Fuzzy Approaches Improve Predictions of Energy Performance

of Buildings

Àngela Nebot and Francisco Mugica

Soft Computing Research Group, Technical University of Catalonia, Jordi Girona Salgado 1-3, Barcelona, Spain

Keywords: Energy Performance, Heating and Cooling Load, Fuzzy Inductive Reasoning (FIR), Adaptive Neuro-Fuzzy

Inference System (ANFIS).

Abstract: The energy consumption in Europe is, to a considerable extent, due to heating and cooling used for domestic

purposes. This energy is produced mostly by burning fossil fuels with a high negative environmental

impact. The characteristics of a building are an important factor to determine the necessities of heating and

cooling loads. Therefore, the study of the relevant characteristics of the buildings with respect to the heating

and cooling needed to maintain comfortable indoor air conditions, could be very useful in order to design

and construct energy efficient buildings. In previous studies, statistical machine learning approaches have

been used to predict heating and cooling loads from eight variables describing the main characteristics of

residential buildings which obtained good results. In this research, we present two fuzzy modelling

approaches that study the same problem from a different perspective. The prediction results obtained while

using fuzzy approaches outperform the ones described in the previous studies. Moreover, the feature

selection process of one of the fuzzy methodologies provide interesting insights to the principal building

variables causally related to heating and cooling loads.

1 INTRODUCTION

In recent years there has been a substantial increase

of research in the area of energy performance of

buildings. The aim is to design and construct more

energy-efficient buildings with the goal of reducing

their energy consumption and CO2 emissions.

During the last four years the European Commission

boosted the research in this area with a programme

framed in the Seventh Framework Programme for

Research (FP7) (European Commission, 2013).

Fuzzy logic-based methods have been applied

sparingly to the energy performance estimation of

buildings; however, there is a considerable amount

of research that uses fuzzy logic instead of classical

controllers to develop advanced control systems

with several building energy goals. The overall

objective is the management of indoor environment

including user preferences. The development of

fuzzy controllers to control thermal comfort, visual

comfort, and natural ventilation, with the combined

control of these subsystems has led to remarkable

results (Dounis and Caraiscos, 2009); (Kurian et al.,

2005). There are also studies that focus on more

specific control purposes such is, for example, the

control of electrochromic windows. In this research

the authors develop an algorithm to control the solar

transmittance of the electrochromic glazing unit,

both in terms of energy and the quality of the indoor

environment (Assimakopoulos et al., 2004).

Another interesting area within the analysis of

energy in buildings where fuzzy logic has been

applied is in multiple criteria decision-making

(FMCDM). We can find works in the literature that

use these techniques with very different goals. For

instance, in (Lee, 2010) a FMCDM is developed to

evaluate and rank the energy performance of office

buildings because it is relevant for energy agencies

and authorities. In (Hsieh et al., 2004) this approach

is used for selecting planning and design alternatives

in public office building. However, FMCDM has

been used mainly in energy planning, in application

areas such are renewable energy, energy resource

allocation, building energy management,

transportation energy management or electric utility

(Pohekar and Ramachandran, 2004).

Although, as has been already mentioned, fuzzy

logic has been used scarcely for the prediction of

energy performance of buildings, machine learning

strategies have been already used to deal with this

504

Nebot À. and Mugica F..

Fuzzy Approaches Improve Predictions of Energy Performance of Buildings.

DOI: 10.5220/0004621405040511

In Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (MSCCEC-2013), pages

504-511

ISBN: 978-989-8565-69-3

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

issue (Tsanas and Xifara, 2012). In the research

presented in this paper the work of Tsanas and

Xifara is taken as a basis to study the performance of

fuzzy approaches for the problem at hand. The

approaches reported in (Tsana and Xifara, 2012), i.e.

classical linear regression approach called Iteratively

Reweighted Least Squares (IRLS) and nonlinear

non-parametric method called Random Forests (RF),

are compared with the two fuzzy approaches

presented in this work, the Fuzzy Inductive

Reasoning (FIR) and the Adaptive Neuro-fuzzy

Inference System (ANFIS) from the prediction

capability perspective and as feature selection tools.

