& Research Article

Fuzzy Cognitive Maps as a BackEnd to Knowledge-based Systemsin Geographically DispersedFinancial Organizations

George Xirogiannis1*, Michael Glykas1 and Christos Staikouras2

1Department of Financial and Management Engineering, University of the Aegean, Greece2Department of Accounting and Finance, Athens University of Economics and Business, Greece

This paper addresses the problem of designing a knowledge management methodology tool toact as a decision support mechanism for geographically dispersed financial enterprises. Theunderlying research addresses the problem of information capture and representation in finan-cial institutions in order to provide an implementation of the virtuous cycle of knowledge flow.The proposed methodology tool utilizes the fuzzy causal characteristics of Fuzzy CognitiveMaps (FCMs) to generate a hierarchical and dynamic network of interconnected financial per-formance concepts. By using FCMs, the proposed mechanism simulates the operational effi-ciency of distributed organizational models with imprecise relationships and quantifies theimpact of the geographically dispersed activities to the overall business model. Generic adap-tive maps that supplement the decision-making process present a roadmap for integrating hier-archical FCMs into the business model of typical financial sector enterprises. Copyright# 2004

John Wiley & Sons, Ltd.

INTRODUCTION

Knowledge has been defined by Western philoso-phy (Russell, 1989) as ‘justified true belief’. How-ever, as long as there is a chance that this belief ismistaken and as long as there is an evolution oftechnologies, theories, practice and behaviours,this definition invites individuals and groups todevelop constantly ‘what they think that theyknow’ (Nonaka and Takeushi, 1994). This continu-ous process of creation of new insights and beliefsis what fuels the entire paradigm of knowledgemanagement and even constitutes the fundamentalrationale for the existence of an enterprise. Some

argue that instead of merely solving problems,organizations create and define problems, developand apply new knowledge to solve problems andthen develop further new knowledge through theaction of problem solving. In this view an enter-prise creates continuously new knowledge throughaction and interaction, not acting simply as aninformation-processing machine (Nonaka andTakeushi, 1994; Spencer and Grant, 1996).

Currently, there is a pressing need for sharingknowledge among the financial managers (e.g.CFO, Head of Accounting, Head of Budgeting,Head of Business Planning). The effect of knowl-edge attrition for customers and investors is knowl-edge intensive. Financial enterprises lose (onaverage) half of their knowledge base every 5–10years due to the turnover of their employees. Thefact is that financial managers are usually morecommitted to their specialized profession, thus

Knowledge and Process Management Volume 11 Number 2 pp 137–154 (2004)

Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/kpm.199

Copyright # 2004 John Wiley & Sons, Ltd.

*Correspondence to: George Xirogiannis, Department of Finan-cial and Management Engineering, University of the Aegean,31 Fostini Street, Chios, 82 100, Greece.E-mail: g.xirogiannis@fme.aegean.gr

losing sight of the enterprise as a whole. Withouteffective sharing and maintenance of knowledge,financial institutions risk losing their crucial knowl-edge through labour mobility. Moreover, knowl-edge has the idiosyncrasy that its value can onlybe realized when it is put in use (i.e. no shelf value).The more knowledge put in use, the more its valueis appreciated (e.g. efficient use through theincrease in confidence of application and learning),rather than depreciated, as other physical assets ofmachinery or natural resources.

This paper addresses the problem of designing anovel knowledge management (KM) methodologytool to act as a decision support mechanism forgeographically dispersed financial organizations(e.g. multi-national enterprises, multi-branchbanks). The proposed methodology tool utilizesthe fuzzy causal characteristics of fuzzy cognitivemaps (FCMs) to generate a hierarchical anddynamic network of interconnected financial per-formance concepts. By using FCMs, the proposedmechanism simulates the operational efficiency ofdistributed organizational models with impreciserelationships and quantifies the impact of the geo-graphically dispersed activities to the overall busi-ness model.

From the KM perspective, it is the belief of thispaper that optimal decision-making can beachieved through the creation of a virtuous circleof knowledge flow: creating and adding knowl-edge, successful searching for the required piecesof knowledge, feedback for impetus to assert qual-ity knowledge again.

Primarily, the proposed model targets the princi-pal beneficiaries and stakeholders of KM projects(financial administration, change management lea-ders, etc.), assisting them to reason effectivelyabout the status of financial performance metrics,given the (actual or hypothetical) implementationof a set of business model changes. Nevertheless,the explanatory nature of the mechanism can proveto be useful in a wider educational setting.

