Expert Systems wth Applcatos 38 (2011) 7270 7276 Cotets lsts avalable at SceceDrect Expert Systems wth Applcatos joural homepage: www.elsever.com/locate/eswa Aget-based dffuso model for a automoble market wth fuzzy TOPSIS-based product adopto process Shtae Km, Keeheo Lee, Jag Kyu Cho, Chag Ouk Km Departmet of Iformato ad Idustral Egeerg, Yose Uversty, Seoul 120-749, Republc of Korea artcle fo abstract Keywords: Product dffuso Automoble market Aget-based model Fuzzy TOPSIS Socal fluece Ths paper focuses o the product dffuso a compettve automoble market. Sce purchasg a car s costly, the cosumers the market ted to behave lke ratoal decso makers. They aturally compare the attrbutes of cars (e.g., brad preferece, fuel ecoomy, safety, comfort) ad make overall decsos. I ths paper, we propose a aget-based (AB) dffuso model cosstg of tes of thousads of teractg agets. I the model, a aget represets a cosumer ad bases ts mult-attrbute decso-makg o fuzzy TOPSIS. The decso-makg process tegrates three purchasg forces: expert s product formato provded by mass meda, subjectve weghts o product attrbutes assged by dvdual cosumers, ad socal fluece (.e., formato delvered from a cosumer s eghbors who have already adopted products). The AB model executes the agets ad observes the collectve behavor. I ths sese, the model ca assst the aalyss of the complex market dyamcs. We coducted a emprcal study to verfy the performace of the AB model. Ó 2010 Elsever Ltd. All rghts reserved. 1. Itroducto Correspodg author. Tel.: +82 2 2123 2711; fax: +82 2 364 7807. E-mal address: kmco@yose.ac.kr (C.O. Km). Automoble markets are hghly compettve. I the markets, smlar fuctog cars compete wth each other for expadg ther market shares, so lauchg ew cars to the markets troduce a cosderable amout of rsk to the carmakers. To reduce the rsk, the carmakers eed to aalyze how crtcal marketg ad producto decsos (e.g., promoto strategy, prce, supply volume) gve mpact o the market shares of the ew cars, based o whch the frms ca choose the best decsos that acheve maxmum profts from the ew cars. However, such what-f aalyss s a qute dffcult task ad requres elaborate forecastg tools. It s tradtoal to use tme-seres techques (Box, Jeks, & Resel, 1994; Cheg, Che, & Wu, 2009) for the aalyss, but the techques requre accumulated sales data as puts, thus they are of o use whe a brad-ew car s released to a market. I such stuato, t s possble that marketers aalyze the dvdual product adopto processes of heterogeeous cosumers ad vestgate how market dyamcs emerge from the dvdual adoptos. I ths paper, we develop a aget-based (AB) model for forecastg product dffuso a full-szed car market. The cetral ssue of ths paper s how exactly the AB model ca predct the market dyamcs whe a ew car s released to the market. The AB model cossts of tes of thousads of teractg autoomous agets. I the model, a autoomous aget represets a cosumer ad has uque characterstcs as a cosumer to make ts ow purchase decso. A set of cosumer-agets wth ther teracto structure correspods to a socal etwork of cosumers ad ca be couted as a vrtual market. I the real world, the product formato evaluated by early product adopters spread out through commucato chaels such as the Iteret ad wordof-mouth. The formato flueces o the purchase decso of potetal cosumers, whch s called socal fluece or word-ofmouth effect (Boe, 1995). I the AB model, socal fluece s rased by the teracto amog the cosumer-agets. The AB model executes the cosumer-agets, whch ca be of dfferet types, ad observes the collectve behavor. I ths sese, the model ca assst the aalyss of the complex market dyamcs. The proposed AB model reflects two realstc huma behavoral factors relatg to product adopto process: heterogeety of cosumers ad fuzzy decso-makg based o multple attrbutes. Cosumers are heterogeeous. Frst, cosumers have dfferet weghts o the mportace of product attrbutes ad they usually express the weghts lgustc terms. For stace, a cosumer may rate very mportat for the fuel ecoomy of car, whereas aother may perceve that the attrbute s ot mportat. Secod, cosumers are ulkely to buy a ew product whe socal fluece s egatve. O the other had, the chace of buyg the ew product becomes hgher as socal fluece creases postvely. However, geeral, to what extet cosumers accept socal fluece s dfferet accordg to dvdual characters. Some people wth strog persoalty mght ot be susceptble to socal fluece, whle others who are very sestve to the tred of publc 0957-4174/$ - see frot matter Ó 2010 Elsever Ltd. All rghts reserved. do:10.1016/j.eswa.2010.12.024