The next section provides an insight into these

two fuzzy approaches. Section 3 presents the data

used for this study and describes the fuzzy models

construction. Section 4 presents and discusses the

results obtained. Finally, section 5 presents the main

conclusions of this work.

2 METHODS

Both, the fuzzy inductive reasoning (FIR) and the

adaptive neuro-fuzzy inference system (ANFIS) are

hybrid methodologies that combine mainly soft

computing approaches. FIR combines fuzzy logic

with machine learning techniques and ANFIS

combines fuzzy logic with neural networks.

2.1 Fuzzy Inductive Reasoning (FIR)

The conceptualization of the FIR methodology

arises of the General System Problem Solving

(GSPS) approach proposed by Klir (Klir and Elias,

2002). This methodology of modeling and

simulation is able to obtain good qualitative relations

between the variables that compose the system and

to infer future behavior of that system. It has the

ability to describe systems that cannot easily be

described by classical mathematics or statistics, i.e.

systems for which the underlying physical laws are

not well understood.

FIR offers a model-based approach to predicting

either univariate or multi-variate time series (Nebot

et al., 2003); (Carvajal and Nebot, 1998). A FIR

model is a qualitative, non-parametric, shallow

model based on fuzzy logic.

Visual-FIR is a tool based on the Fuzzy

Inductive Reasoning (FIR) methodology (runs under

Matlab environment), that offers a new perspective

to the modeling and simulation of complex systems.

Visual-FIR designs process blocks that allow the

treatment of the model identification and prediction

phases of FIR methodology in a compact, efficient

and user friendly manner (Escobet et al., 2008).

FIR methodology has two main processes: a

feature selection process, that allow to develop a

model, and the prediction or simulation process, that

uses the model obtained to infer the future behaviour

of the system.

A FIR model consists of its structure (relevant

variables) and a set of input/output relations (history

behavior) that are defined as if-then rules.

Feature selection in FIR is based on the

maximization of the models' forecasting power

quantified by a Shannon entropy-based quality

measure. The Shannon entropy measure is used to

determine the uncertainty associated with

forecasting a particular output state given any legal

input state. The overall entropy of the FIR model

structure studied, H

is computed as described in

equation 1.

()

HpiH









(1)

where p(i) is the probability of that input state to

occur and H

is the Shannon entropy relative to the

input state. A normalized overall entropy H

defined in equation 2.

max



(2)

is obviously a real-valued number in the range

between 0.0 and 1.0, where higher values indicate an

improved forecasting power. The model structure

with highest H

value generates forecasts with the

smallest amount of uncertainty.

Once the most relevant variables are identified,

they are used to derive the set of input/output

relations from the training data set, defined as a set

of if-then rules. This set of rules contains the

behaviour of the system. Using the five-nearest-

neighbours (5NN) fuzzy inference algorithm the five

rules with the smallest distance measure are selected

and a distance-weighted average of their fuzzy

membership functions is computed and used to

forecast the fuzzy membership function of the

current state, as described in equation 3.

new j j

out rel out

emb w Memb







(3)

The weights

rel

are based on the distances and are

numbers between 0.0 and 1.0. Their sum is always

equal to 1.0. It is therefore possible to interpret the

relative weights as percentages.

FuzzyApproachesImprovePredictionsofEnergyPerformanceofBuildings

505

Figure 1: Example of how a Sugeno model works (evaluation of two fuzzy rules with two input variables or antecedents,

i.e. A and B).

For a more detailed explanation of the fuzzy

inductive reasoning methodology refer to (Escobet

et al., 2008).

2.2 Adaptive Neuro-Fuzzy Inference

System (ANFIS)

The Adaptive Neuro-Fuzzy Inference System

(ANFIS), developed by Jang, is one of the most

popular hybrid neuro-fuzzy systems for function

approximation (Nauck et al., 1997). ANFIS

represents a Sugeno-type neuro-fuzzy system. A

neuro-fuzzy system is a fuzzy system that uses

learning methods derived from neural networks to

find its own parameters. It is relevant that the

learning process is not knowledge-based but data-

driven.

