Fuzzy Modeling Library (FMLib)
ele2-4-1056: Estimation of the medium voltage electrical line maintenance cost in towns


Name: ele2-4-1056
Type: Real-world problem
Number of input variables: 4
Number of examples: 1056
Domain of the input variable 1: [0.5, 11]
Domain of the input variable 2: [0.15, 8.55]
Domain of the input variable 3: [1.64, 142.5]
Domain of the input variable 4: [1, 165]
Range of the output variable: [64.470001, 8546.030273]

The problem involves to estimate the minimum maintenance costs which are based on a model of the optimal electrical network for Spanish towns. The problem has four input variables: sum of the lengths of all streets in the town, total area of the town, area that is occupied by buildings, and energy supply to the town. These values are somewhat lower than the real ones, but companies are interested in an estimation of the minimum costs.

Of course, real maintenance costs are exactly accounted but a model that relates these costs to any characteristic of simulated towns with the optimal installation is important for the electrical companies. We were provided with data concerning the four characteristics of the towns and their minimum maintenance costs in a sample of 1,056 simulated towns.

In this problem, five linguistic terms are usually considered for each variable in linguistic fuzzy modeling.

Data Sets

The original data set of 1,056 examples has been randomly divided into 5 different subsets (four of them with 211 examples and one of them with 212 examples). Joining four of these subsets in a training data set and keeping the fifth subset as test data set it is possible to build 5 different partitions of the original data set at 80%-20%, i.e., a 5-fold cross-validation. Some papers only consider a data set partition, in this case, the first partition is used.

Training (80%, 844/845 examples)Test (20%, 212/211 examples)

You can also download the whole data set here.

The existing dependency of the four input variables with the output variable in the first training and test data sets is shown below.

(X1,Y) in ele2-4-1056.tra (X2,Y) in ele2-4-1056.tra (X3,Y) in ele2-4-1056.tra (X4,Y) in ele2-4-1056.tra
(X1,Y) in ele2-4-1056.tst (X2,Y) in ele2-4-1056.tst (X3,Y) in ele2-4-1056.tst (X4,Y) in ele2-4-1056.tst


Non-Fuzzy Modeling Techniques
Method TypeReferenceMethodNo. RulesNo. LabelsTrainingTestComments
[CHS99]Linear17 nodes5 par.164,66236,819--
[CHS99]2nd-order polynomial77 nodes15 par.103,03245,332--
Neural Network
[CHS99]3 layer perceptron 4-5-1--35 par.86,46933,105--
Genetic Algorithm-Programming
[San00]GA-P50 nodes5 par.18,16821,884--
[San00]Interval GA-P15 nodes4 par.16,26318,325--
Linguistic Fuzzy Modeling
Method TypeReferenceMethodNo. RulesNo. LabelsTrainingTestComments
Learning/tuning also the data base
Extending the model structure
[CHZ01]HSLR974022,65323,817Hiearchical KB
Precise Fuzzy Modeling
Method TypeReferenceMethodNo. RulesNo. LabelsTrainingTestComments
TSK-type FRBSs


The application was originally proposed in:


O. Cordón, F. Herrera, L. Sánchez, Solving electrical distribution problems using hybrid evolutionary data analysis techniques, Applied Intelligence 10 (1999) 5-24.

The data has been also used in the following papers:


L. Sánchez, Interval-valued GA-P algorithms, IEEE Transactions on Evolutionary Computation 4:1 (2000) 64-72.


O. Cordón, F. Herrera, P. Villar, Generating the knowledge base of a fuzzy rule-based system by the genetic learning of the data base, IEEE Transactions on Fuzzy Systems 9:4 (2001) 667-674.


O. Cordón, F. Herrera, L. Magdalena, P. Villar, A genetic learning process for the scaling factors, granularity and contexts of the fuzzy rule-based system data base, Information Sciences 136:1-4 (2001) 85-107.


O. Cordón, F. Herrera, I. Zwir, Linguistic modeling by hierarchical systems of linguistic rules, IEEE Transactions on Fuzzy Systems, 2001. To appear.

Fuzzy Modeling Library (FMLib)

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