applying lca and fuzzy ahp to evaluate building energy conservation
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Applying LCA and fuzzy AHP toevaluate building energy conservationGuozhong Zheng a , Youyin Jing a , Hongxia Huang b & Yuefen Gaoa
a School of Energy and Power Engineering , North China ElectricPower University , Baoding, People's Republic of Chinab School of Electrical and Electronic Engineering , North ChinaElectric Power University , Baoding, People's Republic of ChinaPublished online: 02 Jul 2010.
To cite this article: Guozhong Zheng , Youyin Jing , Hongxia Huang & Yuefen Gao (2011) ApplyingLCA and fuzzy AHP to evaluate building energy conservation, Civil Engineering and EnvironmentalSystems, 28:2, 123-141, DOI: 10.1080/10286608.2010.482655
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Civil Engineering and Environmental SystemsVol. 28, No. 2, June 2011, 123–141
Applying LCA and fuzzy AHP to evaluate buildingenergy conservation
Guozhong Zhenga*, Youyin Jinga, Hongxia Huangb and Yuefen Gaoa
aSchool of Energy and Power Engineering, North China Electric Power University, Baoding,People’s Republic of China; bSchool of Electrical and Electronic Engineering,North China Electric Power University, Baoding, People’s Republic of China
(Received 1 December 2008 )
Reducing energy consumption and environment pollution is an important part in energy sustainability.Building energy conservation evaluation will drive the application of the new energy conservation tech-nology. For building an energy conservation evaluation, energy conservation and environment impacts inall stages of the life cycle should be assessed. In this paper, the fuzzy analytic hierarchical process methodand life-cycle assessment theory are adopted for building energy conservation evaluation. Factors in differ-ent hierarchies are weighted with linguistic variables by pair-wise comparisons, and factors in the lowesthierarchy within the different second hierarchy factors are also evaluated by linguistic variables. The mem-bership degrees and integrated evaluation values are calculated. Then an example is studied to illustrate theproposed approach. The validity of the proposed method is verified and it demonstrates the effectivenessand practicability of the proposed approach. The results provide guidance in evaluating building energyconservation and determining the energy conservation grade of the building.
Keywords: fuzzy AHP; LCA; building energy conservation; linguistic variables
1. Introduction
With the development of the industry, global warming, ozone depletion, energy shortage andthe escalating costs of fossil fuels have been serious problems over the last few yeas (Blockleyand Dester 1999, Hakkinen 2007, Lowe 2008). Buildings are energy gluttons and they have alarge impact on the global climate change and other energy-related environmental issues (Wanget al. 2005). Building energy consumption accounts for approximately 40% of the global energydemands (Jones 1998). In order to reduce energy consumption and environmental pollution,rational design and control of the building energy consumption is important in energy sustainabilityand has become an important strategy in sustainable development.
The establishment of the evaluation framework is the foundation of building energy conser-vation. Its rationality directly affects the veracity and standardisation of the evaluation. If thebuilding energy conservation evaluation framework has been implemented, the developers willactively apply the new technologies to build energy-efficient building, and it will strongly promotethe development of the building energy conservation technology (Jiang and Lin 2005).
*Corresponding author. Email: [email protected]
ISSN 1028-6608 print/ISSN 1029-0249 online© 2011 Taylor & FrancisDOI: 10.1080/10286608.2010.482655http://www.informaworld.com
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124 G. Zheng et al.
Some studies have been carried out in building energy conservation evaluation over the years.Rey et al. (2007) proposed a new methodology called ‘building energy analysis’ that allowsimplementation of Energy Performance of Buildings Directive on energy certification of thebuildings. Patxi et al. (2008) outlined a methodology to develop energy benchmarks and ratingsystems starting from the first step of data collection of the building stock. Wang and Su (2005)established a quantitative systematical building energy evaluation mathematics model combininganalytical hierarchy process (AHP) and attribute mathematics. Shi and Lin (2008), Wu and Yang(2007) and Wu and Li (2006) adopted AHP and fuzzy mathematic method to evaluate buildingenergy conservation. Lu (2007), Ding et al. (2003) and Yan et al. (2005) studied the buildingenergy conservation evaluation by an artificial neural network theory.
From the above literature, the application of the AHP method, artificial neural network theoryand fuzzy AHP method in the field of building energy conservation evaluation has proliferatedin recent years. However, in the above literature, when evaluating building energy conservationperformance, only the performances in use stage are focused. It is not all-around. In the develop-ment of building energy conservation, life-cycle assessment (LCA) should be adopted and energyconservation and environmental impacts on all stages of the life cycle should be assessed. Thus,the adoption of LCA makes the evaluation results more reasonable and all-around. On the basisof such consideration, the application of LCA to building energy conservation will be a feasibleand effective way. This kind of research, however, is not enough by far. The aim of this paper isto propose an evaluation model combining LCA and fuzzy AHP in building energy conservation.
The paper is organised as follows. The first section includes the introductory part. Section 2introduces the methodology. Section 3 describes the evaluation model combining LCA and fuzzyAHP for building energy conservation. Section 4 illustrates a case to use the proposed method.Section 5 validates the fuzzy AHP method. The last section concludes.