S. Km et al. / Expert Systems wth Applcatos 38 (2011) 7270 7276 7271 opo accommodate themselves to the decsos of early product adopters. Whe several hgh-prced products wth smlar fuctos are competed a market, t s ot easy to decde oe product s superor to the others all aspects wthout dffculty. I such codto, cosumers ted to be more tha prudet; they wll behave lke ratoal decso makers. Because the performace of products are usually evaluated wth respect to dvdual attrbutes (e.g., brad preferece, fuel ecoomy, safety, comfort), cosumers aturally compare the products a attrbute-by-attrbute fasho, based o whch they make overall purchase decsos. Cosumers ca access the product evaluato formato through mass meda, such as Cosumer Reports ad the Iteret, ad through the word-ofmouth spread over the socal etwork of cosumers. However, may cases, the product formato s ot expressed quattatvely. People are used to compare product attrbutes relatvely wth lgustc terms such as good, ormal, or bad. For example, cosumers compare the safety of competg cars ad may say the safety of ths car s good but for that car t s bad. The relatve evaluato wth lgustc terms s commo our lfe. TOPSIS (Techque for Order Preferece by Smlarty to Ideal Soluto) s a mult-attrbute decso-makg heurstc. It selects the best soluto from may alteratves, whch s the closest to the postve deal soluto ad the farthest from the egatve deal soluto. Its logc s smlar to a ratoal huma decso-makg process (Hwag & Yoo, 1981). We adapt TOPSIS usg fuzzy set theory for trasformg a lgustc evaluato to a crsp umber. Modelg usg fuzzy set theory has prove to be a effectve way for formulatg decso problems where formato avalable s subjectve ad mprecse (Zmmerma, 2001). Fuzzy TOPSIS has bee troduced for varous mult-attrbute decso-makg problems (Chamodrakas, Alexopoulou, & Martakos, 2009; Chu, 2002; Dağdevre, Yavuz, & Klç, 2009; Su & L, 2009; Wag & Chag, 2007). I ths paper, we adapt fuzzy TOP- SIS for modelg cosumer s product adopto process, whch tegrates three purchasg forces: (1) expert s product formato provded by mass meda, (2) subjectve weghts o product attrbutes gve by dvdual cosumers, ad (3) socal fluece (.e., formato delvered from a cosumer s eghbors who have already adopted products). The expert s product formato s assumed to be objectve ad accessble by all cosumers. Each cosumer persoalzes the product formato by reflectg hs/ her ow weghts o product attrbutes ad makes purchase decso based o the persoalzed product formato ad socal fluece. Tradtoally, aalytcal approaches formalze the aggregate level of peetrato of a ew product based o dfferetal equatos. The Bass model ad ts varats llustrate the dffuso process of product or techology quattatvely at a macro-level (Mahaja, Muller, & Bass, 1990; Meade & Islam, 2006; Wag & Chag, 2009). The models are able to clude socal fluece by classfyg cosumers to categores such as early adopters ad mtators the latter follows the product choce patter of the former. However, the people each group are assumed to be homogeeous; the models are uable to specfy at a mcro-level how dvdual cosumers respod to a ew product ad how cosumers commucate ad fluece each other compettve markets (Chadrasekara & Tells, 2007; Rahmadad & Sterma, 2008). O the other had, AB models are computatoal tools at mcro-level. The models are able to mtate a atural market dyamcs by specfyg dvdual product adopto processes ad mplemetg word-of-mouth whch s aga fed back to dvdual decsomakg of potetal cosumers. Some recet studes based o AB models are capable of represetg dvdual product adopto processes (Alkemade & Castald, 2005; Delre, Jager, Bjmolt, & Jasse, 2007; Delre, Jager, & Jasse, 2007; Sog & Chtaguta, 2003; Zeoba, Weber, & Dam, 2009). However, the prevous AB models do ot cosder cosumer s product adopto process from the vewpot of a mult-attrbute decso-makg problem, or ot reflect lgustc product evaluato ad cosumer s weghts to the product adopto process. The rest of the paper s orgazed as follows. I Secto 2, we preset the proposed AB model. I Secto 3, we coduct a emprcal study to valdate the model s feasblty. Fally, Secto 4, we coclude the mplcatos from the results ad meto o the future research drectos. 