Fuzzy Modeling Library (FMLib)
fun3-2-1089: Modeling of the Three-Dimensional Surface F3


Name: fun3-2-1089
Type: Laboratory problem
Number of input variables: 2
Number of training examples: 1089
Domain of the input variable 1: [-8, 8]
Domain of the input variable 2: [-8, 8]
Range of the output variable: [0, 5835.700684]

The aim in this problem is to model the three-dimensional surface generated by the mathematical function F3 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 1,089 values has been generated for the function F3 taking 33 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 108 (9.1%) examples has been generated.


Precise Fuzzy Modeling
Method TypeReferenceMethodNo. RulesNo. LabelsTrainingTestComments
TSK-type FRBSs


The application was originally proposed in:


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.

Fuzzy Modeling Library (FMLib)

© Jorge Casillas