Fuzzy Time Intervals System Description of the FuTILibrary Hans J - - PowerPoint PPT Presentation

Fuzzy Time Intervals – System Description of the FuTI–Library

Hans J¨ urgen Ohlbach (Edgar Stoffel)

• Inst. f¨

ur Informatik, LMU Munich

H.J. Ohlbach (E. Stoffel) (LMU) FuTI 1 / 7

Background: The CTTN System

CTTN: Computational Treatment of Temporal Notions A WG A1 project. Components: time points and crisp and fuzzy temporal intervals (the FuTI library) periodic temporal notions (the PartLib library) the GeoTemporal Specification language (GeTS) calendars and various support modules

H.J. Ohlbach (E. Stoffel) (LMU) FuTI 2 / 7

Fuzzy Time Intervals: An Example

✲ ✻

R 1 Party Time 6pm 7pm 10pm 12pm 2am 3am

H.J. Ohlbach (E. Stoffel) (LMU) FuTI 3 / 7

Set Operations

✲ ✻

R 1 λ-Complement for λ = 2 6 8

✲ ✻

R 1 Hamacher Intersection and Union

✲ ✻

R 1 Set Difference I \ J Kleene Lukasiewicz Goedel I J

H.J. Ohlbach (E. Stoffel) (LMU) FuTI 4 / 7

Relations

✲ ✻

R 1 Fuzzy Point–Interval Relation 10

✲ ✻

R 1 Interval-Interval Before Relation I J

H.J. Ohlbach (E. Stoffel) (LMU) FuTI 5 / 7

The Class Hierarchy

FuTI::FuTITop FuTI::Interval FuTI::Operation FuTI::Point FuTI::YFunction FuTI::BinaryYFunction FuTI::UnaryYFunction FuTI::SDGoedel FuTI::SDKleene FuTI::SDLukasiewicz FuTI::TCoNorm FuTI::TNorm FuTI::NegationYFunction FuTI::HamacherCoNorm FuTI::HamacherNorm FuTI::lambdaComplement

H.J. Ohlbach (E. Stoffel) (LMU) FuTI 6 / 7

URL

http://www.pms.ifi.lmu.de/CTTN/FuTI/index.html

H.J. Ohlbach (E. Stoffel) (LMU) FuTI 7 / 7