1. Siemens medical Solutions that help Linguistic Variables with Arden Syntax Fuzzy Logical Extensions to the Arden Syntax Sven TiffeSiemens Medical Solutions Sven.Tiffe@siemens.com BD XPL² Henkestr. 127 D-91052 Erlangen Germany

2. 2 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Proposed extensions – so far CExtensions based on fuzzy theoretical concepts BComparison operators: fuzzy comparison by one or two additional parameters (binary or ternary operators) BTruth values: gradual transition from false to true BData types: additional attribute fuzziness to measure fuzzy context of data creation BArden operators: every operator is can handle data with fuzziness or fuzzy truth values

3. 3 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Capabilities – so far CFuzzily defined selection criteria and conditions by fuzzy comparison operators CProcessing of measured fuzziness BFuzzy if-then statements BFuzzy logical operators BAggregation operators BDefuzzification CFuzzy sets for fuzzy comparisons have to be defined each time they are used

4. 4 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Concept of Linguistic Variables CDescription of the relationship between abstract concepts (terms) and (numeric) data BName of linguistic variable BValues (terms) described by fuzzy set BExample: temperature CIndependent from terminology (1) pronounced hypothermia (2) deep hypothermia (3) moderate hypothermia (4) slight hypothermia (5) normal (6) subfebrile (7) moderate fever (8) high fever

5. 5 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Usage CFuzzy control systems BEvaluation in TOSCA project in addition to a commercial fuzzy control system CUsable as linguistic expressions in algorithms, e.g.: Bif temperature is subfebrile then Bif weight is normal and blood_pressure is increased then Auhtors: G. Zahlmann, Siemens, and M. Scherf, GSF

6. 6 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Representation using fuzzy comparisons temperature is normal could be defined as: The fuzzy set has to be (re)defined for every usage. temp_sf := temp is within 36.8 fuzzified by 0.8 to 37.1 fuzzified by 0.5; temp_sf := temp is normal; temp := liguistic variable temperature; Define linguistic variable separately: And compare to term instead compare to numeric values:

7. 7 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Representation as MLM CEach linguistic variable represented by one MLM CSlots in knowledge category: Btype: linguistic variable Bvalues: single terms of LV as Arden terms Binput: input value(s) for this variable numerical data from read statement linguistic variable as result from other MLMs Bdefuzzification: method for defuzzification (optional) Brange: range of valid (numerical) input/output value Bunit: natural language unit of (numeric) data as Arden term Bsets: fuzzy sets for every single term

8. 8 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Example linguistic variable 1.0 0.0 m(x) mmHg 010203040 normalincreased Linguistic variable Intraocular Pressure (IOP)

9. 9 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Usage – declaration CInput variables are initialized: input slot gets executed in these MLMs COutput variables are not initialized CDR diff_lr IOP le normotens_glauco := init linguistic variable 'LV_CDR'; := init linguistic variable 'LV_diff_lr'; := init linguistic variable 'LV_IOP'; := init linguistic variable 'LV_le'; := linguistic variable 'LV_ normotens_glauco;

10. 10 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Usage – evaluation, value assignment CComparison between linguistic variable and term IS returns a fuzzy truth value CAssign term to a linguistic variable (with optional weight) SET TO (WITH ) BValue is influenced by fuzziness of code block (condition) if (CDR is normal' and diff_lr is 'normal' and IOP is 'normal and le is centered) then set normotens_glauco to nowith 1.0; endif; CGet numerical value by defuzzification DEFUZZIFY

11. 11 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Example: Rule block in DIADEM project knowledge: type: data-driven;; data: (CDR, diff_lr, IOP, le) := argument; if CDR is null then /* if module not used with arguments */ CDR:= init linguistic variable 'LV_CDR'; diff_lr:= init linguistic variable 'LV_diff_lr'; IOP:= init linguistic variable 'LV_IOP'; le:= init linguistic variable 'LV_le'; endif; normotens_glauco := linguistic variable 'LV_normotens_glauco'; ;; evoke: /* direct call */;; logic: if (CDR is 'normal' AND diff_lr is 'normal' AND IOP is 'normal' AND le is 'centered') then set normotens_glauco to 'no' with 1.0; endif; if (CDR is 'normal' AND diff_lr is 'normal' AND IOP is 'normal' AND le is 'tempinferior') then set normotens_glauco to 'yes' with 0.398; endif; if (CDR is 'normal' AND diff_lr is 'normal' AND IOP is 'normal' AND le is 'tempsuperior') then set normotens_glauco to 'yes' with 0.398; endif; …

