FUZZY NEURAL NETWORK MODEL FOR MARK-UP ESTIMATION. Chao Li-Chung and Liu Min. School of Building and Real Estate, National University of Singapore,

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1 FUZZY NEURAL NETWORK ODEL FOR ARK-UP ESTIATION Chao L-Chung and Lu n School of Buldng and Real Estate, Natonal Unversty of Sngapore, Kent Rdge Crescent, Sngapore96 e-mal: brep994@nus.edu.sg) Abstract: ar-up estmaton nvolves many uncertan and complex factors mang t dffcult to model them usng conventonal mathematcal methods. Artfcal neural networs ANNs), whch can adapt themselves to tranng data, have recently been appled to mar-up estmaton. However, there are two maor drawbacs of ths applcaton; frstly, an ANN system s unable to explan why and how a partcular recommendaton s made, and secondly the predcton performance of ANNs may not be satsfyng n some crcumstances or near the boundares of the tranng sets. Ths paper proposes a fuzzy neural networ FNN) model to rectfy these drawbacs of ANN for mar-up estmaton. The FNN model embodes the fuzzy logc n a neural networ as a way of retanng the strengths of both methods. Whle experts udgments n lngustc rules are captured by the networ structure, neural networ parameters are fne-tuned through tranng wth obectve quanttatve data. Because the results are produced wthn the scope of clearly stated rules and nterpretable parameters, the nference process s now transparent. At the same tme, the accuracy also mproves. An example s presented to llustrate the performance and applcablty of the proposed FNN model n comparson wth ANN models. Keywords: mar-up, neural networ, fuzzy logc, fuzzy neural networ, constructon management.. INTRODUCTION Every constructon company needs to prepare a bd prce for a constructon ob. Ths prce ncludes the cost for labor, materals and equpment. Ths prce also ncludes the overhead and proft mar-up) factor. Whle the cost of labor, machnery, and materals s based on a calculaton wth scope clearly defned, mar-up estmaton represents the most varable category wthn the structure of the bd prce. Identfyng the optmum mar-up for a ob s crtcal, because even a slghtly dfferent marup percentage would possbly result n a totally dfferent fate of the bd. Estmatng the mar-up s also a challengng ob because so many uncertan and complex factors are nvolved. It s mpossble to provde detaled enough nformaton to the decson-maer. Therefore, for a long tme, mar-up percentage estmaton s looed as a nd of art wor manly based on the estmators ntuton and experence wth some specfc rules and constrants appled []. umber of models have been developed to analyze and smulate the mar-up estmaton mechansm based on uncertan and partal proect nformaton. any of them tred to fnd the regularty by statstcally analyzng past records and used t to estmate the smlar proects. Unfortunately, many professonals tend to deny ther usablty as there seem to be too many 39_TE.doc-

2 uncertan and unque factors nvolved n the constructon process and t s almost mpossble to smulate the estmaton mechansm of experenced experts wth pure mathematcal models. There have also been research efforts attemptng to form expert systems to capture the essence of the human estmatng ablty. But the creaton of nowledge base s a long and expensve process [, 3]. In addton, t s rarely clear how estmatng expertse can be artculated, whch maes t extremely dffcult to acqure nowledge drectly from estmators to form a nowledge base []. Artfcal neural networs ANNs) offer an alternatve source of assstance to mar-up estmaton wth dfferent features. They could self-adust networ parameters wth tranng data and cope wth complex relatons wth ncomplete nformaton. It seems that the propertes of ANNs conform to the characters assocated wth mar-up estmaton. Research efforts have been made n developng ANN-based mar-up estmatng systems. After oselh & Hegazy [4] dentfed the possblty of applyng ANNs n mar-up optmzaton, many applcaton examples emerged. Hegazy & oselh [5] proposed ANN systems for analogy-based soluton to mar-up estmaton. Heng L [] compared the performance of ANNs to a regresson-based method and dentfed the effect of dfferent confguratons of neural networs on estmatng accuracy. L and Love [6] presented a computer