IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1614-d415629.html
   My bibliography  Save this article

Arithmetics of Vectors of Fuzzy Sets

Author

Listed:
  • Hsien-Chung Wu

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan)

Abstract

The arithmetic operations of fuzzy sets are completely different from the arithmetic operations of vectors of fuzzy sets. In this paper, the arithmetic operations of vectors of fuzzy intervals are studied by using the extension principle and a form of decomposition theorem. These two different methodologies lead to the different types of membership functions. We establish their equivalences under some mild conditions. On the other hand, the α -level sets of addition, difference and scalar products of vectors of fuzzy intervals are also studied, which will be useful for the different usage in applications.

Suggested Citation

  • Hsien-Chung Wu, 2020. "Arithmetics of Vectors of Fuzzy Sets," Mathematics, MDPI, vol. 8(9), pages 1-42, September.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1614-:d:415629
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1614/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/9/1614/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hsien-Chung Wu, 2019. "Generalized extension principle for non-normal fuzzy sets," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 399-432, December.
    2. Barnab?s Bede & Luciano Stefanini, 2012. "Generalized Differentiability of Fuzzy-valued Functions," Working Papers 1209, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
    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. Nadeem Salamat & Muhammad Mustahsan & Malik M. Saad Missen, 2019. "Switching Point Solution of Second-Order Fuzzy Differential Equations Using Differential Transformation Method," Mathematics, MDPI, vol. 7(3), pages 1-19, March.
    2. A. Rufián-Lizana & Y. Chalco-Cano & G. Ruiz-Garzón & H. Román-Flores, 2014. "On some characterizations of preinvex fuzzy mappings," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 771-783, July.
    3. Tofigh Allahviranloo & Zahra Noeiaghdam & Samad Noeiaghdam & Juan J. Nieto, 2020. "A Fuzzy Method for Solving Fuzzy Fractional Differential Equations Based on the Generalized Fuzzy Taylor Expansion," Mathematics, MDPI, vol. 8(12), pages 1-24, December.
    4. Nguyen Dinh Phu, 2016. "On Nonlocal Initial Problems for Fuzzy Differential Equations and Environmental Pollution Problems," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 2(8), pages 77-92, 08-2016.
    5. Saed Mallak & Doa’a Farekh & Basem Attili, 2021. "Numerical Investigation of Fuzzy Predator-Prey Model with a Functional Response of the Form Arctan ( ax )," Mathematics, MDPI, vol. 9(16), pages 1-22, August.
    6. Animesh Mahata & Sankar Prasad Mondal & Ali Ahmadian & Fudiah Ismail & Shariful Alam & Soheil Salahshour, 2018. "Different Solution Strategies for Solving Epidemic Model in Imprecise Environment," Complexity, Hindawi, vol. 2018, pages 1-18, May.
    7. Beatriz Hernández-Jiménez & Gabriel Ruiz-Garzón & Antonio Beato-Moreno & Rafaela Osuna-Gómez, 2021. "A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    8. Luciano Stefanini & Barnab?s Bede, 2012. "Generalized Fuzzy Differentiability with LU-parametric Representation," Working Papers 1210, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
    9. Omid Solaymani Fard & Mohadeseh Ramezanzadeh, 2017. "On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach," Complexity, Hindawi, vol. 2017, pages 1-12, September.

    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:8:y:2020:i:9:p:1614-:d:415629. 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.