Dwelling Selection by Applying VIKOR and Fuzzy AHP Method

Transcription

1 DOI: /IPEDR V63. 6 Dwellng Selecton by Applyng VIKOR and Fuzzy AHP Method Thoedtda Thpparat and Thongpoon Thaseepetch 2 Department o Constructon Management, Faculty o Engneerng and Archtecture, Raamangala Unversty o Technology, Bangkok, Thaland 2 Department o Cvl Engneerng, Faculty o Engneerng and Archtecture, Raamangala Unversty o Technology, Bangkok, Thaland Abstract. The purpose o ths study s twoold: rst, t s amed at demonstratng a model o dwellng selecton usng an ntegrated VIKOR and uzzy analytcal herarchy process (FAHP). Second, a selecton among alternatve buldngs and ther heatng system s made usng a proposed VIKOR-uzzy AHP methodology. Types o buldng under consderaton are composed o tradtonal snge lat dwellng house and lot lat dwellng house. In ths paper, alternatves o heatng system nclude coal based, gas based, bomass based, and combned bomass and gas based systems. Eght crtera are used or makng decson. In dwellng decson makng problems, data obtaned rom decson makers are mprecse because the decson makers cannot gve exact values or the crtera. Ths research allows the decson makers to assess the alternatve buldngs by usng lngustc terms. Fuzzy theory s used to address uncertanty n human preerences. Thus, the weghts o the selecton crtera are determned by parwse comparson matrces o uzzy AHP. It was ound that one lat dwellng house wth coal based heatng s the most approprate alternatve buldngs. Keywords: VIKOR, uzzy AHP, Dwellng, Alternatve, Selecton, Heatng System. Introducton The cvl constructon ndustry s one o the greatest sectors n the economy and one o the bggest polluters []. The constructon sector has not only a maor mpact on economc actvty, employment and growth rates, but has also a substantal mpact on the natural envronment, the eects o whch are evdent across the world. Housekeepng was responsble or 2% o the greenhouse gases. In addton wth the 5% o the commercal premses, ths leaded to a total o 7% o the greenhouse gases. To nvestgate the nluence o derent heat systems on the energy perormance level, prevous study undertook a cost analyss o derent heatng systems (condensng gas boler, non-condensng gas boler, ol boler, and heat pump) and ventlaton systems (C and D). The analyss was perormed or three representatve types o dwellngs n Flanders: a terraced, sem-detached and detached dwellng. The analyss clearly ndcated that a condensng gas boler n combnaton wth the heat exchanger was most advantageous. It was the cheapest heatng system and generates the lowest energy level. Ths made the condensng gas boler the best choce or all dwellng types. The am o the study was to search or the cheapest heatng system and the heatng system generatng the best energy level [2]. However, actors such as desgn complexty speed o constructon, durablty, envronment, aesthetcs, constructon complexty, and geometrc desgn should be consdered n a conceptual desgn [3] To make rght decson n dwellng house constructon, decson maker usually has lttle normaton and t s usually ncomplete. Selecton o the dwellng house can be classed as a mult-crtera decson-makng (MCDM) problem [4]. One wdely used method whch can handle both group decsons and uzzness s the uzzy analytc herarchy process (AHP) a urther development o Saaty s wdely used AHP technque [5,6]. Several researches present the applcaton o the uzzy AHP, or example, crtcal decsons n new product development [7]. VIKOR (VlseKrterumska Optmzaca I Kompromsno Resene that means Mult-Crtera Optmzaton and Compromse Soluton) method s one o the most popular methods. A VIKOR method s used to rank alternatve. The VIKOR method provdes the maxmum group utlty or the maorty and mnmum o an ndvdual regret or the opponent. The mult-crtera rankng ndex s obtaned based on the partcular measure o closeness to the deal soluton. The VIKOR method s not based the evaluaton unt o a crteron uncton [8,0]. 26