This paper consists of seven sections. The nextsection presents a short literature overview, whilethe third section addresses the contemporary know-ledge capture and representation problem of finan-cial managers and justifies the need for a novel

adaptive knowledge management methodologytool. The fourth section presents an overview ofthe proposed system, the fifth section discussesthe new approach to knowledge modelling basedon FCMs and the sixth section discusses the majoradvantages of the proposed tool. The final sectionconcludes this paper and briefly discusses futureresearch activities.

LITERATURE OVERVIEW

FCMs as a modelling technique

FCMs are a modelling methodology for complexdecision systems, which originated from the combi-nation of fuzzy logic (Zadeh, 1965) and neural net-works. An FCM describes the behaviour of asystem in terms of concepts; each concept repre-sents an entity, a state, a variable or a characteristicof the system (Dickerson and Kosko, 1997).

FCM nodes are named by such concepts formingthe set of concepts C¼ {C1, C2, . . . ,Cn}. Arcs (Cj, Ci)are oriented and represent causal links betweenconcepts; that is how concept Cj causes concept Ci.Arcs are elements of the set A¼ {(Cj,Ci)ji}�C�C.Weights of arcs are associated with a weight valuematrix Wn�n, where each element of the matrixwji2 [�1, . . . , 1]�R such that if (Cj, Ci) =2A thenwji¼ 0 else excitation (respectively inhibition)causal link from concept Cj to concept Ci giveswji> 0 (respectively wji< 0). The proposed metho-dology framework assumes that [�1, . . . , 1] is afuzzy bipolar interval, bipolarity being used as ameans of representing a positive or negativerelationship between two concepts.

In practice, the graphical illustration of an FCMis a signed graph with feedback, consisting ofnodes and weighted interconnections (e.g. ���!Weight).Signed and weighted arcs (elements of the set A)connect various nodes (elements of the set C) repre-senting the causal relationships that exist amongconcepts. This graphical representation (e.g.Figure 1) illustrates different aspects in the beha-viour of the system, showing its dynamics (Kosko,1986) and allowing systematic causal propagation(e.g. forward and backward chaining).

Figure 1 Basic constructs of FCMs

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Positive or negative sign and fuzzy weightsmodel the expert knowledge of the causal relation-ships (Kosko, 1991). Concept Cj causally increasesCi if the weight value wji> 0 and causally decreasesCi if wji< 0. When wji¼ 0, concept Cj has no causaleffect on Ci. The sign of wji indicates whetherthe relationship between concepts is positive(Cj�!wji Ci) or negative (Cj�!wji � Ci), while the valueof wji indicates how strongly concept Cj influencesconcept Ci. The forward or backward direction ofcausality indicates whether concept Cj causes con-cept Ci or vice versa (e.g. Figure 2).

Simple variations of FCMs mostly used in busi-ness decision-making applications may take triva-lent weight values [�1, 0, 1]. This paper allowsFMCs to utilize fuzzy word weights like strong,medium or weak, each of these words being a fuz-zy set to provide complicated FCMs. In contrast,Kwahk and Kim (1999) adopted only a simplerelative weight representation in the interval[�1, . . . , 1]. To this extent, Kwahk and Kim (1999)offered reduced functionality since it does notallow fuzzy weight definitions.

Generally speaking, FCM concept activations taketheir value in an activation value set V¼ {0, 1} or{�1, 0, 1} if in crisp mode or [��, 1] with �¼ 0 or 1 ifin fuzzy mode. The proposed methodologyframework assumes fuzzy mode with �¼ 1. At stept2N, each concept Cj is associated with an inner acti-vation value aj

t2V, and an external activation valueeajt 2R. FCM is a dynamic system. Initialization is

aj0¼ 0. The dynamic obeys a general recurrent rela-tion atþ1¼ f (g(ea

t, WT at)), 8t � 0, involving weightmatrix product with inner activation, fuzzy logicaloperators (g) between this result and external forcedactivation and finally normalization ( f ). However,this paper assumes no external activation (hence nofuzzy logical operators), resulting in the followingtypical formula for calculating the values of conceptsof FCM:

atþ1i ¼ f

Xnj¼1; j 6¼i

wjiatj

0@

1A ð1Þ

where aitþ1 is the value of concept Ci at step tþ 1,

aja the value of the interconnected concept Cj atstep t, wji is the weighted arc from Cj to Ci andf :R!V is a threshold function, which normalizesactivations. Two normalization functions are us-ually used. The unipolar sigmoid function where�> 0 determines the steepness of the continuousfunction fðxÞ ¼ 1

1þe��x. When concepts can be nega-tive (� < 0), function fðxÞ ¼ tanhðxÞ can also beused.