The main characteristic of the Sugeno inference

system is that the consequent, or output of the fuzzy

rules, is not a fuzzy variable but a function, as

shown in equation 4.

R1: If A is A

and B is B

then z = p

a + q

b + r

R2: If A is A

and B is B

then z = p

a + q

b + r

(4)

Figure 1 describes graphically the inference process

of a Sugeno model composed by the two rules

described in equation 4 works.

The first step of the Sugeno inference is to

combine a given input tuple (in the example of

figure 1: a=3 and b=2) with the rule’s antecedents by

determining the degree to which each input belongs

to the corresponding fuzzy set (left panel of Fig. 1).

The min operator is then used to obtain the weight of

each rule, w

, which are used in the final output

computation,

z (right panel of Fig. 1). Notice that

the Sugeno inference has two differentiated set of

parameters. The first set corresponds to the

membership functions parameters of the input

variables. The second set corresponds to the

parameters associated to the output function of each

rule, i.e. p

, q

and

ANFIS is the responsible of adjusting in an

automatic way these two set of parameters by means

of two optimization algorithms, i.e. back-

propagation (gradient descendent) and least square

estimation. Back-propagation is used to learn the

parameters of the antecedents (membership

functions) and the least square estimation is used to

determine the coefficients of the linear combinations

in the rules’ consequents. ANFIS is a function of the

Fuzzy toolbox that runs under the Matlab

environment. For a more detailed explanation of the

ANFIS methodology refer to (Nauck et al., 1997).

3 DATA

The data used for this study stems from the UCI

machine learning repository (UCI, 2013) and is

called energy efficiency data set. The data was

created by (Tsanas and Xifara, 2012) in the

following way. They generated 768 simulated

buildings using Ecotet. Ecotet is a sustainable

building design software tool that allows the design

of buildings performing a whole building energy,

thermal performance and water usage analysis,

among other functionalities (Ecotet, 2013).

All the buildings have a volume of 771.75 m

but different surface areas and dimensions. All of

them are created with the same materials, that were

selected taking into account the newest and most

common materials in the building construction

industry and the lowest heat loss in each building

element, i.e. wall, floor or roof (U-value).

The simulation assumes that the buildings are

located in Athens, Greece, and are residential

11 1 1

zpaqbr



 

22 2 2

zpaqbr



 

a=3

b=2

min

11 2 2

wz wz

 





SIMULTECH2013-3rdInternationalConferenceonSimulationandModelingMethodologies,Technologiesand

Applications

506

buildings.

They used three types of glazing areas, expressed

as percentages of the floor area: 10%, 25%, and

40%. Furthermore, five different distribution

scenarios for each glazing area were simulated: 1)

uniform: with 25% glazing on each side, 2) north:

55% on the north side and15% on each of the other

sides, 3) east: 55% on the east side and 15% on each

of the other sides, 4) south: 55% on the south side

and 15% on each of the other sides, and 5) west:

55% on the west side and 15% on each of the other

sides. In addition, they obtained samples with no

glazing areas. Finally, all shapes were rotated to face

the four cardinal points.

Each one of the 768 simulated buildings can be

characterized by eight building parameters which

are: Relative Compactness (RC), Surface Area (SA),

Wall Area (WA), Roof Area (RA), Overall Height

(OH), Orientation (O), Glazing Area (GA) and

Glazing Area Distribution (GAD). These parameters

correspond to the input variables. Also, they

recorded the Heating Load (HL) and the Cooling

Load (CL), which correspond to the output

variables. The authors of the data claim that the data

generated represent actual real data with high

probability, enabling energy comparisons of

buildings (Tsanas and Xifara, 2012).

In the work of Tsanas and Xifara basic statistical

analysis of the data were performed and show that

linear techniques are not appropriate for the

available data in this application due to the fact that

the scatter and density plots do not follow a

Gaussian distribution.

3.1 Model Evaluation

In order to test the generalization performance of

FIR and ANFIS fuzzy models we use cross

validation, in this case 10-fold cross validation (CV).