2 Ths paper provdes a systematc approach to dealng wth alternatve desgn o dwellng house. The proposed approach consders both qualtatve and quanttatve assessments. The assessment o alternatve dwellng houses s perormed usng uzzy AHP and VIKOR method. The results can be used to evaluate alternatve uture methods to enhance sustanablty. Ths paper presents an example or beng an nnovatve way o evaluatng derent dwellng houses, takng nto account aects o uncertanty. Ths study consders uzzness, whch s the man reason or the mplementaton o the uzzy AHP and the VIKOR method nstead o the classcal usage o the AHP or other MCDM methods. The result can be used as normaton or developers, contractors and desgners to develop measures or satsyng all requrements (.e., cost, tme, energy). 2. Dwellng Selecton Method Varous crtera related to the dwellng selecton are ntroduced. The mportant crtera are usually assocated wth cost, materal, energy, water. Ten crtera were consdered or selectng best alternatve or dwellng selecton problems [4]. Ten crtera ncluded x materal, used or constructon process (t/m2), x2 energy, used or constructon process (GJ/m2), x3 water, used or constructon process (m3/m2), x4 energy operaton (kwh/m2), x5 enclosures wth heat losses (m2), use or 50 operaton (kg/m2), x7 prce o the apartment ( /m2), x8 labor costs (human hour/m2), x9 Fuel annual prce ( /00m2), and x0 Prce o energy operaton (Lt/m2). Eght alternatves were determned, namely A one lat dwellng house wth coal based heatng, A2 one lat dwellng house wth gas based heatng, A3 one lat dwellng house wth bomass based heatng, A4 one lat dwellng house wth combned bomass and gas based heatng, A5 lot lat dwellng house wth coal based heatng, A6 lot lat dwellng house wth gas based heatng, A7 lot lat wth bomass based heatng, and A8 lot lat dwellng house wth combned bomass and gas based heatng. Eght alternatves were evaluated by consderng ten crtera, smultaneously. To determne these crtera at the same tme or ndng a nal soluton, elements o uncertanty nvolved n these crtera nluence the decson makng process. Decson makers are not only requred to make a decson based on varous crtera, they also have to consder conlctng relatonshps exstng between these crtera o whch the values are subectvely assessed. The uncertanty and the qualtatve human thoughts are dcult to measure n quanttatve value or the crtera assocated wth the dwellng selecton [4]. 3. Fuzzy AHP and VIKOR Method A decson-makng model should well handle vagueness or ambguty because o uzzness and vagueness assocated wth decson-makng problems. Ths secton provdes an overvew o a uzzy AHP or addressng uncertanty n the sustanable unversty o research proect assessment. The parwse comparson consders avorable and adverse eects o uncertanty. The ranges are used to present uncertanty nvolved n the parwse comparsons by usng parameters l and u to present avorable and adverse eects o uncertanty, respectvely. The uzzy AHP s one o the eectve approaches used to address the uncertanty and vagueness rom the subectve percepton and the experence o humans n decson-makng process. By usng the uzzy AHP, the decson makers are allowed to provde the comparng results by the nterval udgement nstead o crsp value udgement whch makes the decson makers eel more convenent and condent. The eects o uncertanty on the parwse comparson are qualtatvely estmated by the decson maker at a gven level regardng ther parent n the next hgher level, based on the requrement o the comparatve udgement prncple. The uzzy AHP ntegrates these ndvdual eects o uncertanty on the parwse comparson by combnng the calculated rato-score local prortes accordng to the requrement o the synthess o prortes. In ths study, the uzzy AHP s appled to evaluate the weght actor by usng ve lngustc terms: equally sgncant, moderately sgncant, strongly sgncant, very strongly sgncant, and extremely sgncant o whch the numercal ratngs are, 3, 5, 7, and 9, respectvely [6]. 27