2. Aget-based model 2.1. Idvdual decso-makg Suppose that a automoble market cossts of m products of P ( =1,..., m) ad the products are evaluated based o a set of attrbutes A j (j =1,..., ). The expert s performace ratgs o the products are represeted as a matrx of E ¼ðr j Þ m I the matrx, the ratg r j of product P wth respect to attrbute A j s represeted usg the lgustc terms gve Table 1 whch each lgustc term s characterzed by a tragular fuzzy umber. As the frst step of product adopto process, cosumers are assumed to access the expert s product formato E through mass meda. Let W k =(w 1k,..., w k ) be a weght vector for attrbutes A j (j =1,..., ) assged by cosumer-aget k usg the lgustc terms Table 1. The weght vector represets the relatve mportace of the attrbutes perceved by the cosumer-aget. The performace ratg matrx S k ¼ðx k j Þ m persoalzed by the cosumeraget ca be derved by multplyg the weght vector W k ad the expert s product formato matrx E. The persoalzed product formato matrx S k reflects the evaluato bas of the cosumer-aget k o the m products. However, sce the matrx E ad the weght vector W k are composed of lgustc ratgs represeted as tragular fuzzy umbers, a fuzzy operato s requred order to multply the tragular fuzzy umbers r j ad w jk.we apply the graded mea tegrato represetato method (Chou, 2003) whch provdes easer uderstadg ad smpler calculato for a multplcato of fuzzy umbers. The method coverts a fuzzy umber to a crsp value as follows (refer to Chou (2003) for the detaled logc). Defto. The graded mea tegrato represetato method trasforms a tragular fuzzy umber X =(x 1, x 2, x 3 ) to a crsp umber Pð e XÞ by Pð e XÞ¼ 1 6 ðx 1 þ 4x 2 þ x 3 Þ Property. The multplcato operator of tragular fuzzy umbers e X ad e Y s defed as Pð e X e Y Þ¼Pð ~ XÞPð ~ YÞ ¼ 1 6 ðx 1 þ 4x 2 þ x 3 Þ 1 6 ðy 1 þ 4y 2 þ y 3 Þ Usg Eq. (3), the persoalzed product formato matrx S k s expressed as ð1þ ð2þ ð3þ
7272 S. Km et al. / Expert Systems wth Applcatos 38 (2011) 7270 7276 Table 1 Lgustc terms ad tragular fuzzy umbers. Varable Lgustc term Performace (r j ) Poor Far Good Very Good Excellet (P) (F) (G) (VG) (E) Weght (w jk ) Very low Low Medum Hgh Very hgh Sestvty to socal fluece (a k ) Very weak Weak Normal Strog Very strog Tragular fuzzy umber ðr 1 j ; r2 j ; r3 j Þ, ðw1 jk ; w2 jk ; w3 jk Þ, ða1 k ; a2 k ; a3 kþ (0, 0, 0.3) (0.1, 0.3, 0.5) (0.3, 0.5, 0.7) (0.5, 0.7, ) (0.7,, ) ð4þ where x k j ¼ Pðr j w jk Þ¼ 1 6 ðr1 j þ 4r2 j þ r3 j Þ1 6 ðw1 jk þ 4w2 jk þ w3 jkþ. The matrx S k s ormalzed to S k ¼ðx k j Þ m by x k j x k j ¼ qffffffffffffffffffffffffffffffffffffffffff P m ¼1 ðxk j Þ2 For the cosumer aget k, the x k j Eq. (5) ca be terpreted as the partal worth of product P for attrbute A j ad the sum of x k j for all attrbutes summarzes the attractveess of product P. I tradtoal product choce models (see Mara (1995) for the studes o product choce models), the attractveess of the product s called utlty. A cosumer chooses a product usg a radom fucto of the utlty. Ths research further cosders socal fluece (.e., word-of-mouth effect) the selecto of a product. As we prevously metoed, t s commo that cosumers respod to socal fluece wth dfferet degrees. I ths paper, dvdual sestvty levels to socal fluece are estmated through a survey ad expressed wth the lgustc terms defed Table 1. The sestvty level of the cosumer-aget k, a k, ca be coverted to a crsp value by usg the graded mea tegrato represetato method defed Eq. (2). Suppose that the umber of product adopters amog the eghbors of the cosumer-aget k s L k ad the trust levels of the eghbors are equal. The overall performace ratg of product P wth respect to attrbute A j estmated by the cosumer-aget k s gve by x k j ¼ð1 a kþx k j þ a X k x l j =jl kj l2l k ¼ 1 1 6 ða1 k þ 4a2 k þ a3 k Þ x k j þ 1 X 6 ða1 k þ 4a2 k þ a3 k Þ x l j =jl kj l2l k Wth the matrx S k updated usg Eq. (6), the cosumer-aget k determes the postve-deal product P k+ ad the egatve-deal product P k as P kþ ¼fx kþ 1 ; xkþ 2 x k j ¼fðmax P k ¼fx k 1 ; xk 2 x k j ¼fðm ;...; xkþ g jj 2 BÞ; ðm ;...; xk g jj 2 BÞ; ðmax x k jjj 2 CÞj ¼ 1; 2;...; mg x k jjj 2 CÞj ¼ 1; 2;...mg ð5þ ð6þ ð7þ where B s a set of beeft attrbutes ad C s a set of cost attrbutes. By defto, the postve-deal product P k+ s optmal wth respect to all attrbutes, ad realty, the product s almost uattaable. Most cosumers wll cosder the postve-deal product as a referece ad choose the best alteratve that s most smlar to the postve-deal product ad most dssmlar to the egatve-deal product. Usg the -dmesoal Euclda dstace, the smlartes of product P to the two deal products P k+ ad P k ca be measured by vffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff vffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff X d kþ u ¼ t ðx k X j xkþ ad d k u ¼ t ðx k j xk j Þ 2 ð8þ j¼1 j Þ 2 By combg the two smlartes, the relatve closeess of product P to the postve-deal products ca be measured by C k ¼ d kþ d k þ d k j¼1 ; ¼ 1; 2;...; m ð9þ Fally, the cosumer-aget k chooses the best product wth the maxmum closeess. I ths secto, we dscussed how dvdual cosumer-agets rak competg products by takg multple product attrbutes to cosderato. I the followg secto, we wll expla how we coordate the executo of the cosumer-agets for geeratg the dffuso dyamcs. 2.2. Dffuso dyamcs Before presetg the executo procedure of the AB model, we dscuss o three tal codtos for the executo. Those are the socal etwork structure of cosumers, the assgmets of weght vectors ad the sestvty levels to socal fluece, ad cosumers product purchase tmes. Frst, a vrtual market should be establshed to smulate a wordof-mouth process. The market s a socal etwork cosstg of cosumer-agets (odes) that are coected by acquataceshps (lks). I the socal etwork, each cosumer-aget makes a purchase through fuzzy TOPSIS ad delvers ts ow persoalzed product formato to ts eghbors lked drectly. The logcal structure of the socal etwork flueces o the speed of wordof-mouth. The speed s fast f everyoe the etwork s reachable a few steps. Otherwse, t takes may steps to delver ay formato from oe to aother throughout the etwork. Watts ad Strogatz (1998) classfed socal etworks to three categores: regular etwork, small-world etwork, ad radom etwork. The regular etwork s a ormal lattce where every ode s lked to ts eghbors wth a fxed degree of coectvty. The small-world etwork emerges as the result of radomly rewrg a fracto of the lks of every ode. The fracto of lks s called rewrg costat. I the small-world etwork, t s possble to coect ay two odes through just a few lks. The radom etwork s a extreme case where every lk the regular etwork s replaced wth a radom lk. Emprcal evdece suggests that socal etworks ofte dsplay the property of small-world etwork (Watts & Strogatz, 1998). I ths paper, we employ the small-world etwork as the logcal model of the vrtual market. Secod, each cosumer-aget should have ts ow weght vector (W k ) ad sestvty level to socal fluece (a k ). I the AB model, these two characterstcs are regarded as radom varables ad assged to the cosumer-agets a probablstc way. I detal, throughout a survey, respodets gve ther ow weghts for product attrbutes ad sestvty levels to socal fluece usg
S. Km et al. / Expert Systems wth Applcatos 38 (2011) 7270 7276 7273 lgustc terms. The acqured data are used for buldg the emprcal dstrbutos of the two radom varables. The each cosumer-aget s assged a radom weght vector ad a radom sestvty level by usg the two emprcal dstrbutos, respectvely. Thrd, product dffuso starts from ovators who have a strog tedecy to test a ew product before others do. Ther decsos are the seed for a wave of word-of-mouth. For each car etry tme, the umber of ovators s set to 2% of the o-adopters who do ot purchase products utl the etry tme. We exclude the case that prevous adopters repurchase cars a short term. The umber of ovators s gve based o the assumpto of the Bass model that ovators ormally accout for 2.8% of the populato of a market (refer to p. 4 Mahaja, Muller, ad Wd (2000)). We assume that the umber of ovators s ot depedet o the umber of car etres. If more tha two cars are released at the same tme, the umber of ovators s just 2% of o-adopters remag at the release tme. Each of the ovators adopts a car amog those that are released