighted power averaging (IFEIWPA) operator based on the revised power weighted averaging operator, and then gives their some desirable properties. Further, by using the IFEIPA operator and the IFEIWPA operator, this paper presents a novel method for the multi-attribute group decision making (MAGDM) problems to solve practical decision-making problems. Lastly, this paper uses some actual application examples to verify the applicability and validity of the proposed MAGDM method, and then demonstrates the superiority of novel method by detailed comparison analysis with other typical methods.

中文翻译：

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基于直觉模糊爱因斯坦交互式运算的多属性群决策方法

直觉模糊数（IFN）近年来已被广泛研究。但是，传统的干扰素操作规则（OR）在解决实际决策问题时仍存在一些缺陷。爱因斯坦t-conorm和t-norm（TAT）是TAT的重要且典型的一类，但是基于爱因斯坦TAT（ETAT）的IFN的OR不能考虑隶属度（MD）与非成员之间的相互作用。隶属度（N-MD），他们可能会在某些现实的决策情况下获得不合理的评估结果。因此，本文针对干扰素提出了一些新的爱因斯坦交互式“或”算法，然后提出了直觉的模糊爱因斯坦交互式加权平均算子（IFEIWA）来克服上述现有缺点，并证明了该算子的一些性质。同时，为了消除某些决策专家在评估属性过程中现有偏差的影响，提出了基于直觉的模糊爱因斯坦交互式乘方平均算子和基于模糊直觉的爱因斯坦交互式加权乘方平均算子（IFEIWPA）。修改后的功率加权平均算子，然后给出它们的一些理想属性。此外，通过使用IFEIPA运算符和IFEIWPA运算符，本文提出了一种用于解决多属性组决策（MAGDM）问题的新方法，以解决实际的决策问题。最后，本文通过一些实际的应用实例来验证所提出的MAGDM方法的适用性和有效性，