based mar-up decson support system that ntegrated a rule-based expert system and an artfcal neural networ based system. However, the wde use of ANNs for marup estmaton has not been seen untl now. One reason for ths s perhaps that the accuracy of estmaton results from ANNs s not hgh enough. Error rates of the output from some ANN systems are so large that the forecastng result becomes unreasonable or even meanngless. A more subtle and seldom quoted reason s that many estmators do not themselves fully apprecate how ther results are arrved at n ANNs, and may tend to reect any further usage of ths model, as the calculaton and reference system of ANNs s n a blac-box. The above two man drawbacs sgnfcantly affect the users acceptance of the ANNs and ther results. Recently, some research efforts have been devoted to solve these problems. L and Love [6] embedded a rule base nto an ANN model to form a mar-up estmaton support system, whch s called InES. They also tred to apply the KT- method to extract rules from the traned ANN model. However, there are stll some lmtatons of these researches. A fully nformatve explanaton faclty cannot be expected because the system does not have the bult-n assocatve nowledge.e., professonal nowledge, nference rules, etc.) needed to explan tself. oreover, the accuracy of the estmate results of ths system s not mproved. In ths paper, a fuzzy neural networ FNN) model for estmatng mar-up percentage s presented. FNN s a computer system, whch combnes fuzzy logc nference mechansm wth a neural networ system. Wth fuzzy logc nference rules emboded n the structure, FNNs could learn nowledge and adust the parameters of the system accordng to the tranng data. By ntegratng the two systems together, the strengths of both sdes are enhanced, thus the drawbacs of ANNs are overcome successfully. The nference processes of relatng consequences to precondtons are shown clearly n the fuzzy rules of the system, whle the accuracy of the estmate results s greatly mproved as all the outputs are calculated wthn the reasonable range of the nference rules. The prncples and basc calculaton processes of the FNN model are ntroduced frst. Second, an FNN mar-up estmaton example s presented to llustrate the usage of the FNN model and compare the performance of FNN wth ANN models, whch demonstrate both advantages and dsadvantages of usng FNN n modelng mar-up estmaton.. Fuzzy logc. BACKGROUND Fuzzy logc s one of the useful tools for decson analyss. One of the most sgnfcant merts of the approach les n that t opens the way for drect storage of nowledge and nference mechansm wth natural language. Natural language s not only the most convenent and effectve means by whch experts use to store and express ther nowledge but also the best way for users and learners to grasp the nowledge from experts. Snce 98s fuzzy theory has been successfully appled to many areas to smulate the human decson process. Fuzzy sets ntroduce vagueness to classcal crsp sets by elmnatng the sharp boundary that dvdes members from nonmembers n the set. 39_TE.doc-

3 One of the mportant uses of fuzzy sets s to descrbe lngustc varables. Usng fuzzy set, the lngustc terms could be transferred nto mathematcs forms based on the defned membershp functons. The membershp functons commonly used are bell-shaped Gaussan) functons, trangular functons, and trapezodal functons. ore complex parameterzed functons or functons defned by users can also be used as membershp functons. In fuzzy logc systems, an expert s nference process could be transferred nto mathematcal forms, and the lngustc terms could also be changed nto numbers. Thus t s possble to smulate an expert s decson process wth mathematcal models. In fuzzy logc, qualtatve reasonng refers to a mode of reasonng n whch the precondton-consequence relaton of a system s expressed as a collecton of fuzzy IF- THEN rules. Gven certan nputs, such a system reaches a concluson as a result of mathematcal operatons on the full rules. For detals of applyng fuzzy logc to a decson analyss problem n constructon, refer to Chao and Sbnews [7]. However, one of the man drawbacs of fuzzy logc systems s that as all of the rules and membershp functons are decded by users experence, a long and expensve