1 / 22

On a Certain Type of Unary Operators

On a Certain Type of Unary Operators. József Dombi Brisbane , Australia 2012. Outline of the presentation. Negation. Two representation theorems , Trillas Representation theorems , Dombi. Negation and its parameters. Modalities. Necessity operator. Dubois.

morton
Download Presentation

On a Certain Type of Unary Operators

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. On a CertainType of Unary Operators József Dombi Brisbane, Australia 2012

  2. Outline of thepresentation

  3. Negation • Tworepresentationtheorems, Trillas • Representationtheorems, Dombi

  4. Negation and itsparameters

  5. Modalities • Necessity operator Dubois

  6. Possibility operator Dubois

  7. Modalitiesinducedbytwonegations

  8. General form of modalities

  9. Particularcase of negations and modalities

  10. Modalitiesbasedondistributiveproperties • Distributivityproperty of themodalities • The solution of theabovefunctionalequations is:

  11. Modalitiesbasedonconnectives

  12. Simultaneousdistributivity • Theorem:

  13. The sharpness operator • Aggregative operator (representableuninorm)

  14. The threetypes of modifiers

  15. General form of modifiers • Theorem: Negation, hedgeand sharpness of thegeneralformofthemodifiers

  16. Modalities and hedges • If we have a logical expression andbefore the logical expression there are modal operators, we can apply these modaloperators directly on the variables.WeinterpretthisactiononthemembershipfunctionasHedge.In this case, ”very true” is the same as ”necessarily true”, or ”who is very young”isthe same as ”he/she is in our opinion necessarily young”.

  17. Modalities and hedges: An example

  18. Charachterizationby a differentequation • Theorem:

  19. Kappafunctioninthe dombi operator case

  20. Kappafunctioninthe dombi operator case

  21. Pliant operator system

  22. THANK YOU FOR YOUR ATTENTION! dombi@inf.u-szeged.hu http://www.inf.u-szeged.hu/~dombi/

More Related