3 The VIKOR method started wth the orm o L p metrc, whch was used as an aggregatng uncton n a compromse programmng method and appled to the multcrtera measure or compromse rankng. In the proposed approach, the alternatves are denoted as A, A2,..., A,..., Am, w s the weght o the th crteron, expressng the relatve mportance o the crtera, where =,2,..., n, and n s the number o crtera. The ratng (score) o the th crteron s denoted by or alternatve ntroduced by Ducksten and Oprcovc and s ormulated as ollows: L p n * p { [ w ( ) ( )] } p / = p = The VIKOR method s developed rom the above orm o Eq. (2)) and p= L (as Q n Eq. (3)) to obtan the rankng measure [3-6] S = L p = = A. The orm o L p metrc was =,2,..., m L p metrc. In addton, t uses n * [ w ( ) ( )] * { w ( )/( ) =,2 n} = p= L (as S n / (2) p = Q = L = max,..., (3) The compromse rankng algorthm VIKOR ncludes the ollowng steps. Step Consder the best *, and the worst values o all crteron unctons, =,2,..., n. In addton, an orgnal ratng matrx and a normalzed weght-ratng matrx o rsk are appled as ollows: where, * r ( ) ( ) = /, * crteron. Step 2 Calculate the values S and s the aspred/desred level and s tolerable level or each Q, =,2,..., m, applyng the relatons n S = = { n} Q = max =,2,..., (5) Step 3 Calculate the ndex values R, =,2,..., m, usng the relaton * * R = v( S S ) /( S S ) + ( v)( Q Q ) /( Q Q ) (6) where S * = mn S (or settng the best S = 0 ) S = max S (or settng the worst S = ) Q * = mnq (or settng the best Q = 0 ), Q = maxq (or settng the worst Q =, and 0 v, where v s ntroduced as a weght. Step 4 Prortze the alternatves, sortng by the value o { S, Q, and R =,2,..., m}, n decreasng order. Propose as a compromse the alternatve ( A ) whch s ranked rst by the measure mn { R =,2,..., m} the ollowng two condtons are satsed: Condton. Acceptable advantage: (2) (2) R ( A ) R( A ) /( m ), where A s the alternatve wth second poston n the rankng lst by R ; m s the number o alternatves. Condton 2: Acceptable stablty n decson makng: Alternatve A must also be the best ranked by { S or / and Q =,2,..., m}. The compromse-rankng method s appled to obtan the compromse. Because o the act that the soluton provdes maxmum group utlty o the maorty 28 (4)

4 (represented by mn S, Eq. (4)), and mnmum ndvdual regret o the opponent (represented by mn Q, Eq. (5)), the soluton s acceptable. The weght stablty ntervals or the gven compromse soluton can be obtaned rom the VIKOR algorthm regardng the nput weghts provded by the experts [8]. 4. Dwellng Selecton Framework and Demonstratve Applcaton To select apartment or lvng, a case study on the dwellng selecton was present [4]. A uzzy game theory was used to develop an assessment model, consderng ten crtera namely, x materal, used or constructon process (t/m2), x2 energy, used or constructon process (GJ/m2), x3 water, used or constructon process (m3/m2), x4 energy operaton (kwh/m2), x5 enclosures wth heat losses (m2), operaton (kg/m2), x7 prce o the apartment ( /m2), x8 labor costs (human hour/m2), x9 Fuel annual prce ( /00m2), and x0 Prce o energy operaton (Lt/m2). Ths approach had combned uzzy set theory wth game theory. It was used n desgn concept apprasal. Ths study proposes a dwellng selecton ramework. To demonstrate an applcaton o the proposed approach to the alternatve buldngs, ths study consders eght desgn alternatves [4]:A one lat dwellng house wth coal based heatng, A2 one lat dwellng house wth gas based heatng, A3 one lat dwellng house wth bomass based heatng, A4 one lat dwellng house wth combned bomass and gas based heatng, A5 lot lat dwellng house wth coal based heatng, A6 lot lat dwellng house wth gas based heatng, A7 lot lat wth bomass based heatng, and A8 lot lat dwellng house wth combned bomass and gas based heatng. Ths study classes the man crtera nto cost, energy, polluton, and resources. Ten sub-crtera [4] are classed based on these our crtera. Table : Weght o crtera Weght o crtera evaluated by respondent C x No. x x x x x x x x x x To apply uzzy AHP, the comparson structure among crtera was developed. Experts wth a vast experence o the apartment constructon were the partcpants o ths study. There were eght respondents ncludng developer, contractor, desgner, and consultant. The s o experences accumulated by all partcpants are more than 50 s o experence n the apartment constructon. In-depth