To understand better the analogy between thesign of the weight and the positive/negative rela-tionship, it may be necessary to revisit the charac-teristics of the fuzzy relation (Kaufmann, 1975; Leeet al., 2002). A fuzzy relation from a set A to a set Bor (A, B) represents its degree of membership inthe unit interval [0, 1]. Generally speaking, sets Aand B can be fuzzy sets. The corresponding fuzzymembership function is mf:A�B! [0, 1]. There-fore, mf(x, y) is interpreted as the ‘strength’ of thefuzzy membership of the fuzzy relation (x, y)where x2A and y2B. Then this fuzzy relation con-cept can be denoted equivalently as x�!�f y andapplied to interpret the causality value of FCM,since wji (the causality value of the arc from nodesCj to Ci) in a certain FCM is interpreted as thedegree of fuzzy relationship between twonodes Cj and Ci. Hence, wji in FCMs is the fuzzymembership value mf(Cj,Ci) and can be denotedas Cj�!wji Ci.

However, we understand that the fuzzy relation(weight) between concept nodes is more generalthan the original fuzzy relation concept. This isbecause it can include negative (�) fuzzy relations.Fuzzy relations mean fuzzy causality; causality canhave a negative sign. In FCMs, the negative fuzzyrelation (or causality) between two concept nodesis the degree of a relation with a ‘negation’ of aconcept node. For example, if the negation of aconcept node Ci is noted as �Ci, then mf(Cj,Ci)¼�0.6 means that mf(Cj, �Ci)¼ 0.6. Conversely,mf(Cj,Ci)¼ 0.6 means that mf(Cj, �Ci)¼�0.6.

FCMs help to predict the evolution of the system(simulation of behaviour) and can be equippedwith capacities of Hebbian learning (Kosko,1986a, 1998). FCMs are used to represent and tomodel the knowledge on the examining system.Existing knowledge of the behaviour of the systemis stored in the structure of nodes and interconnec-tions of the map. The fundamental differencebetween FCMs and neural networks is in the factthat all the nodes of the FCM graph have a strongsemantic defined by the modelling of the concept,whereas the nor input/nor output nodes of thegraph of the neural network have a weak semantic,only defined by mathematical relations.

Figure 2 Simple FCM

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Applications of fuzzy cognitive maps

Over the last 10 years, a variety of FCMs have beenused for capturing—representing knowledge andintelligent information in engineering applications,for instance, geographical information systems Liuand Satur (1999) and fault detection (Ndouse andOkuda, 1996; Pelaez and Bowles, 1995). FCMshave been used in modelling the supervision of dis-tributed systems (Stylios et al., 1997). FCMs havealso been used in operations research (Craigeret al., 1996), web data mining (Hong andHan, 2002; Lee et al., 2000), as a back end tocomputer-based models and medical diagnosis(e.g. Georgopoulos et al., 2002).

Several research reports applying basic conceptsof FCMs have also been presented in the field ofbusiness and other social sciences. Research inAxelrod (1976) and Perusich (1996) have usedFCM for representing tacit knowledge in politicaland social analysis. FCMs have been successfullyapplied to various fields such as decision makingin complex war games (Klein and Cooper, 1982),strategic planning (Diffenbach, 1982; Ramaprasadand Poon, 1985), information retrieval (Johnsonand Briggs, 1994) and distributed decision processmodelling (Zhang et al., 1994). Research like that ofLee and Kim (1997) has successfully applied FCMsto infer rich implications from stock market analy-sis results. Research like that of Lee and Kim (1998)also suggested a new concept of fuzzy causal rela-tions found in FCMs and applied it to analyse andpredict stock market trends. The inference power ofFCMs has also been adopted to analyse the compe-tition between two companies, which are assumedto use differential games mechanisms to set uptheir own strategic planning (Lee and Kwon,1998). FCMs have been integrated with case-basedreasoning technique to build organizational mem-ory in the field of knowledge management (Nohet al., 2000). Recent research adopted FCMs to sup-port the core activities of highly technical functionslike urban design (Xirogiannis, 2004). Summariz-ing, FCMs can contribute to the construction ofmore intelligent systems, since the more intelligenta system becomes, the more symbolic and fuzzyrepresentations it utilizes.

