 Fuzzy Modeling Library (FMLib) fun121681: Modeling of the ThreeDimensional Surface F1
DescriptionName: fun121681 Type: Laboratory problem  Number of input variables: 2 Number of training examples: 1681  Domain of the input variable 1: [5, 5] Domain of the input variable 2: [5, 5] Range of the output variable: [0, 50] 
The aim in this problem is to model the threedimensional surface generated
by the mathematical function F1 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 F1 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. Two test data sets with 168 (9.1%) and 420 (20%)
examples have been generated. Results Linguistic Fuzzy Modeling  Method Type  Reference  Method  No. Rules  No. Labels  Training  Test  Comments  Learning only the rule base (highest interpretability)  [CCH01]  Wang & Mendel  49  21  2.048137  2.287129  Test data set 2  [CCH01]  COR  49  21  1.605482  1.175941  Test data set 2  Learning/tuning also the data base  [CH97]  MOGULD  62  21  0.335800  0.262500    Precise Fuzzy Modeling  Method Type  Reference  Method  No. Rules  No. Labels  Training  Test  Comments  Approximate FRBSs  [CH97]  MOGULA1  76  228  1.462900  0.951800    [HLV98]  MOGULGLP  64  192    0.768021    TSKtype FRBSs  [CH99]  MOGULTSK  49  21  0.006921  0.007498   
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.
 [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.
 [CCH01]  J. Casillas, O. Cordón, F. Herrera, COR: A methodology to improve ad hoc datadriven linguistic rule learning methods by inducing cooperation among rules, IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, 2001. To appear.

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