at the same tme accordg to the fuzzy TOPSIS-based product adopto process. Oce ovators adopt, other cosumer-agets (.e., o-adopters) coected to them through a socal etwork become aware of the product adoptos ad the cosumer-agets are partcpated the word-of-mouth process. Wth the dffuso horzo, the purchase tmes of the o-adopters are radomly determed usg a uform dstrbuto. Ths assumpto s reasoable for the markets of hghly expesve cosumer durables such as automobles ad hgh-ed TVs, because people are used to buy ew products whe they just eed (e.g., whe ther used oes become old), almost depedetly of whe others do. However, ths does ot mea that the cosumers the markets are ot sestve to socal fluece. The cosumers are exposed to socal fluece at ther purchase tmes. The executo procedure of the AB model cossts of two phases. The tal phase cofgures the etwork of cosumeragets; makes them heterogeeous by assgg dfferet weght vectors ad sestvty levels to socal fluece; sets the cosumer-agets purchase tmes. The executo phase starts the dffuso from the ovators at dffuso tme zero. As the dffuso tme passes, the cosumer-agets whose purchase tmes are equal to the curret dffuso tme make purchase decsos wth the cosderato of formato receved from ther eghbors coected to them through a socal etwork. The dffuso cotues utl the curret tme reaches the ed of the dffuso horzo. The executo procedure ca be summarzed as follows. 2.2.1. Assumptos (m 1) products P ( =1,..., m 1) exst at dffuso tme zero ad a ew product P m s troduced at dffuso tme t ew. Expert s product formato for all products s avalable. For each tme whe a ew product eters the market or ew products eter at the same tme, the umber of ovators s set to 2% of o-adopters. 2.2.2. Italzato (Step 1) Create a socal etwork cosstg of cosumer-agets ad ther lks. (Step 2) Usg a survey result, assg each cosumer-aget a weght vector ad a sestvty level to socal fluece. (Step 3) Except for the ovators, geerate cosumer-agets purchase tmes accordg to a uform dstrbuto, Uform(1, Ed-of-Horzo). 2.2.3. Executo (Step 4) At dffuso tme t = 0, troduce the expert s formato o the (m 1) products to all cosumer-agets. (Step 5) For the (m 1) products, determe the locatos of the ovators the socal etwork radomly ad make each of them choose a product amog the (m 1) products accordg to the fuzzy TOPSIS-based product adopto process. The, set t =1. (Step 6) If t t ew, go to step 7. Otherwse, troduce the expert s formato o the ew product P m to the curret o-adopters. For the product P m, determe the locatos of the ovators the socal etwork radomly ad make them choose the product. (Step 7) For the cosumer-agets whose purchase tmes are equal to the curret tme t, they request persoalzed product formato to the eghbors who purchased ay products before the curret dffuso tme t. The they select ther products accordg to the fuzzy TOPSIS-based product adopto process. (Step 8) Set t = t + 1. If the dffuso tme reaches the Ed-of- Horzo, the stop the dffuso. Otherwse, go back to step 6. 3. Emprcal study 3.1. Descrpto Usg a emprcal study, we tested the performace of the aget-based dffuso. The emprcal study s cocered wth a full-szed car market Korea. As of today, sx car models exst the market. Amog those, we focused o three models, deoted as,,, because the remag models have occuped very small market portos, whch have lttle vared over tme. The frst two car models ( ad ) were etered to the market 38 moths ago ad the last model () was released to the market ext 19 moths after the lauch of ad. The ma questo addressed the study was ca we forecast the dyamcs of the car market wth the AB model ad, f so, how socal fluece cotrbutes to the market dyamcs? Before aswerg the questo, we eeded to calbrate two parameters related to the socal etwork of cosumers. As we dscussed the last secto, the etwork structure affects the speed of product dffuso. Although the AB model s capable of smulatg the real purchasg behavors of dvdual cosumers, ts performace may be costraed by the etwork structure. Sce t was mpossble to kow how real cosumers socal etwork s cofgured, we vestgated 16 dfferet etwork structures by varyg the rewrg costat ad the degree of coectvty (.e. the umber of eghbors coected to each cosumer), ad foud the best oe wth