The model parameters are derived using the training

subset and errors are computed using the testing

subset. For statistical confidence, the training and

testing processes are repeated 10 times with the

whole dataset randomly permuted in each run prior

to splitting in training and testing subsets.

Two error measures were used to evaluate the

performance of each of the models. These are: the

mean square error (MSE) and the mean absolute

error (MAE), described in equations 5 and 6,

respectively. These are the same error measures used

in (Tsanas and Xifara, 2012), in order to compare

accurately the methodologies presented in that paper

with the fuzzy methodologies presented in this work.

 



















(5)

 



















(6)

where ŷ(t) is the predicted output, y(t) the system

output and N the number of samples.

3.2 Fuzzy Models Development

In this section the development of ANFIS and FIR

models is described. As mentioned before, in this

application we have two output variables, i.e.

heating load and cooling load, and we want to study

if it is possible to estimate each output by using the

eight input variables that represent different building

parameters. Both, ANFIS and FIR methodologies

allow developing models that have a single output,

i.e. SISO or MISO models. Therefore, for each

methodology two sets of models are obtained, one

for each possible output. The input variables for both

sets of models are the eight variables previously

described. We talk about sets of models because for

each methodology and each output we obtain a

model for each of the 10 folds, and this is repeated

10 times. Therefore, 100 models are derived and

validated for each of the two methodologies and

outputs studied.

Both fuzzy approaches need to discretized the

quantitative data into qualitative data. To this end, it

becomes necessary to define, at least, two

parameters, the number of classes (also called

granularity) chosen for each input variable (and also

for the output variable in the case of FIR models),

and the shape of the membership functions of the

input variables (and also for the output variable in

the case of FIR models).

In this research we have decided to discretize the

input variables RC, SA, WA and GAD into three

classes and RA, OH, O and GA into only two

classes. The output variable is discretized into three

classes in the case of the FIR models. Remember

that ANFIS does not have fuzzy consequents, i.e. the

rules’ output is a function (see Figure 1). A

triangular shape has been used to discretize all the

variables.

These discretization parameters have been

chosen based on the analysis of the data. The

variable OH can take only two possible values, and

therefore it is represented into two classes. Variables

RA, O and GA can take four different values, and

some of these values appear only few times. A

FuzzyApproachesImprovePredictionsofEnergyPerformanceofBuildings

507

discretization with more than two classes does not

enhance the model prediction power and, instead, a

higher number of classes can lead to a curse of

dimensionality problem. Therefore, it was found that

two classes are enough for these variables to obtain

good models. The variables discretized into 3 classes

have a uniform distribution in their dimensionality

space, and, therefore, an odd number of classes seem

more reasonable. Three is the lowest number of

classes that give good results.

3.2.1 ANFIS Models

In order to obtain ANFIS models it is necessary to

define two sets of parameters: the ones related to the

discretization process of the input variables, which

have been explained before, and the parameters

related to the training process. The parameters

needed to perform the training process are: the type

of the output function (i.e. constant or linear), the

optimization method to train the fuzzy inference

system and the number of training epochs.

In this research we use a constant output

function, a hybrid optimization method and 50

epochs. A constant output has been chosen instead

of a linear one because the prediction power of the

resulting models were equivalent and the training

process is much more time consuming when the

linear function is used, due to the additional number

of parameters involved that need to be estimated in

the optimization process.

ANFIS uses the eight input variables to predict

each output, i.e. heating and cooling loads, and does

not perform any kind of feature selection.

3.2.2 FIR Models

As in the case of ANFIS, the first step in order to

obtain the FIR models is to discretize the data, i.e. to

convert quantitative values into fuzzy data. To this

end, it is necessary to specify the two parameters

described before, i.e. granularity and shape of the

membership functions, but also a parameter that

refers to the discretization algorithm. Depending on

the algorithm chosen the distribution of the

membership functions in the variable space may

vary and this has a direct impact to the reasoning

process, and, therefore, to the model predictions.