process s needed to create t and the system s nevtably subectve.. Artfcal Neural Networs Artfcal neural networs are a system that s delberately constructed to mae use of some organzatonal prncples resemblng those of the human bran. They represent the promsng new generaton of nformaton processng systems. ANNs are good at tass such as pattern matchng and classfcaton, functon approxmaton, and data clusterng. It could be composed of many hdden layers and neurons. The output of the neuron s normally a nonlnear functon of a smple aggregaton of the weghts and nput values. any dfferent methods could be used to adust the networ parameters amng at mnmze the error E between the estmated output Y and the target result Y d. 3. FUZZY NEURAL NETWORK ntegratng the above two wll possess the advantages of both neural networs such as learnng abltes, optmzaton abltes and connectonst structures, and fuzzy systems such as IF-THEN rules thnng and ease of ncorporatng expert nowledge. In ths way, we can brng the low-level learnng and computatonal power of neural networs nto fuzzy systems and also hgh-level IF-THEN rules thnng and reasonng of fuzzy systems nto neural networs. Thus, more transparency s obtaned by a possble nterpretaton of the weght matrx followng the learnng stage. The structure of the networ s determned based on the fuzzy nference system. The rules are used to calbrate t for better whole-system performance. Thus the structure s determned ratonally at the begnnng, whle tranng allows automatc tunng of the networ parameters that characterze the fuzzy system In ths paper, we use fuzzy sngleton rules n the followng form: R : IF X s A AND X s A AND AND X n s A n, THEN Y s W. Where W s a real number =,. Ths fuzzy neural system has a networ structure as shown n Fg.. The FNN s composed of 4 layers.. Layer reads the real number nputs for varables X =,, n). Layer fuzzfes X accordng to the membershp functons. Every nput value X has m membershp degrees X ), =, m) A of the lngustc characterstc terms. X ) = f a, b ) ) A 3. Layer3 calculates the actve degree of the rule. = X ) X ) X ) A ) n 4. Layer4 defuzzfes the fnal output Y* of such a fuzzy neural system wth centrod defuzzfcaton equaton as follows. Y*= = = W 3) Fuzzy logc and neural networs are complementary technologes. A system 39_TE.doc- 3 3

4 A X A 3 A R R W X X n 3 R 3 R 4 R 5 W W 3 W 4 W 5 W * Y R m Fgure. The Basc Structure of FNN model Parameter learnng of a sngleton rule FNN system s the tunng of the parameters of the nput membershp functons X ) and the A real numbers W. The learnng rule s the same as the Bac Propagaton BP) method. Assume that Y d s the desred output of the FNN system. The parameter learnng algorthm for the above fuzzy logc rules s derved as the followng equatons 4)-7). d E= Y Y ) 4) E X ) d W Y ) X A ) = Y Y ) a X A ) a 5) X ) E = b E W = = X ) d W Y ) Y Y ) X X A ) ) = X ) Y Y X ) = d X ) A b ) 6) 7) By followng equatons 4)-7), the parameters a, b, and W can be tuned durng networ tranng to decrease the estmaton error defned by Eq. 4). The system wth tuned parameters after tranng has ncorporated the effects of observaton data n the nowledge base of nference rules [8]. 4. EXAPLE Ths secton presents a hypothetcal example of applyng the FNN system to mar-up estmaton. Only maret and proect factors are consdered n the model. Other factors could be added nto the model f needed. The three consdered factors are defned n Table. The membershp functons for each factor are shown n Fg.. The Gaussan Functon s used to defne all membershp functons as: x a = exp 8) A b 39_TE.doc- 4 4

5 TABLE. Three Influence Factors of FNN odel for ar-up Estmaton Number Influence Factors Abbr. Value Range Evaluaton Lngustc Terms aret Condton C - Bad, oderate, Good Proect Complexty PC - Low, oderate Hgh 3 Proect Sze PS - ) Small oderate Large. Antecedent Fs for aret Condton Antecedent Fs for Proect Complexty.. Antecedent Fs for proect Sze bad moderat e goo d Low oderate Hgh Small oderate Large ) a) aret Condton b) Proect Complexty c) Proect Sze Fgure. The embershp Functons of Input Varables before Tranng Only two parameters are needed n ths nd of membershp functons. The three pea-ponts are spaced equally and there are overlaps between adacent