mmum forecastg error. Four rewrg costats (5, 0.1, 5, 0.5) ad four degrees of coectvty (4, 6, 8, 10) were cosdered the calbrato expermet. For the expert s product formato o the three car models, we used the data that was created by the expert group of a famous car magaze. The data have bee accessble through the web ste of the car magaze compay. The performace ratgs of the car models wth respect to e attrbutes are show Table 2. From the table, we could make two observatos. Frst, the expert group cocluded that the model was superor to the others all aspects except brad preferece ad prce. Secod, as for the models ad, the expert group gave smlar ratgs to the e attrbutes. Oly from what s the data, t s ot easy to predct whch car wll be the wer the market. We performed a survey wth 400 potetal cosumers for estmatg dvdual cosumers weghts o the e attrbutes ad
7274 S. Km et al. / Expert Systems wth Applcatos 38 (2011) 7270 7276 Table 2 Product formato created by a expert group. Model Attrbute Brad preferece Prce Accelerato Safety Fuel ecoomy Exteror Iteror Coveece equpmet Comfort G G E VG F VG VG E VG G G VG G F VG E VG E F F E E G E E E E sestvty level to socal fluece. The survey results are summarzed Tables 3 ad 4. From Table 3, we could fd that a large porto of the respodets gave more emphass o the prce attrbute 73% of the respodets assged hgh ad very hgh grades to the attrbute, whle, o average, 46% of them gave the same grades to the other attrbutes. The result Table 4 shows that 65% of the respodets were (ormally, strogly, or very strogly) sestve to socal fluece. I the AB model, the weghts ad the sestvty level to socal fluece were radomly gve to each cosumer-aget by usg the relatve frequecy dstrbutos estmated from the survey results. We used Netlogo (Wlesky, 1999), oe of represetatve multaget tools, to mplemet the AB model. We cosdered smallworld etworks of 10,000 cosumer-agets. The tme ut of the aget-based dffuso was a moth. To harmoze the release tmgs of the three car models the AB model wth realty, we started the dffuso of ad at tme zero ad troduced at the 19th moth. 4. Results ad dscusso The mothly sales volumes of the three car models were collected over 38 moths (Jue, 2006 August, 2009), whch were used for the calbrato expermet. Table 5 shows the result of the calbrato expermet. The performace measure was total mea market-share error, whch was calculated by averagg the mea market-share errors of the three car models. For a executo result, the mea market-share error of a car model was obtaed usg Mea market-share error P jmothly dfferece betwee model data ad real dataj ¼ total umber of moths ð10þ I order to obta a statstcally relable measure whch s 95% statstcal cofdece terval, we executed the AB model eght tmes for a gve etwork structure (Law, 2006) ad averaged the obtaed total mea market-share errors. As show Table 5, the maxmum ad mmum of the total mea market-share errors were 2.61% ad 2.92%, respectvely. The mmum error was obtaed whe the rewrg costat ad the degree of coectvty were set to 0.1 ad 4, respectvely, whle the maxmum error was obtaed whe those parameters were set to 5 ad 10, respectvely. The average error of the 16 Table 4 Cosumers sestvty level to socal fluece. Sestvty level Respodets Relatve frequecy Very strog 87 2 Strog 75 0.19 Normal 96 4 Weak 67 0.17 Very weak 75 0.19 Table 5 Result of calbrato expermet. Number of eghbors Total mea market-share error Rewrg costat 5 0.1 5 0.5 4 2.65% 2.61% (m) 2.63% 2.66% 6 2.83% 2.79% 2.91% 2.91% 8 2.77% 2.86% 2.85% 2.89% 10 2.92% (max) 2.84% 2.91% 2.74% Average 2.79% etwork structures was 2.79%. From the result, t was foud that, wth ths emprcal study, the etwork structure lttle affected the dffuso of the three car models. The reaso may be due to the cosumer-agets preferece of over ad. As show Fg. 1(a), has domated the real market because has prce advatage over ad cosumers were very sestve to the prce of car (see Table 3). I addto, s more compettve tha wth regard to three attrbutes of accelerato, safety, ad coveece equpmet, whle has advatage over regardg two attrbutes of teror ad comfort (see Table 2). As the result, the early adopters the AB model had a strog tedecy to prefer to ad, whch provdes feedback to o-adopters ad affected