Using Fuzzy Cognitive Maps for E-Commerce Strategic Planning

Transcription

1 Usng Fuzzy Cogntve Maps for Commerce Strategc Plannng Athanasos K. Tsadras Department of Appled Informatcs, Unversty of Macedona, Thessalonk, Greece Emal: Abstract. In ths paper we propose the use of Fuzzy Cogntve Map (FCM), a well-establshed Artfcal Intellgence technque that ncorporates deas from Artfcal Neural Networks and Fuzzy Logc, for Commerce strategc plannng. FCMs create models as collectons of concepts and the varous causal relatons that exst between these concepts. The strategc plannng capabltes of the FCM structure are examned and presented usng a model concernng the e- commerce secton of an e-busness company. The model s examned dynamcally through smulatons, n order to smulate scenaros proposed by company s managers. Strategc Plannng s made by vewng dynamcally the consequences of the scenaro s actons. Conclusons are drawn for the use of FCM for e-commerce strategc plannng. 1 Introducton to Fuzzy Cogntve Maps Fuzzy Cogntve Maps have been ntroduced by Kosko [1, 2] based on Axelord's work on Cogntve Maps [3] and are consdered a combnaton of fuzzy logc and artfcal neural networks. FCMs create models as collectons of concepts and the varous causal relatons that exst between these concepts [4]. The concepts are represented by nodes and the causal relatonshps by drected arcs between the nodes. Each arc s accompaned by a weght that defnes the type of causal relaton between the two nodes. The sgn of the weght determnes the postve or negatve causal relaton between the two concepts-nodes. An example of FCM concernng publc health s gven n fgure 1. Two nodes/concepts are connected ether by a drect arc or by a path. An arc between two concepts ndcates a drect causal relaton whle a path between two nodes of the dgraph ndcates an ndrect causal relaton. The sgn of the ndrect causal relatonshp s postve f the path has an even number of negatve drect causal relatonshps, whle t s negatve f the path has an odd number of negatve drect causal relatonshps. The total effect that a concept has to another s gven based on all ndrect causal relatonshps that exst from the one concept to the other and also by the drect causal relaton that mght exst. The followng rules are used to evaluate the total effect: The total effect s postve f all the ndrect causal relatonshps that exst from the one concept to the other are postve and also the drect causal relatonshp that mght exst s also postve.

2 143 The total effect s negatve f all the ndrect causal relatonshps that exst from the one concept to the other are negatve and also the drect causal relatonshp that mght exst s also negatve. The total effect s unknown f all the ndrect causal relatonshps that exst from the one concept to the other are postve and the drect causal relatonshp are not of the same sgn. C 1 Number of people n a cty +0.1 C 2 Mgraton nto cty +0.6 Modernzaton +0.7 C Carbage per area C 3 C 6 Number of dseases per 1000 resdents Bactera per area C 5 Santaton facltes -0.9 C 7 Fgure 1: An FCM concernng publc health [5] The man areas where FCMs are used are: a) Decson Makng, b) Forecastng, c) Explanaton (of actons already made) and d) Strategc Plannng. A great number of FCMs have been developed concernng the busness ndustry and fnancal actvtes. Table I gves some such references found n bblography. Cogntve Map topc Reference Japan s and USA s ndustry [6] The strategy of NeXT computer Company [7] The strategy of Sony Company [7] USA s economy [9] The ntroducton of a new drnk n the market [9] Measurng the effcency of a company s departments [10] The development phases of a company [11] The sales of a company [12] The management of a company [13, 14] The bureaucracy n companes [11] Table 1