In addition, a few modifications have been pro-posed. For example, the research in Silva (1995)proposed new forms of combined matrices forFCMs, the research in Hagiwara (1992) extendedFCMs by permitting non-linear and time delay onthe arcs, and the research in Schneider et al.(1995) presented a method for automatically con-structing FCMs. More recently, Liu and Satur(1999) have carried extensive research on FCMs,

investigating inference properties of FCMs, pro-posed contextual FCMs based on the object-oriented paradigm of decision support and appliedcontextual FCMs to geographical information sys-tems (Liu, 2000).

KNOWLEDGE MANAGEMENT INFINANCIAL ENTERPRISES

The decision-making problem

Financial management is one of the major areas ofbusiness of financial sector institutions. The risksundertaken by fund managers in their investmentdecisions affect directly the institutions’ businesscontinuity, profitability and reputation. Fund man-agers’ work allows direct performance measure-ment, while the rewards based on measuredperformance affect their career prospects and jobsecurity. Junior financial managers are thereforemore risk averse in their portfolio managementdecisions, which they ‘herd’ to follow the markettrends in avoiding investment risks above the mar-ket objective level, whereas senior managers aregiven more discretion in their investment deci-sions. The high monetary rewards, considerationsof job security and market-relative measurementof performance induce financial managers’ self-interests and ownership of critical knowledge,which may create effective investment decisions.Therefore creating an open environment to shareanalytical skills of market signals, intimate knowl-edge of clients, or capability to sense political atmo-sphere and market sentiment among financialmanagers can minimize any miscalculated risks.

The need for knowledge sharing

Knowledge can be reused potentially an infinitenumber of times without wearing off or needingrepair. With each subsequent application of infor-mation processing, the experience of use and back-ground understanding of environmental settingsbuilds up. This potential to apply knowledge aninfinite number of times allows for economies ofscale, which may reduce radically the transactionand/or operational costs. Hence the potential valueof knowledge can only be fully realized if it is lever-aged effectively through sharing and reuse.

Intimate, contextual and firm-specific knowledgeis an intangible asset that is costly to develop,hard to replace and time consuming to replicate.Possession of intimate knowledge with real valueto customers allows enterprises to differentiatethemselves from competitors. Coordinated

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processing of disparate pieces of information todevelop skills and capabilities in a way that helpsan enterprise to achieve its goals is a form of intel-lectual capital and a valuable source of competitiveadvantage. Individuals with different culture andexperiences lack the contextual links associatedwith the enterprise’s specific knowledge. Commu-nication of knowledge separated from its contexthinders thorough understanding and detachesintuitive interpretation through symbolic environ-mental associations. Knowledge so communicatedis inevitably abstract. It consists of generalized ana-lyses of events, and the recipient may find it diffi-cult to comprehend its relevance to a specificsituation. Indeed, skilful masters differentiatefrom novices by the intimate understanding ofthe tasks and the environment linked togetherwith specific contextual interacting factors that dif-ferentiate skillful masters from novice beginners.

Sharing, and only communication, of knowledgecarries a common context where individuals caninteract and engage in a mutual dialogue with com-mon understanding. Effective sharing creates asynergy with value where the sum is more thanits parts. Therefore, effective dissemination of spe-cialized contextual knowledge among members ofthe firm minimizes miscalculation or mispercep-tion of risks.

KM and transaction costs reduction

Sharing of knowledge involves information flowsbetween the distributed organizational entities ofan enterprise. The cost—benefit analysis of knowl-edge flow must consider the enterprise’s specificenvironmental factors in terms of co-location ofdecision rights and knowledge. Colocation refersto the delegation of decision-making authority tothe party holding necessary knowledge (e.g. discre-tionary investment decisions made by financialmanagers within institutional guidelines).

The cost of no knowledge sharing can be propor-tional to the decision-making costs (in practice, thesum of agency and knowledge transfer costs).Agency cost arises from self-interested individualsin conflict with management when decisions aredelegated to them. The time and effort spent bymanagement and possibly the need for policyadjustments, remuneration packages and coordina-tion of individual members are all agency costs.The knowledge transfer costs arise from training,practice and experience needed to equip indivi-duals with the necessary knowledge.

The distance of decision rights from the CEOoffice affects the total decision-making costs andcauses trade-offs between suboptimal decisions

and possession of necessary knowledge. The lackof embedded know-how at central managementcauses suboptimal decisions to be made when thedecision-maker is away from sources of knowl-edge; therefore the knowledge transfer costs owingto poor information sharing is very high. On theother hand, when some knowledge carrier awayfrom central management makes a decision, theneed for control and coordination to maintain con-sistency and integrity incurs high agency costs.There is a cost-optimal point where the sum ofthe agency and transfer costs is at its minimum.Effective knowledge sharing lowers the costs byshifting the optimal point of total organizationalcosts downward, i.e. shifting the knowledge trans-fer cost curve downward. This component identi-fies the agency and knowledge transfer costsinvolved in sharing knowledge in the currentenvironment setting to ensure organizational fit.

