Fuzzy Modeling Library (FMLib)
fun4-2-1681: Modeling of the Three-Dimensional Surface F4


Name: fun4-2-1681
Type: Laboratory problem
Number of input variables: 2
Number of training examples: 1681
Domain of the input variable 1: [-1, 1]
Domain of the input variable 2: [-1, 1]
Range of the output variable: [-2, 3.382745]

The aim in this problem is to model the three-dimensional surface generated by the mathematical function F4, the generalized Rastrigin function, 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 1,681 values has been generated for the function F4 taking 41 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 168 (9.1%) examples has been generated.


Linguistic Fuzzy Modeling
Method TypeReferenceMethodNo. RulesNo. LabelsTrainingTestComments
Learning/tuning also the data base
Precise Fuzzy Modeling
Method TypeReferenceMethodNo. RulesNo. LabelsTrainingTestComments
Approximate FRBSs


The application was originally proposed in:


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:


F. Herrera, M. Lozano, J.L. Verdegay, A learning process for fuzzy control rules using genetic algorithms, Fuzzy Sets and Systems 100 (1998) 143-158.

Fuzzy Modeling Library (FMLib)

© Jorge Casillas