membershp functons. Sx lngustc terms are used for the output factor mar-up. There are Hgh, edum-hgh, edum, edum-low, Low and Very Low wth the ntal values of %, 8%, 6%, 4%, %, and %, respectvely. As the FNN system uses sngleton FNN rules, the output s a real number. Snce there are three nput factors wth three membershp functons each, f all possble combnatons are consdered, there wll be 3 3 = 7 rules produced. Sx of the 7 rules are quoted below.. If C s Bad, PC s Low, PS s Large, THEN s Very Low.. If C s Good, PC s Hgh, PS s oderate, THEN s edum Hgh. 3. If C s Bad, PC s oderate, PS s oderate, THEN s edum. 4. If C s oderate, PC s Low, PS s Large, THEN s Low. 5. If C s Good, PC s Hgh, PS s oderate, THEN s Hgh. 6. If C s oderate, PC s oderate and PS s oderate, THEN s edum. In practce, the subectve rules could be set by experts or experenced managers, whle the obectve data needed to tran the model could be ganed from the past records. In ths example 76 bddng examples of buldng proects are produced. The 76 examples are separated nto two sets: one for tranng and one for testng. The membershp functons of the nput after tranng are shown n Fg. 3. There are some changes n the pea-ponts and shapes of the nput factors membershp functons. The values of the output factor after tranng have also changed to some degree. The adusted W for the sx levels from Hgh to Very Low level are 9.8%, 7.%, 5.7%, 4.5%,.9%, and.% respectvely. An ANN model s also developed for comparson. The same tranng and testng data are used n the ANN model. Comparsons of the average and maxmum errors for testng data between the FNN and ANN models are shown n Table. From the comparsons we can see the accuracy of FNN s mproved and the estmaton result of FNN s more acceptable because of the use of nference rules n the FNN system. TABLE. Estmaton Errors of FNN and ANN odels Errors FNN ANN Average.73%.93% 39_TE.doc- 5 5

6 axmum.8%.7%. Antecedent Fs for aret Condton after Tranng. Antecedent Fs for Proect Complexty after Tranng Antecedent Fs for Proect Sze after Tranng. Bad oderate Good Low oderate Hgh Small oderate Large Fgure ) a) aret Condton b) Proect Complexty c) Proect Sze Fgure 3. The embershp Functons of Input Varables after Tranng 5. CONCLUSION We have descrbed a fuzzy neural networ based approach to estmatng mar-up percentage. Our example shows that the fuzzy neural networ s able to model the complex relatonshps between the nfluence factors and the mar-up and acheve an acceptable estmaton accuracy. The strength of fuzzy neural networs s the transparent nference mechansm of the system, where the relaton between precondtons and consequences are stated clearly n the rules. oreover, the accuracy of estmaton s better than the results of ANN, as all the outputs are drawn n the scope of fuzzy logc nference rules. Ths research demonstrates the potental for applyng fuzzy neural networs to constructon management problems. To mae ths methodology more generc and applcable to other types of applcatons n constructon, further experment on mplementaton s recommend. REFERENCES: [] L, H., Neural networ models for ntellgent support of mar-up estmaton, Internatonal Journal of Engneerng Constructon and Archtectural anagement. Vol. 3 ), pp 69-8, 996. [3] Ahmad, I. & narah, I., An expert system for selectng bd marup. Proceedngs of Ffth Conference on Computng n Cvl Engneerng, ASCE, pp 9-38, 998. [4] oselh, O. & Hegazy, T., Neural networs as tools n constructon. ASCE Journal of Constructon and Engneerng anagement, Vol 74), pp 66-65, 99. [5] Tare Hegazy & Osama oselh, Analogybased soluton to marup estmaton problem Journal of Computng n Cvl Engneerng, Vol 8 ) pp 7-87, 994. [6] L, H. and Peter E. D. Love, Combnng rule-based expert systems and artfcal neural networs for mar-up estmaton. Constructon anagement and Economcs, Vol. 7, pp 69-76,999. [7] Chao, L. C. & Sbnews,. J., Fuzzy logc for evaluatng alternatve constrcton technology. Journal of Constructon Engneerng and anagement, ASCE. Vol. 4 4), [8] Chn-Teng Ln & C. S. George Lee Neural fuzzy systems. Prentce Hall P T R: USA, 996. [] oselh, O., Hehazy, Y. and Fazo, P. DBID: analogy based DSS for bddng n Constructon, Journal of Constructon Engneerng and management, Vol. 99 3), pp 466-7, _TE.doc- 6 6