ntervews wth organzed questonnares were used to collect data. Ater usng the uzzy AHP to calculate weghts o crtera, the experts were asked to rate alternatves wth respect to each crteron. For prortzng alternatves, accordng to the VIKOR method, the calculated data along wth the nal values o R were presented. In ths study, eght alternatves were ranked. Based on p Eqs., (4), (5) and (6), the ollowng calculatons are consdered or L,S, Q,R ; =, 2, 3, 4,5,6,7, and 8. The nal rankng o eght alternatves was determned based on ten crtera. The obtaned results were vered based on two condtons n Step 4 so that the nal rankng and compromse soluton can be acheved. The acceptance advantage (Condton ) s satsed. Table 2 shoesults obtaned rom the proposed evaluaton ramework usng ten crtera. Raw data was obtaned rom Medneckene, et.al. [4]. Based on results obtaned rom the uzzy AHP method, the most mportant crteron was the enclosures wth heat losses and was ollowed by labor costs and prce o the apartment. The least mportant crtera was CO2 operaton and was ollowed by uel annual prce and energy operaton, respectvely. It was ound that the one lat dwellng house wth coal based heatng was the best alternatve. It was ollowed by the one lat dwellng house wth gas based heatng and the one lat dwellng house wth bomass based heatng, respectvely. The worst alteratve was one lat dwellng house 29

5 wth combned bomass and gas based heatng and was ollowed by lot lat dwellng house wth combned bomass and gas based heatng and the lot lat dwellng house wth gas based heatng, respectvely. It s mportant to know strengths and weakness o the alternatve dwellng houses n order to make an ndustry and researchers aware o potental strengths and weakness so they know what steps to take. The strengths and weaknesses o alternatves can be dented as shown n Table 3. The maor strength o the best alternatve was enclosures wth heat losses and was ollowed by labor costs and materal, used or constructon process. The weakness o the best alternatve was prce o the apartment and was ollowed by the energy operaton and the Prce o energy operaton. To overcome the maor weakness o the best alternatve, the desgners should learn how to reduce prces based on alternatve 6 and 7, lot lat dwellng house wth the gas based heatng or bomass based heatng. To mprove the worst alternatve, the desgners should learn how to reduce prces based on alternatve 6 and 7, lot lat dwellng house wth the gas based heatng or bomass based heatng. Table 2: Results obtaned rom the ntegrated VIKOR and uzzy AHP method Crtera A A2 A3 A4 A5 A6 A7 A8 * - w x x x x x x x x x x w r w 9 9 r S Q S Q R No Remark: x materal, used or constructon process (t/m2), x2 energy, used or constructon process (GJ/m2), x3 water, used or constructon process (m3/m2), x4 energy operaton (kwh/m2), x5 enclosures wth heat losses (m2), x6 CO2 operaton (kg/m2), x7 prce o the apartment ( /m2), x8 labor costs (human hour/m2), x9 Fuel annual prce ( /00m2), and x0 Prce o energy operaton (Lt/m2), A one lat dwellng house wth coal based heatng, A2 one lat dwellng house wth gas based heatng, A3 one lat dwellng house wth bomass based heatng, A4 one lat dwellng house wth combned bomass and gas based heatng, A5 lot lat dwellng house wth coal based heatng, A6 lot lat dwellng house wth gas based heatng, A7 lot lat wth bomass based heatng, and A8 lot lat dwellng house wth combned bomass and gas based heatng, w s weght o crtera, * s the best value, and - s the worst value. 30