2. Methodology
2.1. LCA for building energy conservation
LCA is a powerful and internationally accepted system analysis tool that studies the environmentalaspects and potential impacts of a product or service system throughout its life cycle (Gonzálezet al. 2003). The evaluation is performed for the whole life cycle of the process or activity,including the extraction and treatment of raw materials, the fabrication, transport, distribution,use, recycling, reuse and final disposal (Arena and Rosa 2003).
LCA is applied at two levels (Yasutaka 2004): conceptually as a through process to guidethe selection of options for design and improvement; methodologically to build a qualita-tive/quantitative inventory of environmental burdens or releases, evaluate the impacts of thoseburdens or releases and consider alternative to improve the environmental performance. The con-ceptual process (life-cycle thinking) is a unique way of addressing environmental problems froma systems or holistic perspective. In this way of thinking, a product or system is evaluated ordesigned with a goal of reducing environmental impacts and energy consumption over its wholelife cycle. The life-cycle thinking does not attempt to do so in a quantitative fashion but rather ina conceptual or qualitative fashion (Yasutaka 2004).
As products, buildings are special since they have a comparatively long life, often have multiplefunctions, contain many different components, are normally unique (there are seldom many of thesame kind) and are integrated with the infrastructure (Ignacio et al. 2009). Given the complexitiesof interaction between the building and the natural environment, LCA represents a comprehensiveapproach to examine the environmental impacts of an entire building.
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Table 1. Application of LCA in building sector.
Type of user Stage of the process Purpose of LCA use
Consultants advisingmunicipalities, urbandesigners
Preliminary phase Setting gargets at the municipal levelDefining zones where residential/office
building is encouraged or prohibitedSetting targets for development areas
Property developers andclients
Preliminary phase Choosing a building site
Sizing a projectSetting environmental target in a
programme
Architects Early design (sketch) and detailed designin collaboration with engineers
Comparing design options (geometry/orientation, technical choices)
Design a renovation project
Engineers/consultants Early design in collaboration witharchitects and detailed design
Comparing design options (geometry,technical choices)
Design of a renovation project
The LCA method is a quantitative approach to assess load magnitude in both natural and builtenvironments in different patterns attributable to various influential factors at each stage of buildingsystems (Chen et al. 2006). It also allows an analysis of the relation between the energy savingsrealised with extremely low-energy buildings and the embodied energy needed to create thesebuildings (Griet and Hugo 2007). Buildings consume energy throughout their whole life cycle(Chris et al. 2003). It should consider not only the building material and energy consumption inthe construction and use stage, but also the production and transportation of the building materials,and even the material recyclability and waste management in the breaking stage.
Table 1 (Ignacio et al. 2009) presents the main target groups for applying LCA in the early designphases of a building. From Table 1, the drivers of applying LCA are marketing benefit, simplifieddata acquisition, environmental labelling of buildings and environmental targets for buildings.There are also some barriers to be overcome, such as prejudices about LCA complexity, accuracyand arbitrary results, low demand for LCA, poor cooperation between application manufacturersand potential customers, lack of legal requirements and poor incentives and low link with theenergy certification applications (Ortiz et al. 2009).
LCA in the building appears to be developing quickly. The LCA method was introduced to theconstruction industry in the 1970s (Bickley 1974, Tufty 1976). In the past 30 years, it has developedanother main stream of assessment theory in the building and construction industry (Chen et al.2006). Kanghee et al. (2009) developed an LCA programme for the building’s planning stage.Su et al. (2008) studied the energy consumption and emissions in the steel-framed building andthe concrete-framed building based on LCA. Gian (2009) set up a detailed LCA model for abuilding to study demolition and recycling potential. Fulvio et al. (2008) assessed the energy andenvironmental benefits and drawbacks of an eco-profile of the kenaf-fibre thermal insulation boardused in residential buildings. Chris et al. (2003) conducted a comprehensive LCA for a six-storeybuilding with a projected 75-year lifespan, located on the University of Michigan campus.
2.2. Fuzzy AHP-based LCA for building energy conservation
2.2.1. AHP
The building is a complicated system. Since there are different pathways by which the environ-mental effects and energy conservation performances can be affected, the analysis of a system
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126 G. Zheng et al.
will usually involve multiple objectives or criteria which analyse tradeoffs between potentiallyconflicting goals (Raymond 2005). The model for building energy conservation evaluation,which integrates energy consumption, sustainable development and environmental protection,is a multiple-criteria decision-making (MCDM) problem. In different stages of a building, theenergy conservation indexes are different. By the indexes in different stages, the final energyconservation performance can be regarded as the guideline for energy conservation assessmentof the building. As the life cycle of the building is an embedded process, the indexes are moreand more detailed. Thus, the assessment for building energy conservation is not only general, butalso a system with multi-layer and multi-structure. Thus, AHP is adopted in this study.
AHP was developed by Saaty (1980) to solve complex decision-making problems, whichinvolves ranking and choosing of alternatives. It is one of the extensively used MCDM meth-ods. One of the main advantages of this method is its simplicity in handling multiple criteria.Furthermore, AHP is easier to understand and it can effectively handle both qualitative andquantitative data. The application of AHP does not involve cumbersome mathematics. AHPinvolves the principles of decomposition, pair-wise comparisons and priority vector generation andsynthesis.