3 144 2 Certanty Neuron Fuzzy Cogntve Maps Although n FCMs the degree of the causal relatonshps could be represented by a number n the nterval [-1,1], each concept could be ether actvated or not actvated, n a strct bnary manner. In 1997, Certanty Neuron Fuzzy Cogntve Maps (CNFCMs) were ntroduced [4] to overcome ths lmtaton. CNFCMs provde addtonal fuzzfcaton to FCMs by allowng each concept s actvaton to be actvated just to a degree. In ths way the actvaton level of each concept can be any value of the nterval [-1,1] and not only one of the two levels 1 and 1. The aggregaton of the nfluences that each concept receves from other concepts s handled by functon f () that was used n MYCIN Expert System [15, 16] for certanty factors handlng. M The dynamcal behavour and the characterstcs of ths functon are studed n [17]. Certanty Neurons are defned as artfcal neurons that use ths functon as ther threshold functon [18]. Usng such neurons, the updatng functon of CNFCMs as a dynamcal evolvng system s the followng: t+1 t t t A = f M ( A, S )- d A (1) where, t+1 A s the actvaton level of concept C at tme step t+1, t t S w A s the sum of the weght nfluences that concept C receves at tme = j j j step t from all other concepts, d s a decay factor and t t t t t t t t t A + S (1 A ) = A + S S A f A 0, S 0 t t t t t t t t t t t t t (2) f(a,s ) = A + S (1+ A ) = A + S + S A f A < 0, S < 0 A, S 1 t t t t t t (A + S ) ( 1 mn( A, S )) f A S < 0 s the functon that was used for the aggregaton of certanty factors to the MYCIN expert system. 3 Commerce Fuzzy Cogntve Map To examne the strategc plannng capabltes of the FCM structure, we wll use the FCM model of fgure 2. The FCM model of fgure 2 s a modfed verson of the model presented n [19] and concerns an magnary busness company. Accordng to the FCM model of the e-busness company of Fgure 2, the concepts that were dentfed as playng mportant role n the strategc plannng process of the e-busness company are the followng: C1: Busness Profts C2: Busness Sales C3: Prces Cutoffs C4: Customers Satsfacton C5: Staff Recrutments C6: Impact from Internatonal Busness Competton C7: Better Commerce Servces

4 145 C1 Busness Profts C2 Busness Sales C7 Better Commerce Servces C3 Prces Cutoffs C6 Impact from Internatonal Busness Competton C4 Customers' Satsfacton C5 Staff Recrutments Fgure 2. FCM model of an e-busness company The weghts of the causal relatonshps that accordng to the company s managers and experts exst n the model and construct the weght matrx of the model, are presented n Appendx A. Lettng ntally all concepts of the FCM system to free nteract wth each other (scenaro #1), the dynamcal behavour of fgure 3 s exhbted. The system gets nto a perodc - lmt cycle - dynamcal behavour, wth actvaton of all concepts to ncrease and decrease n turn. In terms of economy, ths means that the concepts are n struggle wth each other, all concepts tryng to get equlbrum but none of them to reach t. Perodcally ncrease and decrease of these concepts are predcted. Fgure 3. Smulaton of e-commerce company model for scenaro #1 - (lmt cycle behavour)

5 146 In the above scenaro, accordng to the model, Staff Recrutment has a medum negatve mpact to concept Prces Cutoffs (weght w 53 =-0.4), meanng that staff recrutment wll negatvely affect prces cutoffs. Ths s because the company wll not easly be able to have prces cutoffs f t acqures new staff. Ths could be partally caused by the fact that e-commerce techncal staff requres hgh salares, no gvng the opportunty to the company to have hgh prce cutoffs. Fgure 4. Smulaton of e-commerce company model for scenaro #2, ( w =-0.2, equlbrum) 53 Introducng a dfferent scenaro to the FCM system, weght w s be set from to -0.2 lowerng the negatve affect of Staff Recrutment to concept Prces Cutoffs (scenaro #2). Ths can be done perhaps by of a changng company s structure (use cheaper techncal staff from all over the world, usng teleworkng) or ncrease of e-busness techncal staff avalablty. Usng smulatons to get the mpact from ths change (that can be an act of strategc plannng), the FCM model exhbted the dynamcal behavour of fgure 4. The system after a short transton phase, reaches an equlbrum pont. The actvaton lever of each concept of the model at equlbrum s that of Table 2. Busness Profts Busness Sales Prces Cutoffs Customers Satsfacton Staff Recrutments Impact from Internatonal Busness Competton Better Commerce Servces 0,307 0,745 0,4 0,865 0,810 0,534 0,755 Table 2 The equlbrum can be justfed as follows: The strong mpact (0.534) from nternatonal e-busness competton, led the e-commerce company to hghly ncrease ts staff ( Staff Recrutments =0.810) n order to provde better e-commerce servces (0.755) to ts customers. In parallel, the company managed to have prces cutoffs (0.4) to e-commerce products, whch together wth better servces caused a very bg ncrease to Customer Satsfacton (0.865). Ths led to an ncrease to e-busness

