Fuzzy Modeling Library (FMLib)

Fuzzy Modeling Library (FMLib)
fun2-2-674: Modeling of the Three-Dimensional Surface F2

Description

Name: fun2-2-674
Type: Laboratory problem

Number of input variables: 2
Number of training examples: 674

Domain of the input variable 1: [0, 1]
Domain of the input variable 2: [0, 1]
Range of the output variable: [0, 10]

The aim in this problem is to model the three-dimensional surface generated by the mathematical function F2 shown below.

In this problem, seven linguistic terms are usually considered for each variable in linguistic fuzzy modeling.

Data Sets

A training data set uniformly distributed in the two-dimensional definition space has been obtained experimentally. In this way, a set with 674 values has been generated for the function F2 taking 26 values for each one of the two input variables considered to be uniformly distributed in their intervals.

On the other hand, the test data is obtained generating the input variable values at random in the concrete universes of discourse for each one of them, and computing the associated output variable value. A test data set with 67 (9.1%) examples has been generated.

Training data set (674 examples): fun2-2-674.tra
Test data set (67 examples): fun2-2-674.tst

Results

Linguistic Fuzzy Modeling
Method Type	Reference	Method	No. Rules	No. Labels	Training	Test	Comments
Learning/tuning also the data base
	[CH97]	MOGUL-D	98	21	0.027300	0.016700	--
	[CHV01]	Gr+MF	80	21	0.025370	0.017120	--
	[CHMV01]	Gr+MF+Context	81	27	0.015390	0.014220	--
Extending the model structure
Extending the model structure	[CH00]	ALM	55	21	0.019083	0.022120	Double consequent

Precise Fuzzy Modeling
Method Type	Reference	Method	No. Rules	No. Labels	Training	Test	Comments
Approximate FRBSs
Approximate FRBSs	[CH97]	MOGUL-A1	93	279	0.072100	0.052200	--
TSK-type FRBSs
TSK-type FRBSs	[CH99]	MOGUL-TSK	49	21	0.009331	0.006155	--

References

The application was originally proposed in:

[CH97]

O. Cordón, F. Herrera,A three-stage evolutionary process for learning descriptive and approximate fuzzy logic controller knowledge bases from examples,International Journal of Approximate Reasoning 17:4 (1997) 369-407.

The data has been also used in the following papers:

[CH99]	O. Cordón, F. Herrera,A two-stage evolutionary process for designing TSK fuzzy rule-based systems,IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics 29:6 (1999) 703-715.
[CH00]	O. Cordón, F. Herrera,A proposal for improving the accuracy of linguistic modeling,IEEE Transactions on Fuzzy Systems 8:3 (2000) 335-344.
[CHV01]	O. Cordón, F. Herrera, P. Villar,Generating the knowledge base of a fuzzy rule-based system by the genetic learning of the data base,IEEE Transactions on Fuzzy Systems 9:4 (2001) 667-674.
[CHMV01]	O. Cordón, F. Herrera, L. Magdalena, P. Villar,A genetic learning process for the scaling factors, granularity and contexts of the fuzzy rule-based system data base,Information Sciences 136:1-4 (2001) 85-107.