2.2.2. Fuzzy logic
In LCA for building energy conservation, the evaluation of the environmental effects and energyconservation performances involves significant uncertainties concerning data, models and prac-titioner’s choices, making problems less tangible and decision-making difficult and it presentsfuzziness (Funtowicz et al. 1999). Fuzzy logic has been used within MCDM and also been appliedto LCA mainly to assess uncertain values or to use on individuals’ judgements as input data inLCA studies (Valérie et al. 2006). The fuzzy logic can also be used in a life-cycle methodologyto take advantage of the simplicity of a qualitative questionnaire without introducing any analystinterpretation biases.
‘Fuzzy’ refers to the uncertainties existing in a particular event or something that cannot beexactly defined (Zhadi 1984). Fuzzy logic has been considered a useful tool to deal with imprecise,uncertain or ambiguous data or relationships among data sets because of the high nonlinearityand complexity of ecosystems and ecological and environmental issues (Fulvio et al. 2004).
The process controls to energy consumption and pollution during each process of the lifecycle rely on intuition or empirical insights and are usually difficult to quantify using a set ofexact values. This understanding can be described using linguistic variables as ‘good’ or ‘bad’.It is considered that the fuzzy quantitative approach is suitable to describe experts’ elicitation onthose variables, such as the environmental and energy conservation performance, which cannot bequantified by using certain values (Yao et al. 2007). In fuzzy logic, the environmental effects andenergy conservation performances can be described by linguistic terms, such as excellent, good,very poor, etc. Linguistic terms are subjective categories for the linguistic variable. Therefore,a description of the performance with the help of fuzzy logic would seem to be more realisticthan with exact numbers. Just as numerical variables take numerical values, in fuzzy logic, thelinguistic terms are associated with the degrees of membership in the set. Therefore, based onthe analysis of the decision situation in building energy conservation, fuzzy analysis method isapplied to incorporate fuzzy nature into assessment results.
2.2.3. Fuzzy AHP
Based on the concept of fuzzy set theory, fuzzy AHP was originally introduced by Zaddeh (1965).It can handle the inherent uncertainty and imprecision of the human decision-making process.
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It has shown advantages within uncertainty, vagueness, provides formalised tools for dealingwith the imprecision intrinsic to many problems and can effectively handle both qualitative andquantitative data in the multi-attribute problems (Felix and Niraj 2007). Therefore, this paperproposes a fuzzy AHP and LCA-based approach to evaluate building energy conservation.
2.3. Calculation process
The proposed LCA and fuzzy AHP method to assess building energy conservation is composedof the following steps:
(1) establish the expert group;(2) establish the evaluation model combining LCA and fuzzy AHP;(3) determine evaluation grade;(4) collect data;(5) determine the weights of the evaluation factors;(6) evaluate the building energy conservation.
3. Building energy conservation evaluation
3.1. Establish the expert group
In order to assess building energy conservation, an expert group composed of scientists, real-estateappraisers, designers, officials and other specialists should be formed. In order to ensure that theviews of the expert group are representative, the experts should be authorities in the correspondingfield, knowledge coverage and different academic viewpoints of the experts should be consideredand the ratio of scientists, real-estate appraisers, designers, officials and other specialists shouldbe reasonably considered. In order to ensure the impartiality of the evaluation, the expert shouldbe from the third party and publicity of the members should be completed before the evaluation.If the expert group is established as above, fair and reliable evaluation results can be obtained.
3.2. Establish the evaluation model combining LCA and fuzzy AHP
Series of meetings and discussions are organised with these experts to ensure the different pointsof view on determining the factors in a consensus. The indexes are selected based on the fourstages of building’s life cycle as follows (Chris et al. 2003, Gian 2009).
3.2.1. Design stage
The largest part of these energy consumption and environmental burden are produced during theuse stage of the building’s life, and the right time to reduce them is acting during the design ofthe building, that is, the design stage (Arena and Rosa 2003).
To diminish the energy consumption, building form (such as orientation, shape, size and floor toceiling height) and building envelopes (such as wall, roof, glazing ratio and sun-shading) should bepaid attention. In building equipment system, highlighting the use of renewable resources, makingrational use of energy and the adoption of less energy-intensive material should be consideredin the design stage. Besides, in order to achieve reduction in the environmental effects producedduring the use stage, it is necessary to use new materials and components which consume lessenergy and release fewer emissions.
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3.2.2. Construction stage
Construction stage covers the manufacturing and transportation of building materials and includesburdens from electricity used for power tools and lighting, as well as diesel fuel used by heavyequipment at the construction site. Activities include site preparation, structural and envelopeinstallation, mechanical, electrical equipment installation and interior finishing (Chris et al. 2003).Energy consumption, material consumption and environmental impacts are all concluded in thestage.
3.2.3. Use stage
Use stage encompasses all activities related to the use of the house. These activities include alloperating energy consumed for heating, cooling, sanitary water production, lighting, cooking andequipment operation. Energy consumption, resources consumption, utilisation degree of renew-able energy, recycling degree of resources, waste disposal, pollutants management, the utilisationof the green material and life cycle are included in the stage.
