IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2023i1p139-d1311337.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/1/139/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/1/139/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Saidjon Shiralievich Tavarov & Pavel Matrenin & Murodbek Safaraliev & Mihail Senyuk & Svetlana Beryozkina & Inga Zicmane, 2023. "Forecasting of Electricity Consumption by Household Consumers Using Fuzzy Logic Based on the Development Plan of the Power System of the Republic of Tajikistan," Sustainability, MDPI, vol. 15(4), pages 1-14, February.
    2. Zeeshan Ali & Tahir Mahmood & Miin-Shen Yang, 2020. "TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators," Mathematics, MDPI, vol. 8(10), pages 1-19, October.
    3. Deveci, Muhammet & Erdogan, Nuh & Pamucar, Dragan & Kucuksari, Sadik & Cali, Umit, 2023. "A rough Dombi Bonferroni based approach for public charging station type selection," Applied Energy, Elsevier, vol. 345(C).
    4. Zaoli Yang & Xin Li & Harish Garg & Meng Qi, 2020. "Decision Support Algorithm for Selecting an Antivirus Mask over COVID-19 Pandemic under Spherical Normal Fuzzy Environment," IJERPH, MDPI, vol. 17(10), pages 1-27, May.
    5. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:139-:d:1311337. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.