 Fuzzy Modeling Library (FMLib) fun22674: Modeling of the ThreeDimensional Surface F2
DescriptionName: fun22674 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 threedimensional 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 SetsA training data set uniformly distributed in the
twodimensional 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. Results Linguistic Fuzzy Modeling  Method Type  Reference  Method  No. Rules  No. Labels  Training  Test  Comments  Learning/tuning also the data base  [CH97]  MOGULD  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  [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  [CH97]  MOGULA1  93  279  0.072100  0.052200    TSKtype FRBSs  [CH99]  MOGULTSK  49  21  0.009331  0.006155   
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:
[CH99]  O. Cordón, F. Herrera,A twostage evolutionary process for designing TSK fuzzy rulebased systems,IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics 29:6 (1999) 703715.
 [CH00]  O. Cordón, F. Herrera,A proposal for improving the accuracy of linguistic modeling,IEEE Transactions on Fuzzy Systems 8:3 (2000) 335344.
 [CHV01]  O. Cordón, F. Herrera, P. Villar,Generating the knowledge base of a fuzzy rulebased system by the genetic learning of the data base,IEEE Transactions on Fuzzy Systems 9:4 (2001) 667674.
 [CHMV01]  O. Cordón, F. Herrera, L. Magdalena, P. Villar,A genetic learning process for the scaling factors, granularity and contexts of the fuzzy rulebased system data base,Information Sciences 136:14 (2001) 85107.

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