3.2.4. Breaking stage
Breaking stage comprises the demolishing of the building shell and the final disposal of wasteinventories. The recyclability of the materials, solid refuse and energy consumption for breakingare included in the stage.
Based on the discussion and the literature, a five-level hierarchical diagram is first constructedas shown in Tables 2–6. The 0th level represents the ultimate goal. The first hierarchy containsthe four first hierarchy factors: design stage (C1), construction stage (C2), use stage (C3) andbreaking stage (C4). Furthermore, the second hierarchy factors corresponding to these four firsthierarchy factors are placed in the second level of the hierarchy. The third hierarchy factors areplaced in the third level. The fourth hierarchy factors are in the lowest level.
3.3. Determine evaluation grade
In order to conduct evaluation, according to the index system, the evaluation grade is determinedby the expert group. Based on the application experiences, the evaluation grades are ranked intosix levels: very good (VG), good (G), medium (M), qualified (Q), poor (P) and very poor (VP).
3.4. Collect data
Based on the evaluation indexes, the initial step of the energy conservation evaluation of a buildingshould be examined in detail to acquire the initial data.
Table 2. The first hierarchy factors in building energy conservationevaluation.
0th hierarchy First hierarchy
Building energy conservation evaluation Design stage (C1)
Construction stage (C2)
Use stage (C3)
Breaking stage (C4)
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Table 3. The factors in the design stage C1.
First hierarchy Second hierarchy Third hierarchy Fourth hierarchy
Design stage (C1) Building form design(C11)
Orientation (C111)
Sizing (C112)
Shape (C113)
Floor to ceiling height (C114)
Envelope design (C12) Wall (C121) Wall structure system (C1211)
Exterior wall material (C1212)
Wall insulation (C1213)
Interior wall material (C1214)
Roof (C122) Roof structure (C1221)
Roof isolation (C1222)
Glazing ratio (C123)
Sun-shading (C124)
Building equipmentsystem design (C13)
Heating and air conditioning (C131)
Building electrical system (C132)
Water supply and drainage (C133)
Table 4. The factors in the construction stage C2.
First hierarchy Second hierarchy Third hierarchy
Construction stage (C2) Environmental impacts bybuilding material (C21)
Environmental impacts by buildingmaterial production (C211)
Environmental impacts by buildingmaterial transport (C212)
Pollutant (C213)
Material consumption (C22)
Construction waste (C23)
Energy consumption inconstruction stage (C24)
Energy consumption for building materialproduction (C241)
Energy consumption for building materialtransport (C242)
Table 5. The factors in the use stage C3.
First hierarchy Second hierarchy Third hierarchy
Use stage (C3) Practical utilisation of energyand resources (C31)
Energy consumption (C311)
Resources consumption (C312)
Utilisation degree of renewable energy (C313)
Recycling degree of resources (C314)
Environmental impacts (C32) Waste disposal (C321)
Pollutants management (C322)
Utilisation of the green material (C323)
Life cycle (C33)
Table 6. The factors in the breaking stage C4.
First hierarchy Second hierarchy
Breaking stage(C4) The recyclability of the materials (C41)
Solid refuse (C42)
Energy consumption for breaking (C43)
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130 G. Zheng et al.
First, the expert group is asked to make pair-wise comparison for the elements at a given levelwith the same above factor. Linguistic variables and 9-scale are used to compare the relativeimportance between any two dimensions. Theses linguistic variables and 9-scale are shown inTable 7 (Wu et al. 2008).
Secondly, each member in the expert group is then required to fill in Table 8 to evaluate theperformance of each factor in the lowest hierarchy within each second hierarchy factor. In thisstudy, the membership functions of these linguistic variables are shown in Figure 1, and theaverage values related with these variables are shown in Table 9.
Table 7. Scale of relative importance.
Scale of relative importance Linguistic variable Comparative judgement
1 Equally important Tiand Tj are equally important3 Weakly important Ti is weakly more important than Tj
5 Essentially important Ti is essentially more important than Tj
7 Very strongly important Ti is very strongly more important than Tj
9 Absolutely important Ti is absolutely more important than Tj
2, 4, 6, 8 are intermediate scales
Table 8. The fuzzy AHP evaluation table.
Fuzzy AHP
Linguistic variablesa
First hierarchy Second hierarchy Third hierarchy Fourth hierarchy VG G M Q P VP Traditional AHP
C1 C11 C111 /C112 /C113 /C114 /
C12 C121 C1211C1212C1213C1214
…b … … … … … … …… … … … … … … … …
… … … … … … … … … …C4 C41 / /
C42 / /C43 / /
Note: The bold is the lowest hierarchy within each second hierarchy factor.aThe decision group member fills ‘
√’ in the table.
bThe ellipsis indicates that the assessment factors are omitted for the limitation of the paper length.
0 0.2 0.4 0.6 0.8 1.0
1.0VGGMQPVP
Figure 1. Membership functions of linguistic values for energy conservation grade.
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Table 9. Linguistic variables and mean fuzzy numbers.
Linguistic variables Mean fuzzy numbers
Very good (VG) 1Good (G) 0.8Medium (M) 0.6Qualified (Q) 0.4Poor (P) 0.2Very poor (VP) 0
When filling in Table 8, the experts are asked to make their decision freely. They have intervaljudgements according to their experiences and knowledge.
