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Power Geometric Operations of Trapezoidal Atanassov’s Intuitionistic Fuzzy Numbers Based on Strict t-Norms and t-Conorms and Its Application to Multiple Attribute Group Decision Making

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Abstract

Trapezoidal Atanassov’s intuitionistic fuzzy numbers (TrAIFNs) is one of the useful tools to manage the fuzziness and vagueness in expressing decision data and solving decision making problems. In this paper, based on the operation laws defined by strict t-norms and t-conorms, four kinds of power geometric operators, i.e., triangular (co)norms-based (T-based) power geometric operator of TrAIFNs, T-based weighted power geometric operator of TrAIFNs, T-based power ordered weighted geometric operator of TrAIFNs, and T-based power hybrid geometric operator of TrAIFNs, are developed. To minimize loss of information in process, a new ranking method of TrAIFNs are presented based on the newly proposed possibility differences of TrAIFNs; Moreover, utilizing strict t-conorms, a new similarity measurement of TrAIFNs is innovated. Thereby, in combination with all the referred elements, two approaches to multiple attributes group decision making using TrAIFNs are developed. In the end, the feasibility of those methods and the superiority over the existing methods are demonstrated by a numerical example.

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Acknowledgements

Zhihong Yi is very grateful to Prof. Shuping Wan (Jiangxi University of Finance and Economics) for his valuable suggestions on the preparation of the manuscript, and Prof. Feng Qin (Jiangxi Normal University) and Prof. Hongquan Li for their directions. This work is supported by PhD Research Startup Foundation of Nanchang Normal University under Grant NSBSJJ2020015, Jiangxi Natural Science Foundation (No. 20224BAB201015), and the Scientific Research Foundation of Jiangxi Provincial Education Department (No. GJJ2202014), and National Natural Science Foundation of China(No.12261049).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Nanchang Normal University, Ruixiang RD, Nanchang, 330000, Jiangxi, People’s Republic of China

    Zhihong Yi & Lijuan Yao

  2. School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, Punjab, 147004, India

    Harish Garg

  3. Department of Mathematics, Graphic Era Deemed to be University, Dehradun, 248002, Uttarakhand, India

    Harish Garg

  4. Applied Science Research Center, Applied Science Private University, Amman, 11931, Jordan

    Harish Garg

  5. College of Technical Engineering, Department of Medical Devices Engineering Technologies, National University of Science and Technology, Dhi Qar, Nasiriyah, Iraq

    Harish Garg

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Yi, Z., Yao, L. & Garg, H. Power Geometric Operations of Trapezoidal Atanassov’s Intuitionistic Fuzzy Numbers Based on Strict t-Norms and t-Conorms and Its Application to Multiple Attribute Group Decision Making. Int. J. Fuzzy Syst. 26, 239–259 (2024). https://doi.org/10.1007/s40815-023-01591-1

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