Performance

Evaluation of a stock on a [0,1] scale

Diagram

Information

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The output y is the dimensionless degree of membership to the set of "good performances" or "good outcomes" according to a chosen type of membership function. Using the PerformanceIndicator allows to quickly grasp how a system is currently performing with regard to some criterion with a value of 1 indicating best possible performance and a value of 0 indicating worst possible (and possbily unsustainable) performance.

The following grid displays all available membership function types without inversion (invertResults = false):

Membership Functions

Parameters

Membership Function Type a b c d

ramp foot shoulder

triangular left foot center right foot

trapezoidal left foot left shoulder right shoulder right foot

sshaped foot shoulder

sigmoidal steepness of transition area center of transition area

pishaped left foot left shoulder right shoulder right foot

psigmoidal steepness of left transition center of left transition area steepness of right transition center of right transition area

gaussian half width at half maximum center of curve (maximum)

bell width of core steepness center of core

Parameters
Membership Function Type	a	b	c	d
ramp	foot	shoulder
triangular	left foot	center	right foot
trapezoidal	left foot	left shoulder	right shoulder	right foot
sshaped	foot	shoulder
sigmoidal	steepness of transition area		center of transition area
pishaped	left foot	left shoulder	right shoulder	right foot
psigmoidal	steepness of left transition	center of left transition area	steepness of right transition	center of right transition area
gaussian	half width at half maximum		center of curve (maximum)
bell	width of core	steepness	center of core

When inversion is turned on (invertResult = true) the result obtained from the membership function as specified will be subtracted from 1. Thus the ramp shown above can be made to ramp down from left to right with a being the shoulder and b the foot by inverting the results.

Implementation

DiagramView

Notes

The amount in the connected stock (stockInfoInput) will be normalized by divison either by a constant referenceValue (default = 1) or by the exogenous input u (hasConstantReference = false).

Using a polarity (+,-,±) it is possible to indicate the basic relation between the amount in the stock and its performance value (e.g., + indicating a "more-is-better" type of evaluation.

Parameters (10)

pol	Value: "±" Type: String Description: Polarity
referenceValue	Value: 1 Type: ReferenceType Description: Constant reference value to normalize input
hasConstantReference	Value: true Type: Boolean Description: = true, if the reference value is given by a constant parameter
hasStockInfoInput	Value: true Type: Boolean Description: = true, if the input is given by the input connector u instead of stockInfoInput
a	Value: Type: Ratio Description: Parameter to control shape of membership function
b	Value: unspecified Type: Ratio Description: Parameter to control shape of membership function
c	Value: unspecified Type: Ratio Description: Parameter to control shape of membership function
d	Value: unspecified Type: Ratio Description: Parameter to control shape of membership function
mft	Value: MFT.ramp Type: MembershipFunctionTypes Description: Membership function type to use
invertResult	Value: false Type: Boolean Description: = true, if the degree of membership is to be inverted (i.e., y = 1 - mf(u))

Connectors (4)

	stockInfoInput	Type: StockInfoInput Description: Input of record with stock-related information
	u_ref	Type: RealInput Description: Reference value for stock
	y	Type: RealOutput Description: Output of output type
	u	Type: RealInput Description: Input for lookup (optional)

Components (3)

	normalizedStock	Type: DmnlInput Description: Input u will be stated as dimensionless fraction with regard to a reference value
	absoluteSensor	Type: AbsoluteSensor Description: Reports basic stock–related information
	performanceIndicator	Type: PerformanceIndicator Description: Indicator function using fuzzy membership functions