3.5. Determine the weights of the evaluation factors
Each factor has its own contribution to evaluation. Weight value of evaluation indexes is theinfluence coefficient to the evaluation. In this passage, weights of the factors in different levels ofthe hierarchy are calculated.
The detailed process of the AHP weighting method of each hierarchy is as follows.
(1) Establish the pair-wise comparison matrixLinguistic variables to compare the relative importance between any two dimensions are
used. These linguistic variables and the numerical scale used for assigning values to thesecomparative ratings are shown in Table 7 (Wu et al. 2008).
(2) By performing pair-wise comparisons of the concerned dimensions, a fuzzy matrix A isconstructed
A = (aij )n×n, (1)
where aij is the scale of Ti comparing with Tj , while the scale is 1/aij whenTj comparingwith Ti .
(3) Calculate weightsWhen the comparison matrix is available, the weights of criteria are obtained and the
consistency of the judgements is determined. The weights of criteria can be obtained bycalculating the principal eigenvector w of the matrix A. That is,
Aw = λmaxw. (2)
When the vector w is normalised, it becomes the vector of weights of the criteria with respectto the goal. λmax is the largest eigenvalue of the matrix A and the corresponding eigenvectorw contains only positive entries.
(4) Consistency checkThe consistency of the comparison matrix can be determined by the consistency ratio (CR),
which is defined as
CR = CI
RI, (3)
CI = (λmax − n)
(n − 1), (4)
where CI is the consistency index, RI the random index and n the matrix size.
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Table 10. The average consistencies of random matrices (RI).
Size (n) 1 2 3 4 5 6 7 8 9
RI 0.00 0.00 0.58 0.90 1.12 1.24 1.32 1.41 1.45
RI is the consistency index of a randomly generated reciprocal matrix from the 9-point scale.The RI values for matrixes of different sizes (Wu et al. 2008) are shown in Table 10.
When the size of the comparison matrix is 1 or 2, RI is formally, and the comparison matrixis always consistent. As a rule, only if CR<0.10, the consistency of the matrix is considered asacceptable, otherwise the pair-wise comparisons should be revised.
After obtaining the weight vector, it is then multiplied with the weight coefficient of the elementat a higher level (that was used as criterion for pair-wise comparisons). The procedure is repeatedupward for each level, until the top of the hierarchy is reached.
3.6. Evaluate the building energy conservation
With the evaluation tables filled by the expert group, the expert numbers who give the samelinguistic variables for a certain factors can be obtained. Thus, the membership degrees of eachlinguistic variable with respect to each factor in the lowest hierarchy can be calculated.
The fuzzy AHP evaluation process is listed as follows (Pang 2007, Metin and Ihsan 2008).
(1) Calculate the evaluation result of the lowest hierarchy factor
Establish the evaluation comments set V
V = {v1, v2, . . . , vp}, (5)
where p is the number of evaluation grade.Assume that the factor set U = {u1, u2, . . . , un}. The fuzzy judgement matrix R is expressed
by
R =
⎡⎢⎢⎢⎣
r11 r12 · · · r1p
r21 r22 · · · r2p
...... · · · ...
rn1 rn2 · · · rnp
⎤⎥⎥⎥⎦ , (6)
where R is the evaluation results of the factor set U and rij is the degree of membership of theith factor ui to the j th evaluation rank vj , which reflects the fuzzy relationship of every factor.
(2) Calculate the evaluation result of the factors above the lowest level
The comprehensive evaluation result vector S is obtained according to the following equation:
S = [w1 w2 · · · wn
]⎡⎢⎢⎢⎣
r11 r12 · · · r1p
r21 r22 · · · r2p
...... · · · ...
rn1 rn2 · · · rnp
⎤⎥⎥⎥⎦ = [s1 s2 · · · sp], (7)
where wi is the weight of the corresponding factors.
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Civil Engineering and Environmental Systems 133
(3) Calculate the evaluation results of the factors in different hierarchies
Assume that Sm = (sm1 , sm
2 , . . . , smp ) (m ≥ 2) is the evaluation result of the mth hierarchy factor
with the same above factor, then the evaluation result of the (m−1)th hierarchy factor can becalculated as follows:
Sm−1 = [w1 w2 · · · wn
]
⎡⎢⎢⎢⎢⎣
sm11 rm
12 · · · sm1p
sm21 sm
22 · · · sm2p
...... · · · ...
smn1 sm
n2 · · · smnp
⎤⎥⎥⎥⎥⎦
, (8)
where Sm−1 = [sm−11 sm−1
2 · · · sm−1p ] is the evaluation result of the (m−1)th hierarchy factor.
(4) Calculate the integrated evaluation value
Based on the fuzzy mathematics theory, the integrated evaluation value, Z, of any factor in differenthierarchies can be expressed as
Z = S · C = [s1 s2 · · · sp][c1 c2 · · · cp]T, (9)
where C is the set of the mean fuzzy numbers for the evaluation grades, which is shown in Table 9.