FUNDAMENTALS OF THEMETHODOLOGY TOOL

The knowledge flow cycle

Many financial analysts and investigation reportsabout multi-million dollar losses at Sumitomo andBarings attribute the losses to the neglect of payingattention to operational risk. Operational riskresults in losses due to deficiencies in information,personnel unavailability, human error, and inade-quate procedures and control. Also, financial man-agers who have practical knowledge about tradingrisks become reluctant to share their knowledgewith other organizational entities. By nature, mostof these risks are difficult to quantify and thereforeare handled arbitrarily. Thus, many analystsrecommend that financial enterprises utilize com-prehensive systems for capturing and monitoringrisk, accompanied by an automated risk-reportingprocess. These reports should be easily read andunderstood by top management.

Such problems require technology and manage-ment tools to motivate financial managers’ willing-ness to offer information, identify the need forinformation processing, support top managementto deal with multi-attribute problems and achievebalanced and well-informed decisions. It is theview of this paper that optimal decision-makingcan be achieved through the creation of a virtuouscycle of knowledge flow (Figure 3). This paperadopts this knowledge flow sequence to propose,under the non co-location situation, an adaptiveenabling mechanism that will allow a financialenterprise to integrate knowledge capture as aback end to its intelligent decision-making process.

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Knowledge flow implementation

The proposed tool addresses the following KM pro-blems of financial institutions in order to provide animplementation of the virtuous cycle of knowledgeflow as presented in Figure 3: the tool aims tobecome ameans for knowledge sharing and capture,as well as distributed KM in financial enterprises.The current implementation of the proposed metho-dology tool consists of the following modules:

� Knowledge capture. This module allows the userto generate graphically adaptive and highly flex-ible entity relationship diagrams (e.g. influencediagrams, cause- and -effect diagrams) from theinformation items provided by internal data-bases as well as external relevant sources. Infor-mation items then are linked in FCMs for theassertion of knowledge in a distributed (butcooperative) manner.

� FCM hierachy. Knowledge capture allows distri-buted FCMs to be associated and concepts to becomposed/decomposed via node linking. Inpractice, node linking generates multi-branchFCM hierarchies (as defined in Xirogiannis et al.,2004). FCM hierarchies are twofold:—distributed decomposition of FCMs to encode

and analyse specific contexts in their indivi-dualistic behaviour;

—adaptive synchronization of FCMs on a pro-ject level (e.g. major organizational units,functional areas) in the hierarchy.

� Knowledge alerts. This module associates specificalerts to the predefined threshold values ofknowledge entities and distributes correspond-ing messages to individual managers. Alertsand real-time data is to be provided via the exist-ing intranet/Internet message-passing technol-ogy of the enterprise.

� Work flow simulator. This module implementsthe FCM inference engine based on the FCM

value generator algorithms (see next section).The FCM inference engine may interact dynami-cally with methodology tools, which plan andmonitor business performance (such as theAdjust engine also implemented by the researchteam) to define and measure specialized perfor-mance indicators. Moreover, the inference enginecan be extended (on demand) with intelligentfunctions like abductive reasoning (Flach andKakas, 1998) to integrate intelligent reverse engi-neering functionality.

� Database link module. Future implementation ofthe system will also provide the user with thecapability to interface existing databases of theenterprise directly with the Know Fuz system.

These core modules (Figure 4) form the currentimplementation (also know as ‘Know Fuz’ imple-mentation) of the proposed system, which mayassociate both quantitatively and qualitatively dis-perse financial information stored in the internaland external databases to extract meaningfulknowledge as a back end to intelligent decisionmaking.

