1 / 31

FUZZY LOGIC AND ITS APPLICATION TO SWITCHING SYSTEMS

FUZZY LOGIC AND ITS APPLICATION TO SWITCHING SYSTEMS. Introduction. The first step in this direction was made by Zadeh who propsed a so called “Fuzzy Set” theory dealing with events and situations having subjectively ascribed attributes. Illustrations of Situations.

crevan
Download Presentation

FUZZY LOGIC AND ITS APPLICATION TO SWITCHING SYSTEMS

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. FUZZY LOGIC AND ITS APPLICATION TO SWITCHING SYSTEMS Fuzzy Logic

  2. Introduction The first step in this direction was made by Zadeh who propsed a so called “Fuzzy Set” theory dealing with events and situations having subjectively ascribed attributes Fuzzy Logic

  3. Illustrations of Situations • The set of all real numbers much greater than 100 (Is 125 a member of this set?) • The set of all intelligent humans.(Do I belong to this set?) • The set of all poor people.(Am I a member of this set?) Obviously, all the above sets are very fuzzily defined and their members do not possess sharply defined attributes Fuzzy Logic

  4. Fuzzy Sets Let X and Y be two fuzzy sets, and x and y be the membership grades of an object with respect to sets X and Y, respectively Definition 1: Two fuzzy sets X and Y are equal (X=Y) if, and only if, for every object -i one has that its membership grade Xi in X is equal to its membership grade Yi in Y Fuzzy Logic

  5. Definition 2: A fuzzy set is the complement of another fuzzy set X and is denoted by X’ if and only if, for every object-i one has that its member-ship grade Xi’ in X’ is equal to 1-Xi, where Xi is the member ship grade of the object -i in X Fuzzy Logic

  6. Definition 3: A fuzzy set X is contained in another fuzzy set Y if and only if for every object i one has that Xi <= Yi Fuzzy Logic

  7. Definition 4: Two fuzzy sets X and Y form a union, denoted by Z = X + Y if and only if, for every object i one has that Zi = max(Xi,Yi) Fuzzy Logic

  8. Definition 5: Two fuzzy sets X and Y form an intersection, denoted by Z = X.Y, if and only if for every object i one has that Zi = min(Xi,Yi) Fuzzy Logic

  9. Fuzzy Logic

  10. Fuzzy Logic

  11. CLASSIFICATION OF FUZZY FUNCTIONS where, 1>a1>a2>……>an-1>0 Fuzzy Logic

  12. Fuzzy Logic

  13. Relationship (9) is satisfied if and only if the variables(x,y,z) satisfy the following relations: Fuzzy Logic

  14. 2 Fuzzy Logic

  15. Fuzzy Logic

  16. Fuzzy Logic

  17. Fuzzy Logic

  18. Fuzzy Logic

  19. ……(17) Fuzzy Logic

  20. Fuzzy Logic

  21. ……(18) Fuzzy Logic

  22. Example: Fuzzy Logic

  23. Fuzzy Logic

  24. Fuzzy Logic

  25. Fuzzy Logic

  26. Fuzzy Logic

  27. Fuzzy Logic

  28. Fuzzy Logic

  29. Fuzzy Logic

  30. Fuzzy Logic

  31. Fuzzy Logic

More Related