4. Case study
A new residential building is selected to illustrate how to use this evaluation model combiningLCA and fuzzy AHP. An expert group of 10 members is established. The expert group is asked to
Table 11. Weights calculation of the factors in the first hierarchy.
C1 C2 C3 C4 Weights λmax CR Consistency check
C1 1 2 1 2 0.333 4 3.33E-08 PassedC2 1/2 1 1/2 1 0.167C3 1 2 1 2 0.333C4 1/2 1 1/2 1 0.167
Table 12. Weights calculation of the factors in the first hierarchy within design stage C1.
C11 C12 C13 Weight λmax CR Consistency check
C11 1 1 1 0.333 3 0 PassedC12 1 1 1 0.333C13 1 1 1 0.334
Table 13. Weights calculation of the factors in the first hierarchy within the construction stage C2.
C21 C22 C23 C24 Weight λmax CR Consistency check
C21 1 1/2 1 1/2 0.1667 4 3.33E-08 PassedC22 2 1 2 1 0.3333C23 1 1/2 1 1/2 0.1667C24 2 1 2 1 0.3333
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Table 14. Weights calculation of the factors in the first hierarchy within the use stage C3.
C31 C32 C33 Weight λmax CR Consistency check
C31 1 1 1 0.333 3 0 PassedC32 1 1 1 0.333C33 1 1 1 0.334
Table 15. Weights calculation of the factors in the first hierarchy within the breaking stage C4.
C41 C42 C43 Weight λmax CR Consistency check
C41 1 1 1/2 0.25 3 0 PassedC42 1 1 1/2 0.25C43 2 2 1 0.5
Table 16. Weights of the factors in different hierarchies.
First hierarchy Second hierarchy Third hierarchy Fourth hierarchy
Factor Weight Factor Weight Factor Weight Factor Weight
C1 0.333 C11 0.333 C111 0.2448C112 0.2911C113 0.2911C114 0.1731
C12 0.333 C121 0.3333 C1211 0.25C1212 0.25C1213 0.25C1214 0.25
C122 0.3333 C1221 0.33C1222 0.67
C123 0.1667C124 0.1667
C13 0.334 C131 0.334C132 0.333C133 0.333
C2 0.167 C21 0.1667 C211 0.4C212 0.2C213 0.4
C22 0.3333C23 0.1667C24 0.3333 C241 0.334
C242 0.333C243 0.333
C3 0.333 C31 0.333 C311 0.1667C312 0.1667C313 0.3333C314 0.3333
C32 0.333 C321 0.4C322 0.4C323 0.2
C33 0.334
C4 0.167 C41 0.25C42 0.25C43 0.5
Note: The bold is the lowest hierarchy within each second hierarchy factor.
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make pair-wise comparisons for the factors in different hierarchies with the same above factors.Pair-wise comparisons are made according to Table 7. Then, the expert group members are askedto fill in the fuzzy AHP part of Table 8.
(1) Calculate the weights of the factors in different hierarchies
Based on a detailed discussion, pair-wise comparisons at a given level are made by the expertgroup. The pair-wise comparison matrixes of the first hierarchy factors and second hierarchyfactors are given in Tables 11–15. There is no space here to list the calculation process of thefactors in the other hierarchies, but the calculation results are listed in Table 16.
(2) Calculate the membership degrees of the factors in different hierarchies
With the evaluation tables, the expert numbers who give the same linguistic variables for a certainfactor can be obtained. Thus, the membership degrees of each linguistic variable with respect to
Table 17. The summarisation of the evaluation.
Fuzzy AHPMembership degree Traditional AHP
First hierarchy Second hierarchy Third hierarchy Fourth hierarchy VG G M Q P VP Average value
C1 C11 C111 0.2 0.5 0.3 0 0 0 0.728C112 0.1 0.7 0.2 0 0 0 0.716C113 0 0.8 0.2 0 0 0 0.695C114 0.1 0.8 0.1 0 0 0 0.755
C12 C121 C1211 0 0.8 0.1 0.1 0 0 0.686C1212 0 0.7 0.2 0.1 0 0 0.671C1213 0 0.4 0.5 0.1 0 0 0.646C1214 0 0.4 0.4 0.2 0 0 0.626
C122 C1221 0 0.3 0.6 0.1 0 0 0.628C1222 0 0.4 0.6 0 0 0 0.643
C123 0 0.2 0.7 0.1 0 0 0.61C124 0 0.4 0.6 0 0 0 0.653
C13 C131 0 0.1 0.7 0.1 0.1 0 0.573C132 0 0.1 0.6 0.2 0.1 0 0.539C133 0 0.3 0.4 0.3 0 0 0.574
C2 C21 C211 0 0.2 0.6 0.2 0 0 0.598C212 0.1 0.5 0.4 0 0 0 0.738C213 0 0.2 0.7 0.1 0 0 0.621
C22 0 0.2 0.6 0.2 0 0 0.602C23 0 0.1 0.3 0.5 0.1 0 0.52C24 C241 0 0.3 0.6 0.1 0 0 0.634
C242 0.1 0.5 0.4 0 0 0 0.73C243 0 0.3 0.7 0 0 0 0.64
C3 C31 C311 0 0.2 0.6 0.2 0 0 0.582C312 0 0.3 0.5 0.2 0 0 0.606C313 0 0 0.4 0.5 0.1 0 0.453C314 0 0 0.2 0.7 0.1 0 0.404
C32 C321 0.1 0.7 0.1 0.1 0 0 0.747C322 0.1 0.8 0.1 0 0 0 0.773C323 0 0.2 0.7 0.1 0 0 0.612
C33 0 0.3 0.5 0.1 0.1 0 0.582
C4 C41 0 0.1 0.7 0.2 0 0 0.576C42 0 0.3 0.5 0.1 0.1 0 0.586C43 0 0.2 0.6 0.2 0 0 0.591
Note: The bold is the lowest hierarchy within each second hierarchy factor.