Contrarily to FIR, ANFIS does not have this

discretization parameter. ANFIS distributes

uniformly all the membership functions that describe

a specific variable. Figure 2 shows an example of

uniform (upper plot) and non-uniform (lower plot)

distribution of the membership functions of a

variable.

Figure 2: Example of uniform (upper plot) and non-

uniform (lower plot) membership functions distribution of

four classes that represent a given variable.

In this research, FIR uses the equal with partition

(EWP) algorithm for the discretization of the RA

and OH variables, and the equal frequency partition

(EFP) algorithm for the discretization of the rest of

the variables. The EWP algorithm is the one that

performs a uniform distribution of the membership

functions. The EFP algorithm distributes the

membership functions of a variable in such a way

that all the classes contain the same number of data

points. Visual-FIR allows the modeller to choose

between 15 discretization algorithms, some of them

belonging to the hierarchical family and others to the

fuzzy family (Escobet et al., 2008).

Once the data has been discretized, FIR

methodology performs a feature selection process

where the more relevant causal relations between the

input variables and the output variable are identified.

To this end, we used the model structure

identification process of the fuzzy inductive

reasoning methodology that performs a feature

selection based on the entropy reduction measure as

described in section 2.

FIR founds that for both outputs, HL and CL, the

features that have higher relevant causal relation are

Relative Compactness (RC) and Glazing Area (GA).

The use of the other variables does not improve the

predictive power of FIR models. Therefore, these

two variables represent the minimum subset of

variables needed to accurately estimate the heating

load and cooling load.

Variable

SIMULTECH2013-3rdInternationalConferenceonSimulationandModelingMethodologies,Technologiesand

Applications

508

4 RESULTS AND DISCUSSION

The MSE and MAE obtained by ANFIS and FIR

models, for both HL and CL output variables are

summarized in tables 1 and 2, respectively. In both

tables, the prediction results reported in (Tsanas and

Xifara, 2012) for the Iteratively Reweighted Least

Squares (IRLS) and Random Forest (RF) algorithms

are also included in order to study their performance

when compared with fuzzy approaches. IRLS is a

linear regression algorithm that adjusts weights in

the coefficients of the classical regression scheme in

order to diminish the effect of the outliers when

obtaining the fitting curve (Bishop, 2007). RF is a

non-linear method which was first put forward by

Breiman (2001). RF is a set of classification and

regression trees, where the training sample set for a

base classifier is constructed by using the Bagging

algorithm (Breiman, 1996). When building a base

classifier, inner nodes are spitted with a random

candidate attribute set. The final classification rule

or regression function is the simple majority voting

method or the simple average method.

In tables 1 and 2 the errors of ANFIS and FIR

models over the 10 cross validation realisations were

averaged. Tsanas and Xifara performed 100 cross

validations for both, IRLS and RF models. Tables 1

and 2 show the average errors of these 100 CV. We

found out that the models errors for each realisation

were very similar and, therefore, we think that 10

CV are enough to ensure a fair comparison.

Table 1: Mean square prediction errors obtained by the

methodologies: IRLS, RF, ANFIS and FIR, for the HL

models and the CL models. The results are given in the

form of mean ± standard deviation.

MSE IRLS RF ANFIS FIR

9.87±2.41 1.03±0.54 0.49±0.1 0.24±0.07

11.46±3.63 6.59±1.56 3.04±0.62 2.96±0.73

Table 2: Mean absolute prediction errors obtained by the

methodologies: IRLS, RF, ANFIS and FIR, for the HL

models and the CL models. The results are given in the

form of mean ± standard deviation.

MAE IRLS RF ANFIS FIR

2.14±0.24 0.51±0.11 0.52±0.05 0.35±0.04

2.21±0.28 1.42±0.25 1.06±0.11 1.09±0.16

From tables 1 and 2 it can be seen that the linear

regression approach, IRLS, has the lowest

performance. All the non-linear approaches have

good results and FIR is the one that performs much

better for both outputs. It is interesting to notice that

FIR mean square errors are a 75% and 50% lower

than the errors obtained by the RF, for HL and CL

models, respectively. The ANFIS errors are also

significantly lower (50%) than the MSE of the RF

models. Therefore, both fuzzy approaches

outperform the RF in the application at hand. It is

relevant to mention that the standard deviations

obtained by ANFIS and FIR models are really much

lower than the ones obtained by RF models. A low

standard deviation indicates that all the predictions

errors (100 as described in the previous section) tend

to be very close to the mean.