6 147 sales (0.745) that caused an ncrease to e-busness profts (0.307) although addtonal expenses exst due of the new staff. Accordng to the model, weght w = 0, meanng that there s no drect nfluence from concept Better Commerce Servces to concept Impact from Internatonal Busness Competton. Next scenaro (scenaro #3) apples when companes experts clams that such a small negatve nfluence exsts, e.g. w = Introducng ths change to the FCM model, the system reaches once agan equlbrum, but now to a dfferent pont. The actvaton levels of all concepts at ths new equlbrum pont appear to Table 3. The transton phase to ths equlbrum s shown n fgure 5. Busness Profts Busness Sales Prces Cutoffs Customers Satsfacton Staff Recrutments Impact from Internatonal Busness Competton Better Commerce Servces 0,459 0,711 0,245 0,845 0,778 0,438 0,744 Table 3 Fgure 5. Smulaton of e-commerce company model for scenaro #3, ( w = 0. 3, equlbrum) Comparng ths equlbrum pont wth that of scenaro #2 we see that the mpact from Internatonal e-busness competton s now lower, leadng to less staff recrutments. Customers Satsfacton reman hgh (0,845) but prces cutoffs are now lower (0.245 compared to 0.4 of scenaro #2). Ths led to have almost the same e- busness sales, but hgher e-busness profts. To check once agan the strategc plannng and predctng capabltes of FCM method, let s change the way that the mpact of nternatonal e-busness competton affect the e-company s prce cutoffs. To scenaros #1,#2 and #3 weght w was set to 0.4. Ths was part of company s polcy accordng whch the reacton to strong foregn competton s to cut prces and get new staff to provde better e-commerce servces. Lets magne a new case (scenaro #4) where prces can not get hgh cutoffs.

7 148 In ths case weght w s changed from 0.4 to 0.2. Smulatng ths scenaro and lettng all model s concepts free to nteract, we get the dynamcal behavour of fgure 6. The system after a short transton phase gets nto a lmt cycle behavour wth all concepts perodcally to ncrease and decrease. No clear conclusons can be drawn for the outcome of the small prce cutoffs of scenaro #4, n contrary to the clear conclusons that were found for scenaro #3 where prce cutoffs were hgher. Fgure 6. Smulaton of e-commerce company model for scenaro #4, ( w = 0. 2, lmt cycle) To study more the affect of ths strategc plannng acton, another smlar scenaro can be ntroduced (scenaro #5). At ths scenaro, the way that the mpact of nternatonal e-busness competton affects the e-company s prce cutoffs are much (hgher w from 0.2 s set to 0.8). The dynamcal behavour of ths scenaro appears to fgure 7. The system after a long transton phase reaches an equlbrum pont. The actvaton levels of model s concepts at equlbrum are presented at Table 4. Busness Profts Busness Sales Prces Cutoffs Customers Satsfacton Staff Recrutments Impact from Internatonal Busness Competton Better Commerce Servces 0,470 0,790 0,500 0,8 0,708 0,303 0,702 Table 4 The frst that we should menton s that now a equlbrum s found n contrast wth the lmt cycle behavour of scenaro #4 where w =0.2. Comparng the new equlbrum pont wth that of scenaro #3, we see that the change of weght w led to hgher prces cutoffs (0.500 compared to of scenaro #3), lower mpact from nternatonal e-busness competton (0.303 compared to of scenaro #3) and almost the same e-busness profts (0.470 compared to of scenaro #3). Ths can be mportant concluson from e-busness company s managers, n the way that they plot the e-commerce strategy.

8 149 Fgure 7. Smulaton of e-commerce company model for scenaro #5, ( w = 0. 8, equlbrum) Fgure 8. Smulaton of e-commerce company model for scenaro #6, ( w = 0. 8, w = 0, equlbrum) The last scenaro (scenaro #6) ntroduced to the system s a combnaton of scenaros #2 and #5 havng w = 0. 8 (as n scenaro #5) but settng weght w to 0 meanng that there s no drect nfluence from concept Better e-commerce Servces to concept Impact from Internatonal e-busness competton (as n scenaro #2). The dynamcal behavour of scenaro #6 appears to fgure 8. The system after a transton phase reaches a equlbrum pont. The actvaton levels of model s concepts at equlbrum are presented at Table 5.