ther purchase decsos (.e., socal fluece). The preferece tedecy seemed to chage lttle regardless of the dffuso speed whch s determed by the two etwork parameters. Therefore, the 16 etwork structures made smlar dffuso results. So dd the errors. Fg. 1(a) shows the mothly market shares of the three car models where the mothly market share of each product s defed as the mothly sales volume of the product over the total mothly sales volume. Fg. 1(b) shows the tme-average market shares of those models. As the two graphs dcate, has kept a domat posto sales over the others. However, as was aouced, Table 3 Cosumers weghts o e attrbutes. Weght Attrbute Brad preferece Prce Accelerato Safety Fuel ecoomy Exteror Iteror Coveece equpmet Comfort Very low 32 (8) 20 (5) 68 (0.17) 75 (0.19) 76 (0.19) 41 (0.10) 79 (0) 45 (0.11) 67 (0.17) Low 49 (0.12) 32 (8) 97 (4) 68 (0.17) 64 (0.16) 75 (0.19) 75 (0.19) 69 (0.17) 49 (0.12) Medum 86 (2) 55 (0.14) 87 (2) 91 (3) 80 (0) 98 (5) 88 (2) 85 (1) 76 (0.19) Hgh 101 (3) 110 (7) 76 (0.19) 112 (8) 94 (4) 108 (7) 72 (0.18) 97 (4) 94 (4) Very hgh 132 (0.33) 183 (6) 72 (0.18) 54 (0.14) 86 (1) 78 (0) 86 (2) 104 (6) 114 (9)
S. Km et al. / Expert Systems wth Applcatos 38 (2011) 7270 7276 7275 Tme (a) Mothly market share (real data) Tme (b) Tme-average market share (real data) Tme (c) Mothly market share (model data) Tme (d) Tme-average market share (model data) Fg. 1. Comparso betwee real data ad model data. Tme (a) Mothly market share (model data) Tme (b) Tme-average market share (model data) Fg. 2. Model data wthout socal fluece. suffered from a strog eroso by for a whle, but has begu to recover ts market share after the eroso (see Fg. 1(a)). Whereas, the market share of has decreased gradually due to the troducto of. Fg. 1(c) ad (d) shows the dffuso paths of the three car models created by the AB model whe the etwork was cofgured wth the rewrg costat of 0.1 ad the degree of coectvty of 4. I Fg. 1(c), the mothly market shares of the AB model could ot reflect the radom varatos made realty as show Fg. 1(a). Ths s because the fuzzy TOPSIS-based product adopto process does ot cosder the ucertates huma s decsos makg. I the real stuato, some of the cosumers would have ot behaved lke ratoal decso makers. Whereas, the AB model assumed all cosumer-agets to be ratoal; the cosumer-agets selected the best oes cosderg both ther persoalzed product ratgs ad the socal fluece that they receved from eghbors. However, the AB model was able to forecast the overall treds of the mothly market shares of the three car models. The total mea market-share error was 7.37%. I addto, we obtaed a meagful result whe we evaluated the performace of the AB model from the aspect of the tme-average measure whch s kow to smooth the radom varatos. The tme-average market shares of the three car models Fg. 1(d) are smlar to the real oes Fg. 1(b). The total mea of the tme-average errors of the three car models was 1.44%. Fally, we cosdered a dffuso scearo wthout socal fluece. For ths, the sestvty levels to socal fluece of all cosumer-agets (a k ) were set to zero ad we executed the AB model. Uder the scearo, every cosumers-aget made purchase decso based o oly ts ow persoalzed product formato. The result s show Fg. 2 where absorbed the market share of more tha the amout the real market. The result demostrated the power of socal fluece. ad have already bee sold the market durg 18 moths before the troducto of. These two car models ( ad ) wo good reputatos from the early adopters ad, as the result, a wave of postve word-of-mouth s made. Although was superor to ad almost every aspect, t was dffcult for to expad ts market share rapdly because of the lock- effect of ad. If the effect was weak, the, just lke Fg. 2, could have bee successful to crease ts market share more tha the real oe.