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Table 18. Calculation results of the membership degree.
Membership degree
Factor VG G M Q P VP Grade
C1 0.032 0.426 0.430 0.090 0.022 0.000 MC2 0.014 0.249 0.539 0.181 0.017 0.000 MC3 0.027 0.341 0.368 0.209 0.055 0.000 MC4 0.000 0.200 0.600 0.175 0.025 0.000 MC11 0.095 0.698 0.207 0.000 0.000 0.000 GC12 0.000 0.414 0.517 0.069 0.000 0.000 MC13 0.000 0.166 0.567 0.200 0.067 0.000 MC21 0.020 0.260 0.600 0.120 0.000 0.000 MC22 0.000 0.200 0.600 0.200 0.000 0.000 MC23 0.000 0.100 0.300 0.500 0.100 0.000 QC24 0.033 0.367 0.567 0.033 0.000 0.000 MC31 0.000 0.083 0.383 0.467 0.067 0.000 QC32 0.080 0.640 0.220 0.060 0.000 0.000 GC33 0.000 0.300 0.500 0.100 0.100 0.000 MC41 0.000 0.100 0.700 0.200 0.000 0.000 MC42 0.000 0.300 0.500 0.100 0.100 0.000 MC43 0.000 0.200 0.600 0.200 0.000 0.000 M
each factor in the lowest hierarchy can be calculated. The summarisation of the evaluation andthe membership degrees are listed in Table 17.
Based upon the membership degrees, the calculation results of the membership degrees of thesecondary hierarchy factors and first hierarchy factors are shown in Table 18.As shown in Table 18,in the first hierarchy, the energy conservation grade of the four stages are all ‘Medium’. In thesecond hierarchy, energy conservation grades of most factors are ‘Medium’. Energy conservationgrades of the factors ‘Building form design’ and ‘Environmental impacts’ are ‘Good’, while thefactors ‘Construction waste’ and ‘Practical utilisation of energy and resources’ are ‘Qualified’.
(3) Calculate the integrated evaluation value
According to Equation (9), the integrated evaluation value Z can be calculated. The integratedevaluation value of the case building is 0.630.
In order to realise the evaluation results of each factor in different hierarchies, the integratedevaluation values of each factor are calculated. The calculation results are shown in Figures 2–4.
Figure 2 shows the integrated evaluation values of the first hierarchy factors. It shows thatamong the four stages in the life cycle, the design stage is the best, for which the integratedevaluation value Z is 0.671, while the breaking stage is the worst. It also demonstrates that theenergy conservation performances of the four stages are balanced.
Figure 3 shows the integrated evaluation values of the second hierarchy factors. The factors‘Building form design’ and ‘Environmental impacts’ receive a better assessment, of which theenergy conservation grade is ‘Good’. The factors ‘Construction waste’ and ‘Practical utilisationof energy and resources’ receive a relatively bad assessment, for which the integrated evaluationvalues Z are only 0.480 and 0.497. The integrated evaluation values Z of the other factors arebetween 0.5 and 0.7, for which the energy conservation grade is ‘Medium’.
Figure 4 shows the integrated evaluation values of the third hierarchy factors within designstage, construction stage and use stage. In the design stage, the factor ‘Floor to ceiling height’receives the best evaluation result, for which Z is 0.800. The factors ‘Heating and air conditioning’and ‘Building electrical system’receive relatively bad results, whose Z are 0.560 and 0.540. In theconstruction stage, Z values are between 0.600 and 0.740, which indicate that energy conservation
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performances of the third hierarchy factors in construction stage are balanced. In the use stage, theenergy conservation performances of the third hierarchy factors are in great difference. ‘Pollutantsmanagement’ receives the best evaluation result, for which Z is 0.800, while ‘Recycling degreeof resources’ receives the worst result, for which Z is only 0.420.
5. Validity of the fuzzy AHP method
To signify the difference between the proposed fuzzyAHP method and the traditionalAHP method,comparisons between the fuzzy AHP results and the traditional AHP results were made. In thetraditionalAHP method, the experts give accurate scores for the evaluation index, then the averagescore of each evaluation index is calculated and the integrated evaluation results are calculated bythe product of the average scores and the weights of the evaluation indexes. In order to verify theproposed method, after the expert group completes the fuzzy AHP part of Table 8, each expertgroup member is asked to give an accurate score for the lowest hierarchy factors in the traditionalAHP part of Table 8. With the procedure of the traditional AHP (Gu and Liang 2008), all thefactors in different hierarchies and their corresponding weights used in the traditional AHP modelare the same with those of the proposed method. The final integrated evaluation results of the casebuilding and the evaluation results of the factors are presented. The integrated evaluation resultby the traditional AHP method is Z = 0.641. The integrated value calculated by the fuzzy AHPmethod (Z = 0.630) is quite close to the value calculated by the traditionalAHP. The comparisonsof the integrated evaluation results of the factors are shown in Figures 2–4. From the figures, theevaluation results of each factor in different hierarchies by these two methods are also very closeand the differences between these two methods are in reasonable scope.
