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q-Rung orthopair fuzzy inequality derived from equality and operation

  • Fuzzy systems and their mathematics
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Abstract

The q-rung orthopair fuzzy set is an extension of fuzzy set, whose remarkable characteristic is that the sum of q power of membership degree, non-membership degree and hesitation degree is equal to 1. Inequalities on q-rung orthopair fuzzy set are of importance in theory of uncertainty. In this paper, firstly, some q-rung orthopair fuzzy inequalities are constructed based on the equality in definition. Then, their inequalities are proved by well-known inequalities, including Rearrangement, Mean, Chebyshev, Nesbitt, Power-Mean, Cauchy, Carlson, Wei-Wei dual, Hölder, Minkowski, Jensen, Tangent, Schur, Muirhead, Vasc or their mix forms. Finally, we derive other q-rung orthopair fuzzy inequalities based on some existing operations, which provides a new basis for the q-rung orthopair fuzzy inequalities.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (62006155, 62102261), Guangdong Key Construction Discipline Research Capacity Enhancement Project (2022ZDJS049), Special Innovation Projects of Universities in Guangdong Province (2022KTSCX126), and Science and Technology Project of Shaoguan City (220606114533116).

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Authors and Affiliations

  1. School of Information Engineering, Shaoguan University, Shaoguan, 512005, China

    Xindong Peng

  2. College of Computer, National University of Defense Technology, Changsha, 410073, China

    Xindong Peng & Zhigang Luo

  3. School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, 221116, China

    Yanru Wang

Authors
  1. Xindong Peng
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  2. Yanru Wang
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  3. Zhigang Luo
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Contributions

All authors contributed to the study conception and design. Material preparation was performed by XP. The first draft of the manuscript was written by XP and then polished by YW and ZL. All authors read and approved the final manuscript.

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Correspondence to Xindong Peng.

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Peng, X., Wang, Y. & Luo, Z. q-Rung orthopair fuzzy inequality derived from equality and operation. Soft Comput 27, 5233–5255 (2023). https://doi.org/10.1007/s00500-023-07950-2

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