 Fuzzy Modeling Library (FMLib) fun421681: Modeling of the ThreeDimensional Surface F4
DescriptionName: fun421681 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 threedimensional 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 SetsA training data set uniformly distributed in the
twodimensional 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. Results Linguistic Fuzzy Modeling  Method Type  Reference  Method  No. Rules  No. Labels  Training  Test  Comments  Learning/tuning also the data base  [CH97]  MOGULD  249  21  0.367600  0.379500    Precise Fuzzy Modeling  Method Type  Reference  Method  No. Rules  No. Labels  Training  Test  Comments  Approximate FRBSs  [CH97]  MOGULA1  245  735  0.167400  0.198800    [HLV98]  MOGULGLP  119  357    0.270455   
ReferencesThe application was originally proposed in:
[CH97]  O. Cordón, F. Herrera,A threestage evolutionary process for learning descriptive and approximate fuzzy logic controller knowledge bases from examples,International Journal of Approximate Reasoning 17:4 (1997) 369407.
 The data has been also used in the following papers:
[HLV98]  F. Herrera, M. Lozano, J.L. Verdegay, A learning process for fuzzy control rules using genetic algorithms, Fuzzy Sets and Systems 100 (1998) 143158.

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