An important issue is that FIR, which is the

methodology that has a better performance, is the

only one that performs a feature selection process.

FIR finds that two of the eight input variables, i.e.

relative compactness (RC) and glazing area (GA),

are highly causally related to the outputs, and

therefore, FIR models only use these two building

characteristics to predict the heating and cooling

loads. This is a very interesting result because, in the

one hand, is consistent with Tsanas and Xifara

outcomes that claim that the GA is the most

important predictor for both HL and CL.

On the other hand, it allows concluding that the

rest of the six variables, i.e. surface area (SA), wall

area (WA), roof area (RA), overall height (OH),

orientation (O), and glazing area distribution (GAD),

are redundant or irrelevant. Again, this is consistent

with the previous work that infer that variables RC,

SA, WA, RA and OH appear reasonably strongly

associated with the output variables, and at the same

time founds that some input variables are highly

correlated. Based on the FIR feature selection

process, it becomes reasonably to think that the

relative compactness variable, RC, includes the

information of other relevant variables involved in

the study, as SA or RA. In fact, this is true because

there is an analytic formula linking the RC the SA

and the volume (Tsanas and Xifara, 2012). The WA

variable is clearly directly related to the GA, so it is

redundant. Therefore, the five variables that appear

reasonably strongly associated with the output

variables contain redundant information if SA and

GA are already selected.

Figure 3 shows real versus predicted ANFIS and

FIR results for HL and CL models. In both cases we

present the fold that gives larger MSE, in order to

show that even for the worse prediction results the

difference with the real data is almost

indistinguishable, especially in the case of the

heating load model.

FuzzyApproachesImprovePredictionsofEnergyPerformanceofBuildings

509

Figure 3: Real vs. ANFIS and FIR prediction results for the Cooling Load (upper plot) and Heating Load (lower plot)

models. The results of the Cooling Load correspond to fold #1 in one of the 10 iterations. The MAE and MSE obtained by

the ANFIS model in this fold are 1.08 and 2.91, respectively. The MAE and MSE obtained by the FIR model in this fold are

1.16 and 3.03, respectively. The results of the Heating Load correspond to fold #7 in one of the 10 iterations. The MAE and

MSE obtained by the ANFIS model in this fold are 0.54 and 0.46, respectively. The MAE and MSE obtained by the FIR

model in this fold are 0.42 and 0.38, respectively.

5 CONCLUSIONS

The main goal of this work is to study the feasibility

of fuzzy approaches to estimate the energy

performance of buildings. The characteristics of a

building are an important factor to determine the

necessities of heating and cooling loads. Therefore,

the study of the relevant characteristics of the

buildings with respect to the heating and cooling

needed to maintain comfortable indoor air

conditions, could be very useful in order to design

and construct energy efficient buildings. This work

follows a previous study (Tsanas and Xifara, 2012),

that creates a set of 768 buildings with different

characteristics by means of the Ecotet software, with

the goal of predict the heating and cooling load of

buildings taking into account eight variables that

represent different building characteristics, i.e.

relative compactness, surface area, wall area, roof

area, overall height, orientation, glazing area and

glazing area distribution.

Two fuzzy methodologies have been studied, the

fuzzy inductive reasoning (FIR) and the adaptive

neuro-fuzzy inference system (ANFIS). In order to

test the generalization performance of FIR and

ANFIS fuzzy models we use 10-fold cross

validation. The training and testing processes are

repeated 10 times with the whole dataset randomly

permuted in each run prior to splitting in training

and testing subsets. Therefore, 100 models are

derived and validated for each of the two

methodologies and outputs studied.