7276 S. Km et al. / Expert Systems wth Applcatos 38 (2011) 7270 7276 5. Cocludg remarks I ths paper, we proposed the aget-based product dffuso model ad appled t to the market of full-szed cars Korea. Throughout the emprcal study, we vestgated the performace of the AB model wth the sales data obtaed the automoble market. Although the emprcal study showed a ecouragg result, ths s ot suffcet to support that the AB model s approprate for the markets of dfferet types of products. The AB model was developed for forecastg the dffuso of hgh-prced products wth log product lfe cycles such as cars ad hgh-ed TVs. Cosumers other markets probably show dfferet behavors purchasg products. For example, cosumers the markets of fashoable goods are lkely to mmc actvely what ther eghbors do. I such case, threshold-based models, whch cosumers adopt products whe the umber of freds who adopt the products exceeds the thresholds of the cosumers, may be approprate. We are curretly geeralzg the AB model to accommodate the threshold-based product adopto process. Ackowledgemet Ths work was supported by the Korea Research Foudato Grat (KRF-2009-013-D00136). Refereces Alkemade, F., & Castald, C. (2005). Strateges for the dffuso of ovatos o socal etworks. Computatoal Ecoomcs, 25, 3 23. Boe, P. F. (1995). Word-of-mouth effects o short-term ad log-term product judgmets. Joural of Busess Research, 32, 213 223. Box, G. E. P., Jeks, G. M., & Resel, G. C. (1994). Tme seres aalyss, forecastg ad cotrol. Eglewood Clffs, New Jersey: Pretce Hall. Chamodrakas, I., Alexopoulou, N., & Martakos, D. (2009). Customer evaluato for order acceptace usg a ovel class of fuzzy methods based o TOPSIS. Expert Systems wth Applcatos, 36, 7409 7415. Chadrasekara, D., & Tells, G. J. (2007). A crtcal revew of marketg research o dffuso of ew products. Revew of Marketg Research, 39, 80. Cheg, C.-H., Che, Y.-S., & Wu, Y.-L. (2009). Forecastg ovato dffuso of products usg tred-weghted fuzzy tme-seres model. Expert Systems wth Applcatos, 36, 1826 1832. Chou, C.-C. (2003). The caocal represetato of multplcato operato o tragular fuzzy umbers. Computers ad Mathematcs wth Applcatos, 45, 1601 1610. Chu, T. C. (2002). Selectg plat locato va a fuzzy TOPSIS approach. Iteratoal Joural of Advaced Maufacturg Techology, 20, 859 864. Dağdevre, M., Yavuz, S., & Klç, N. (2009). Weapo selecto usg the AHP ad TOPSIS methods uder fuzzy evromet. Expert Systems wth Applcatos, 36, 8143 8151. Delre, S. A., Jager, W., Bjmolt, T. H. A., & Jasse, M. A. (2007). Targetg ad tmg promotoal actvtes: A aget-based model for the takeoff of ew products. Joural of Busess Research, 826, 835. Delre, S. A., Jager, W., & Jasse, M. A. (2007). Dffuso dyamcs small-world etworks wth heterogeeous cosumers. Computatoal Mathematcal Orgazato Theory, 13, 185 202. Hwag, C. L., & Yoo, K. (1981). Multple attrbute decso makg: Methods ad applcatos. Berl: Sprger. Law, A. (2006). Smulato modelg ad aalyss (4th ed.). Hll: McGraw. Mahaja, V., Muller, E., & Bass, F. (1990). New product dffuso models marketg: A revew ad drectos for research. Joural of Marketg, 54, 1 26. Mahaja, V., Muller, E., & Wd, Y. (2000). New-product dffuso models. Norwell, Massachusetts: Kluwer Academc Publshers. Mara, A. K. (1995). Mathematcal models of brad choce behavor. Europea Joural of Operatoal Research, 82, 1 17. Meade, N., & Islam, T. (2006). Modellg ad forecastg the dffuso of ovato A 25-year revew. Iteratoal Joural of Forecastg, 22, 519 545. Rahmadad, H., & Sterma, J. (2008). Heterogeety ad etwork structure the dyamcs of dffuso: Comparg aget-based ad dfferetal equato models. Maagemet Scece, 54, 998 1014. Sog, I., & Chtaguta, P. K. (2003). A mcromodel of ew product adopto wth heterogeeous ad forward-lookg cosumers: Applcato to the dgtal camera category. Quattatve Marketg ad Ecoomcs, 1, 371 407. Su, C.-C., & L, G. T. R. (2009). Usg fuzzy TOPSIS method for evaluatg the compettve advatages of shoppg webstes. Expert Systems wth Applcatos, 36, 11764 11771. Wag, T.-C., & Chag, T.-H. (2007). Applcato of TOPSIS evaluatg tal trag arcraft uder a fuzzy evromet. Expert Systems wth Applcatos, 33, 870 880. Wag, F.-K., & Chag, K.-K. (2009). Modfed dffuso model wth multple products usg a hybrd GA approach. Expert Systems wth Applcatos, 36, 12613 12620. Watts, D. J., & Strogatz, S. H. (1998). Collectve dyamcs of small-world etworks. Nature, 393, 440 442. Wlesky, U. (1999). NetLogo. Ceter for coected learg ad computer-based modelg. Northwester Uversty. Zeoba, B., Weber, C., & Dam, T. (2009). Artfcal markets: A revew ad assessmet of a ew veue for ovato research. Techovato, 29, 338 350. Zmmerma, H.-J. (2001). Fuzzy set theory ad ts applcatos. Bosto: Kluwer Academc Publshers.