6 Rankng 2 x5 enclosures wth heat losses (m2), Alternatves A A2 A3 A4 A5 A6 A7 A8 x x4 x5 x5 x5 materal, energy use enclosures enclosures enclosures used or or 50 x9 Fuel wth heat wth heat wth heat constructon operaton annual operaton losses losses losses process prce (m2), (m2), (m2), (t/m2), (kwh/m2), ( /00m2), (kg/m2), x8 labor costs (human hour/m2), x materal, used or constructon process x8 labor costs (human hour/m2), x9 Fuel annual prce ( /00m2), x9 Fuel annual prce ( /00m2), operaton x8 labor costs (human hour/m2), operaton x2 energy, used or constructon process (GJ/m2), x3 water, used or constructon process (m3/m2), x0 Prce o energy operaton (Lt/m2). x7 prce o the apartment ( /m2), operaton (kg/m2), x7 prce o the apartment ( /m2), x0 Prce o energy operaton (Lt/m2). x9 Fuel annual prce ( /00m2), 3 (t/m2), (kg/m2), (kg/m2), Remark A one lat dwellng house wth coal based heatng, A2 one lat dwellng house wth gas based heatng, A3 one lat dwellng house wth bomass based heatng, A4 one lat dwellng house wth combned bomass and gas based heatng, A5 lot lat dwellng house wth coal based heatng, A6 lot lat dwellng house wth gas based heatng, A7 lot lat wth bomass based heatng, and A8 lot lat dwellng house wth combned bomass and gas based heatng. 5. Concluson Ths paper presents an applcaton o a mult-crtera decson makng (MCDM) model or evaluaton alternatves, dwellng house n ths case, or the dwellng selecton problem. For ths purpose, an ntegrated methodology s structured, n whch the the VIKOR uses the uzzy AHP result weghts as nput weghts. Fnally, an applcaton example o the dwellng house selecton regardng ten crtera s demonstrated. The applcablty and sutablty o the proposed methodology are presented. The quanttatve and qualtatve evaluaton can be conducted or searchng the sutable level whch n turn ncreases the complexty o the desgn evaluaton. A quanttatve method or copng wth multple decson crtera s propose. It s sutable or assstng a decson maker durng the conceptual desgn o dwellng proect. The proposed method employs the uzzy AHP method to perorm the parwse comparson and calculate the weghts o crtera. The VIKOR method s used to compute the total score o the crtera. In ths way, the proposed method accurately examnes uncertanty nvolved n the parwse comparsons and the calculaton o the weghts and total score o the crtera n a smply manner. It s mportant to know strengths and weakness o the desgn alternatves. Any ptall o exstng assessment methods could elmnate by usng the proposed ramework. The result can be used as normaton or developers, desgners, and contractors to develop a sutable desgn or dwellng house constructon. In addton, results obtaned rom the developed evaluaton ramework make a constructon ndustry and researchers realze the potental strengths and weakness so they can provde manageral mplcatons to mprove the desgn crtera and constructon methods. 6. Reerences Table 3: Rankng strengths o alternatves [] M. Ilha, L. Olvera; O. Goncalves. Envronmental assessment o resdental buldngs wth an emphass on water conservaton, Buldng Servces Engneerng Research and Technology, 2009, 30 : [2] A. Audenaerta, L. De Boeckc,d, K. Geudensa, M. Buyle, Cost and E-level analyss o derent dwellng types and derent heatng systems wth or wthout heat exchanger, Hub Research Papers, 20, 33, -4. [3] H. Malekly, S. Meysam Mousav a, H. Hashem b, A uzzy ntegrated methodology or evaluatng conceptual brdge desgn, Expert Systems wth Applcatons, 200, 37 : [4] M. Medneckene, E. K. Zavadskas, and Z. Tursks, Dwellng selecton by applyng uzzy game theory, Archves o Cvl and Mechancal Engneerng, 20, 6 (3): -5. 3

7 [5] Zadeh, Fuzzy set. In. Control, 965, 8 : [6] Saaty, Fundamentals o decson makng and prorty theory wth the analytcal herarchy process, 6 Pttsburgh: RWS Publcatons, 994. [7] A. J. Ansar, I. Ashra, B. Gopal. Integrated Fuzzy VIKOR and AHP Methodology or Selecton o Dstrbuted Electrcty Generaton through Renewable Energy n Inda, Internatonal Journal o Engneerng Research and Applcatons, 20, (3): 0-3 [8] H. C. Lu, L. Lu, N. Lu, and L. X. Mao. Rsk evaluaton n alure mode and eects analyss wth extended VIKOR method under uzzy envronment, Expert Systems wth Applcatons, 202, 39: [9] A. Sanaye, S. F. Mousav, and A. Yazdankhah. Group decson makng process or suppler selecton wth VIKOR under uzzy envronment. Expert Systems wth Applcatons, 200, 37: [0] J. Grubha and R. S. Vnodh. Applcaton o uzzy VIKOR and envronmental mpact analyss or materal selecton o an automotve component. Materals and Desgn. 202, 37: [] A. C. Kutlu, M. Ekmekcog, Fuzzy alure modes and eects analyss by usng uzzy TOPSIS-based uzzy AHP, Expert Systems wth Applcatons. 202, 39: