IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i6p886-d366092.html
   My bibliography  Save this article

A Method of Generating Fuzzy Implications from n Increasing Functions and n + 1 Negations

Author

Listed:
  • Maria N. Rapti

    (Section of Mathematics and Informatics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, 67100 Kimeria, Greece)

  • Basil K. Papadopoulos

    (Section of Mathematics and Informatics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, 67100 Kimeria, Greece)

Abstract

In this paper, we introduce a new construction method of a fuzzy implication from n increasing functions g i : [ 0 , 1 ] → [ 0 , ∞ ) , ( g ( 0 ) = 0 ) ( i = 1 , 2 , … , n , n ∈ ℕ ) and n + 1 fuzzy negations N i ( i = 1 , 2 , … , n + 1 , n ∈ ℕ ). Imagine that there are plenty of combinations between n increasing functions g i and n + 1 fuzzy negations N i in order to produce new fuzzy implications. This method allows us to use at least two fuzzy negations N i and one increasing function g in order to generate a new fuzzy implication. Choosing the appropriate negations, we can prove that some basic properties such as the exchange principle (EP), the ordering property (OP), and the law of contraposition with respect to N are satisfied. The worth of generating new implications is valuable in the sciences such as artificial intelligence and robotics. In this paper, we have found a novel method of generating families of implications. Therefore, we would like to believe that we have added to the literature one more source from which we could choose the most appropriate implication concerning a specific application. It should be emphasized that this production is based on a generalization of an important form of Yager’s implications.

Suggested Citation

  • Maria N. Rapti & Basil K. Papadopoulos, 2020. "A Method of Generating Fuzzy Implications from n Increasing Functions and n + 1 Negations," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:886-:d:366092
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/6/886/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/6/886/
    Download Restriction: no
    ---><---

    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:6:p:886-:d:366092. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.