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On Extended L r -Norm-Based Derivatives to Intuitionistic Fuzzy Sets

Author

Listed:
  • A. S. Wungreiphi

    (School of Fundamental and Applied Sciences, Assam Don Bosco University, Sonapur 782402, Assam, India)

  • Fokrul Alom Mazarbhuiya

    (School of Fundamental and Applied Sciences, Assam Don Bosco University, Sonapur 782402, Assam, India)

  • Mohamed Shenify

    (College of Computer Science and IT, Albaha University, KSA, Albaha 65527, Saudi Arabia)

Abstract

The study of differential equation theory has come a long way, with applications in various fields. In 1961, Zygmund and Calderón introduced the notion of derivatives to metric L r , which proved to be better in applications than approximate derivatives. However, most of the studies available are on Fuzzy Set Theory. In view of this, intuitionistic fuzzy L r -norm-based derivatives deserve study. In this study, the L r -norm-based derivative for intuitionistic fuzzy number valued functions is introduced. Some of its basic properties are also discussed, along with numerical examples. The results obtained show that the proposed derivative is not dependent on the existence of the Hukuhara difference. Lastly, the Cauchy problem for the intuitionistic fuzzy differential equation is discussed.

Suggested Citation

  • A. S. Wungreiphi & Fokrul Alom Mazarbhuiya & Mohamed Shenify, 2023. "On Extended L r -Norm-Based Derivatives to Intuitionistic Fuzzy Sets," Mathematics, MDPI, vol. 12(1), pages 1-19, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:139-:d:1311337
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    References listed on IDEAS

    as
    1. Muhammad Azam & Muhammad Sajjad Ali Khan & Shilin Yang & Musavarah Sarwar, 2022. "A Decision-Making Approach for the Evaluation of Information Security Management under Complex Intuitionistic Fuzzy Set Environment," Journal of Mathematics, Hindawi, vol. 2022, pages 1-30, February.
    2. Zeeshan Ali & Tahir Mahmood & Miin-Shen Yang, 2023. "Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making," Mathematics, MDPI, vol. 11(9), pages 1-21, April.
    3. Gulfam Shahzadi & Muhammad Akram & Ahmad N. Al-Kenani, 2020. "Decision-Making Approach under Pythagorean Fuzzy Yager Weighted Operators," Mathematics, MDPI, vol. 8(1), pages 1-20, January.
    4. Qianli Zhou & Hongming Mo & Yong Deng, 2020. "A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis," Mathematics, MDPI, vol. 8(1), pages 1-20, January.
    5. Wajid Ali & Tanzeela Shaheen & Iftikhar Ul Haq & Hamza Ghazanfar Toor & Tmader Alballa & Hamiden Abd El-Wahed Khalifa, 2023. "A Novel Interval-Valued Decision Theoretic Rough Set Model with Intuitionistic Fuzzy Numbers Based on Power Aggregation Operators and Their Application in Medical Diagnosis," Mathematics, MDPI, vol. 11(19), pages 1-18, October.
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