Hesitant Fermatean fuzzy Bonferroni mean operators for multi-attribute decision-making

IF 5 2区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Complex & Intelligent Systems Pub Date : 2023-09-12 DOI:10.1007/s40747-023-01203-3

Yibo Wang, Xiuqin Ma, Hongwu Qin, Huanling Sun, Weiyi Wei

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Abstract

Abstract Hesitant Fermatean fuzzy sets (HFFS) can characterize the membership degree (MD) and non-membership degree (NMD) of hesitant fuzzy elements in a broader range, which offers superior fuzzy data processing capabilities for addressing complex uncertainty issues. In this research, first, we present the definition of the hesitant Fermatean fuzzy Bonferroni mean operator (HFFBM). Further, with the basic operations of HFFS in Einstein t-norms, the definition and derivation process of the hesitant Fermatean fuzzy Einstein Bonferroni mean operator (HFFEBM) are given. In addition, considering how weights affect decision-making outcomes, the hesitant Fermatean fuzzy weighted Bonferroni mean (HFFWBM) operator and the hesitant Fermatean fuzzy Einstein weighted Bonferroni mean operator (HFFEWBM) are developed. Then, the properties of the operators are discussed. Based on HFFWBM and HFFEWBM operator, a new multi-attribute decision-making (MADM) approach is provided. Finally, we apply the proposed decision-making approach to the case of a depression diagnostic evaluation for three depressed patients. The three patients' diagnosis results confirmed the proposed method's validity and rationality. Through a series of comparative experiments and analyses, the proposed MADM method is an efficient solution for decision-making issues in the hesitant Fermatean fuzzy environment.

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多属性决策的犹豫fermatan模糊Bonferroni均值算子

摘要犹豫Fermatean模糊集(HFFS)可以在更大范围内表征犹豫模糊元素的隶属度(MD)和非隶属度(NMD)，为解决复杂的不确定性问题提供了优越的模糊数据处理能力。在本研究中，我们首先给出了犹疑Fermatean模糊Bonferroni mean算子(HFFBM)的定义。在此基础上，利用爱因斯坦t-范数中HFFS的基本运算，给出了犹豫不决fermatan模糊Einstein Bonferroni mean算子(HFFEBM)的定义和推导过程。此外，考虑到权重对决策结果的影响，提出了犹豫不决Fermatean模糊加权Bonferroni均值算子(HFFWBM)和犹豫不决Fermatean模糊爱因斯坦加权Bonferroni均值算子(HFFEWBM)。然后，讨论了算子的性质。基于HFFEWBM和HFFEWBM算子，提出了一种新的多属性决策方法。最后，我们将提出的决策方法应用于三名抑郁症患者的抑郁症诊断评估案例。3例患者的诊断结果证实了该方法的有效性和合理性。通过一系列的对比实验和分析，所提出的MADM方法是一种有效的解决犹豫费马模糊环境下决策问题的方法。

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来源期刊

Complex & Intelligent Systems COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-

CiteScore

9.60

自引率

10.30%

发文量

297

期刊介绍： Complex & Intelligent Systems aims to provide a forum for presenting and discussing novel approaches, tools and techniques meant for attaining a cross-fertilization between the broad fields of complex systems, computational simulation, and intelligent analytics and visualization. The transdisciplinary research that the journal focuses on will expand the boundaries of our understanding by investigating the principles and processes that underlie many of the most profound problems facing society today.