12. 12 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Evaluation CCADIAG-II/RHEUMA: expert system with large knowledge base (about 3000 MLMs); using basically fuzzy comparisons and logical operators, but is based (and thus extendable) on linguistic variables CTOSCA: fuzzy control rule set for glaucoma screening, 17 linguistic variables and 11 production rule blocks; using linguistic variables CHypertension guideline (University Pierre & Marie Curi, Medical School, Paris); using fuzzy comparisons [1] [1] MC Jaulent, et.al., Modeling uncertainty in computerized guidelines using fuzzy logic, proceedings of AMIA symposium 2001

13. 13 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Conclusion – Linguistic Variables CPluses BFormalization of relationship between terms and data BCentralized definition BArden knowledge bases describe relationship between data and linguistic concepts, independently from terminology BNo need to define fuzzy sets in each MLM, where the fuzzy set (term) is used CMinuses BAdditional data type – how shall Arden operators handle these variable? (similar problem to usage of object variables) So far, no additional operator uses these values.

14. 14 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Summary CIntegration fuzzy theoretical concepts BFuzzy comparison operators (applying concept of fuzzy sets) BFuzzy truth values BLinguistic variables CNot a fuzzy mathematical framework – only slight modifications to the programming language CYes, it runs! CEvaluation BLarge knowledge bases in different projects (CADIAG, DIADEM) BSmall knowledge bases or single rules have still to be defined

15. 15 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Summary, cont. COther uncertainty models BFuzzy logic is not the only model to represent uncertainty (probabilistic approaches, Demster-Shafer, neuronal nets) BBut: fuzzy logical extensions are easy embeddable in a procedural and rule based environment like Arden CAdditional data attribute uncertainty has to be handled by every operator BLinguistic variables result in an entirely new data type Extension of every single operator Do not modify operators and ignore these data types BSimilar problem: introduction of object oriented data types

16. 16 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Outlook CContext dependent linguistic variables BCrisp fuzzy set selection by selection criteria (e.g., sex, pregnancy) BTwo-dimensional fuzzy sets fuzzy sets are dependent on fuzzily defined patient age range CResults of evaluation

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18. 18 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Example: fuzzy fan control CProduction rules: BIf temperature is cool set speed to slow BIf temperature is moderate set speed to medium BIf temperature is hot set speed to fast CLinguistic variables: 1.0 0.0 m(x) °C 10203040 coolhot Linguistic variable temperature moderate 1.0 0.0 m(x) RPM 1000200030004000 Linguistic variable speed slowmediumfast

19. 19 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Fan control: input fuzzification CAssume, measured temperature is 28°C CTemperature is cool: 0.00 CTemperature is moderate: 0.40 CTemperature is hot: 0.60 1.0 0.0 m(x) °C 10203040 coolhot Linguistic variable temperature moderate

20. 20 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Fan control: production rules CIf temperature is cool set speed to slow CAs temperature is definitely not cool, speed has not value slow 1.0 0.0 m(x) °C 10203040 coolhot Linguistic variable temperature moderate 1.0 0.0 m(x) RPM 1000200030004000 Linguistic variable speed slowmediumfast

21. 21 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Fan control: production rules CIf temperature is moderate set speed to medium CSpeed is set to medium by a degree of 0.40 1.0 0.0 m(x) °C 10203040 coolhot Linguistic variable temperature moderate 1.0 0.0 m(x) RPM 1000200030004000 Linguistic variable speed slowmediumfast

22. 22 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Fan control: production rules CIf temperature is hot set speed to fast CSpeed is set to fast by a degree of 0.60 1.0 0.0 m(x) °C 10203040 coolhot Linguistic variable temperature moderate 1.0 0.0 m(x) RPM 1000200030004000 Linguistic variable speed slowmediumfast

23. 23 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Fan control: output value CThe output variable speed has the value (0.0, 0.4, 0.6) CIn order to control the fan speed, the linguistic variable has to be defuzzified 1.0 0.0 m(x) RPM 1000200030004000 Linguistic variable speed slowmediumfast

24. 24 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Fan control: defuzzification CCenter of Gravity: B2600,1 RPM CCenter of Maximum: B2600 RPM CMean of Maximum: B3000 RPM CThe examples have been computed using fuzzyTECH ® 5.51

25. 25 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Fan control: sample MLMs

26. 26 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Fan control: sample MLMs

27. 27 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Fan control: sample MLMs

28. 28 © 2001 Siemens Medical Solutions Siemens medical Solutions that help Sven Tiffe, MED BD XPL², Sven.Tiffe@siemens.com Fan control: sample MLMs