The results obtained by ANFIS and FIR

methodologies are compared with the ones presented

in the work of Tsanas and Xifara, where the linear

regression Iteratively Reweighted Least Squares

(IRLS) algorithm and the non-linear Random Forest

(RF) algorithm are used to predict heating and

cooling loads.

From the results it can be concluded that the non-

linear approaches (RF, ANFIS and FIR) perform

much better than the IRLS. All the non-linear

SIMULTECH2013-3rdInternationalConferenceonSimulationandModelingMethodologies,Technologiesand

Applications

510

approaches have good results and FIR is the one that

performs much better for both models, i.e. heating

and cooling loads. Both fuzzy approaches

outperform the RF in the application at hand.

Moreover, the standard deviations obtained by

ANFIS and FIR models are really much lower than

the ones obtained by RF models.

An interesting result is that the feature selection

process of FIR methodology finds that only two

input variables, i.e. relative compactness and glazing

area, contain the relevant information needed to

predict accurately the heating and cooling loads.

The results are very encouraging and we think

that these fuzzy methodologies can be good

alternatives to deal with different energy analysis

problems in the context of the smart grid.

REFERENCES

Assimakopoulos, M. N., Tsangrassoulis, A., Guarracino,

G., Santamouris, M., 2004. Integrated energetic

approach for a controlable electrochromic device.

Energy and Buildings, 36(5), 415-422.

Bishop, C. M., 2007. Pattern recognition and machine

learning, springer.

Breiman, L., Random Forests, Mach. Learn., vol. 45(1),

p.p. 5-32, 2001

Breiman, L., Bagging predictors, Machine Learning, vol.

24 (2), p.p. 123140, 1996

Carvajal, R., Nebot, A., 1998. Growth Model for White

Shrimp in Semi-intensive Farming using Inductive

Reasoning Methodology. Computers and Electronics

in Agriculture 19, 187-210.

Dounis, A. I., Caraiscos, C., 2009. Advanced control

systems engineering for energy and comfort

management in a building environment—A review.

Renewable and Sustainable Energy Reviews, 13(6–7),

1246-1261.

Ecotet, 2013. http://usa.autodesk.com/ecotect-analysis/

Escobet, A., Nebot., A., Cellier, F. E., 2008. Visual-FIR:

A tool for model identification and prediction of

dynamical complex systems. Simulation Modelling

Practice and Theory 16, 76-92.

European Commission, 2013: http://ec.europa.eu/research/

industrial_technologies/energy-efficient-buildings_en.

html

Hsieh, T. Y., Lu, S. T., Tzeng, G. H., 2004. Fuzzy MCDM

approach for planning and design tenders selection in

public office buildings, International Journal of

Project Management, 22(7), 573-584.

Klir, G., Elias, D., 2002. Architecture of Systems Problem

Solving, Plenum Press. New York, 2

edition.

Kurian, C. P., Kuriachan, S., Bhat, J., Aithal, R. S., 2005.

An adaptive neuro-fuzzy model for the prediction and

control of light in integrated lighting schemes.

Lighting Research and Technology, 37(4), 343–52.

Lee, W. S., 2010. Evaluating and ranking energy

performance of office buildings using fuzzy measure

and fuzzy integral. Energy Conversion and

Management, 51(1), 197-203.

Nauck, D., Klawonn, F. and Kruse R. (1997). Neuro-

Fuzzy Systems, John Wiley & Sons.

Nebot, A., Mugica, F., Cellier, F., Vallverdú, M., 2003.

Modeling and Simulation of the Central Nervous

System Control with Generic Fuzzy Models.

Simulation 79(11), 648-669.

Pohekar, S. D., Ramachandran, M., 2004. Application of

multi-criteria decision making to sustainable energy

planning—A review. Renewable and Sustainable

Energy Reviews, 8(4), 365-381.

Tsanas, A., Xifara A., 2012. Accurate quantitative

estimation of energy performance of residential

buildings using statistical machine learning tools.

Energy and Buildings, 49, 560-567.

UCI, 2013. http://archive.ics.uci.edu/ml/

FuzzyApproachesImprovePredictionsofEnergyPerformanceofBuildings

511