The merits of the traditional AHP method are simple, direct and easy to operate. The useof AHP does not involve cumbersome mathematics (Pang 2007). However, in some instances,the expert group members feel difficult to give accurate numerical scores for evaluating theperformances of the factors. The fuzzy AHP method resembles human reasoning in its use ofapproximate information and uncertainty to generate decisions. It can adequately handle theinherent uncertainty and imprecision of the human decision-making process and provide theflexibility and robustness needed for the decision-maker to understand the decision problem(Mu et al. 2008). Based on linguistic variables, despite the convenience of AHP in handling
0.52
0.54
0.56
0.58
0.6
0.62
0.64
0.66
0.68
0.7
C1 C2 C3 C4
Factor
Z
Fuzzy AHP Traditional AHP
Figure 2. Integrated evaluation values of the first hierarchy factors.
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00.10.20.30.40.50.60.70.80.9
C11 C12 C13 C21 C22 C23 C24 C31 C32 C33 C41 C42 C43
C1 C2 C3 C4
Factor
Z
Fuzzy AHP Traditional AHP
Figure 3. Integrated evaluation values of the second hierarchy factors.
00.10.20.30.40.50.60.70.80.9
C11
1
112
C C11
3
C11
4
C12
1
C12
2
C12
3
C12
4
C13
1
C13
2
C13
3
C21
1
C21
2
C21
3
C24
1
C24
2
C24
3
C31
1
C31
2
C31
3
C31
4
C32
1
C32
2
C32
3
C11 C12 C13 C21 C24 C31 C32
C1 C2 C3
Factor
Z
Fuzzy AHP Traditional AHP
Figure 4. Integrated evaluation values of the third hierarchy factors.
both quantitative and qualitative criteria of MCDM problem, fuzziness and vagueness existing inmany decision-making problems may contribute to the imprecise judgements of decision-makersin conventional AHP approaches (Bouyssou et al. 2000).
6. Conclusions
Building energy conservation assessment is essential throughout the various stages of buildingdevelopments and utilisations.Accurate building energy conservation assessment can help assist inselecting and adopting energy-efficient and cost-effective measures to achieve energy conservationin buildings.
In this study, an assessment model combining LCA and fuzzy AHP is developed in order toassess building energy conservation performance. The AHP method and 9-scale pair-wise com-parison are used to determine the weights of the factors in different hierarchies. The membershipdegrees, the evaluation results of factors in different hierarchies and the integrated evaluation
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value are calculated and the energy conservation performances of the building can be obtained.A case is then fed into the model to assess the building energy conservation performance.
The contributions of this study are given as follows.
(1) It combines LCA and fuzzy AHP into an evaluation of building energy conservation suc-cessfully. The study proposes an evaluation framework that relates energy conservation andenvironmental performances. The indexes are selected based on the four stages of building’slife cycle: design stage, construction stage, use stage and breaking stage. Based on the dis-cussion and the literature, a five-level hierarchical diagram is first constructed. The evaluationgrades are ranked into six levels: very good (VG), good (G), medium (M), qualified (Q), poor(P) and very poor (VP) in order to represent the quality of data.
(2) LCA studies have generally an intrinsic uncertainty related to various factors. The life-cyclethinking is a unique way of addressing environmental problems from a systems or holisticperspective. In this way of thinking, a product or system can be evaluated or designed with agoal of reducing environmental impacts and energy consumption over its whole life cycle.
(3) This paper has presented a model, based on the fuzzy logic, to evaluate building energy con-servation. It can systematically evaluate and contains interdependency relationships amongcriteria under uncertainty. It also considers the energy conservation performance of the build-ing in its whole life cycle. The fuzzy AHP can be used not only as a way to handle the innerdependences within a set of aspects and criteria, but also as a way of producing more valu-able information for decision making. The results of the present study still illustrates that theprocedure is simple and straightforward in calculations and prioritising. Therefore, it is verysuitable for solving MCDM problems.
The aim of this study is to use sustainability indicators in the whole life cycle and also to supportdecision-making within the building sector. This study has to be considered as a preliminary studyevaluating building energy conservation from the point of view of environmental impacts andenergy saving in order to provide energy and environmental sustainability indicators within thebuilding sector. It can be used by stakeholders such as engineers, architects and environmentalistsas an important point of reference for building energy conservation.
Acknowledgements
This research has been supported by the Youth Teacher Scientific Research Foundation of North China Electric PowerUniversity (Grant No. 200811010) and the Key Laboratory of Condition Monitoring and Control for Power Plant Equip-ment of Ministry of Education, China. The authors also wish to express their gratitude to the anonymous reviewers fortheir insightful comments and for the precious advice given to improve this paper.
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