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Multiple Attribute Group Decision Making Method Based on Intuitionistic Fuzzy Einstein Interactive Operations

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Abstract

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.

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Acknowledgment

This paper is supported by the National Natural Science Foundation of China (Nos. 71771140, 71471172 and 71801142), 文化名家暨“四个一批”人才项目(Project of cultural masters and “the four kinds of a batch” talents), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045), the Humanities and Social Sciences Research Project of Ministry of Education of China (17YJC630077).

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  1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250014, Shandong, China

    Peide Liu & Peng Wang

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  1. Peide Liu
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Liu, P., Wang, P. Multiple Attribute Group Decision Making Method Based on Intuitionistic Fuzzy Einstein Interactive Operations. Int. J. Fuzzy Syst. 22, 790–809 (2020). https://doi.org/10.1007/s40815-020-00809-w

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