9 150 Busness Profts Busness Sales Prces Cutoffs Customers Satsfacton Staff Recrutments Impact from Internatonal Busness Competton Better Commerce Servces 0,305 0,796 0,6 0,875 0,6 0,410 0,733 Table 5 Comparng the new equlbrum pont wth that of scenaro #5, we see that the change of weght w led to even hgher prces cutoffs (0.6 compared to of scenaro #5), hgher mpact from nternatonal e-busness competton (0.410 compared to of scenaro #5) and almost the less e-busness profts (0.305 compared to of scenaro #5). It can be sad that certan strategc movements can not brng the ntal predcted outcome and ths makes FCM technque very useful. 4 Summary - Conclusons In ths paper the strategc plannng capabltes of FCM structure were examned, usng an FCM model concernng an e-busness company. Varous scenaros that could be presented by company s managers were ntroduced to the model and through computer smulatons, predctons were made. The representng and strategc plannng capabltes of the FCM structure were presented. The FCM technque was dentfed as a useful Strategc Plannng tool, snce t s capable to provde support to company s managers, by makng predctons on varous scenaros that are mposed to the FCM model. The use of a FCM model s hghly apprecated when managers can test ther strategc movements, by applyng them to the FCM and see the consequences to the concepts of the model. The uncertanty handlng capabltes of the FCM structure make also the technque sutable for busness decsons were uncertanty and fuzzness exst. References 1. B. Kosko, Fuzzy Cogntve Maps, Internatonal Journal of Man-Machne Studes, 24:65-75, (1986) 2. B. Kosko, Neural Networks and Fuzzy Systems: Prentce Hall, (1992) 3. R. Axelrod, Structure of Decson. The Cogntve Maps of Poltcal Eltes. Prnceton Unversty Press, (19) 4. A.K. Tsadras, K.G. Margarts, Cogntve Mappng and Certanty Neuron Fuzzy Cogntve Maps, Informaton Scences, 101: (1997) 5. M. Maruyama, The Second Cybernetcs: Devaton-amplfyng Mutual Causal Process, Amercan Scentst, 51: , (19) 6. R. Taber, Knowledge Processng wth Fuzzy Cogntve Maps, Expert Systems wth Applcatons, 2:83-87, (1991) 7. M. G. Bougon, Congregate Cogntve Maps: a Unfed Dynamc Theory of Organzaton and Strategy, Journal of Management Studes, 29: , (1992) 8. M. Caudll, Usng Neural Nets: Fuzzy Cogntve Maps, AI Expert, (1990) K. Langfeld-Smth, A. Wrth, Measurng Dfferences Between Cogntve Maps, Journal of Operatonal Research Socety, 43: , (1992) 10. A. R. Montazem, D. W. Conrath, The Use of Cogntve Mappng for Informaton Requrements Analyss, MIS Quarterly, 10:44-55, (1986)

10 M. Masuch, Vcous Crcles n Organzatons, Admnstratve Scence Quarterly, 30:14-33, (1985) 12 W.E. Pracht, GISMO: A Vsual Problem-Structurng and Knowledge-Organzaton Tool, IEEE Transactons on Systems, Man, and Cybernetcs, 16: , (1986) 13 P. Cossette, M. Audet, Mappng of an Idosyncratc Schema, Journal of Management Studes, 29: , (1992) 14 B. Bllman, J.F. Courtney, Automated Dscovery n Manageral Problem Formulaton: Formaton of Causal Hypotheses for Cogntve Mappng, Decson Scences`, 24:23-41, (1993) 15 E.H. Shortlffe, Computer-based Medcal Consultatons: MYCIN. Elsever, New York (19) 16 B.G. Buchanan, E. H. Shortlffe, Rule-Based Expert Systems. The MYCIN Experments of the Stanford Heurstc Programmng Project. Addson-Wesley, Readng, MA (1984) 17. A.K. Tsadras, K.G. Margarts, The MYCIN Certanty Factor Handlng Functon as Unnorm Operator and ts Use as Threshold Functon n Artfcal Neurons, Fussy Set and Systems, 93:2-274, (1998) 18. A.K. Tsadras, K. G. Margarts, Usng Certanty Neurons n Fuzzy Cogntve Maps, Neural Network World, 6: , (1996) 19. R.C. Eberhart, R.W. Dobbns, Neural Network PC Tools: Academc Press, (1990) Appendx A: Weght Matrx of e-busness Company FCM Model Concepts / Weghts C1 C2 C3 C4 C5 C6 C7 C1: Hgh Profts 0 0,9-0,4 0-0,5 0 0 C2: Customer Satsfacton 0 0 0,7 0,8 0-0,7 0 C3: Hgh Sales ,2 0,8 0 C4: Internal Affars 0 0,2 0, ,9 C5: Promoton ,8 0 C6: Competton 0,9 0-0, C7: Lower Prces ,3 0,7 0 0