FCMs in financial modelling

The proposed system extends this typical FCMalgorithm (also used in Kwahk and Kim, 1999) byproposing the following new algorithm aiming atmodelling more effectively the geographically dis-persed nature of the financial enterprise domain:

Atþ1i ¼ f

�k1A

ti þ k2 �

Xnj¼1; j6¼1

Wj1Atj

�ð2Þ

The coefficient k1 represents the proportion of thecontribution of the value of the concept Ai at time tin the computation of the value of Ai at time tþ 1.In practice, this is equivalent to assuming that

Figure 3 Virtuous circle for knowledge flow

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Wii¼ k1. The incorporation of this coefficient resultsin smoother variation of concept values during theiterations of the FCM algorithm. The coefficientk2 expresses the ‘influence’ of the interconnectedconcepts in the configuration of the value of theconcept Ai at time tþ 1. In practice, it indicatesthe centralized or decentralized importance (e.g.decentralization distance) of the concept Ai incomparison to other concepts of the map. Also, itmay indicate the sufficiency of the set of concepts

Aj j 6¼ i, in the estimation of the value of the con-cept Ai. This paper also assumes that k1 and k2can be fuzzy sets, extending previous relevantresearch.

To demonstrate financial modelling using FCMs,consider Figure 5, which depicts a graphical exam-ple of fuzzy relationships with no feedback loops,followed by sample numerical calculations usingformula (2), with k1¼ k2¼ 1 and �¼ 5 as the steep-ness of the normalization function.

Figure 4 Know Fuz functional overview

Figure 5 Sample FCM calculations with no feedback loop

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Setting the input value of ‘sales volume’ to 0.5(1st scenario) triggers the FCM formula. The for-mula then calculates the current values of allrelated concepts. A ‘zero’ concept value indicatesthat the concept remains neutral, waiting for causalrelationships to modify its current value. A genericinterpretation of the first scenario indicates that ifsales volume increases by 50% then the incomemay increase by 88.07% and the profitability by95.61%. In contrast, if the sales volume increasesby 20% (2nd scenario), then the income and pro-fitability may increase by 59.86% and 89.04%respectively.

Figure 6 presents a typical example of a feedbackloop. Similarly to Figure 5, changing the inputvalue of ‘sales volume’ triggers the FCM formula.However, the feedback loop dictates that calcula-tions stop only when an equilibrium state for allaffected concepts has been reached, modifying allinput values accordingly.

FCMS IN KNOWLEDGE MODELLING

FCM categories

The current implementation of the proposed sys-tem encodes generic maps that can supplementthe knowledge modelling of typical geographicallydispersed financial organizations. The proposedFCMs may store concepts under different mapcategories (Figure 7); for example:

� Business category: all concepts relating to corefinancial activities.

� Technical category: all infrastructure-related con-cepts, with emphasis on technology infrastructure.

� Social category: all HR-related concepts, accom-panied by external stimuli (e.g. market character-

istics, local economy principles such as interestrates, etc.).

� Integrated category: essentially all top-most con-cepts (e.g. a concept Ai with no backward causal-ity such that 8j :wji¼ 0), or concepts which mayfall under more than one main categories.

This categorization is compatible both witheither the ‘process view’ or the ‘organizationalview’ (as adopted by Kwahk and Kim, 1999) ofthe enterprise to allow greater flexibility in model-ling dispersed knowledge flows. The hierarchicaldecomposition of knowledge concepts generates aset of dynamically interconnected hierarchical

Figure 6 Sample FCM calculations with feedback loop

Figure 7 Map categories

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maps. Each map analyses further the relationshipsamong concepts at the same hierarchical level. Con-sider, for example, a generic organizational chart ofa typical bank (Figure 8). A simple rule of thumbfor generating hierarchies is by aligning FCMswith the organizational levels of the enterprise.Figure 9 presents such a sample map hierarchy,which also serves as the FCMs overview.

Currently, the mechanism integrates more than250 concepts, forming a hierarchy of more than15 maps. Its dynamic interface allows its users toutilize a subset of these 250 concepts by settingthe value of the redundant concepts and/or thevalue of the associated weights to zero.

The proposed system can portray the financialmodel following either a holistic or a scalable

Figure 8 Alignment of the organizational hierarchy with the FCM knowledge hierarchy

Figure 9 Sample FCM hierarchy

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approach. This is analogous to seeing the enter-prise either as a single, ‘big bang’ event or as anongoing activity of targeting successive tasks ofselected sub-processes. The proposed mechanismcan accommodate both approaches. Essentially,the implementation can decompose concepts totheir constituent parts (sub-concepts) on demandand let the user reason about lower-level hierar-chies of FCM before it passes values to the higher-level hierarchies. The proposed mechanism alsoallows the user to specify the degree of FCMdecomposition during the map traversal. Insteadof waiting for a lower-level FCM to traverse itsnodes and pass its value to higher-level map hier-archies, the user may assign directly an externalvalue to nodes which link hierarchies. In practice,the simulation is carried out as if there are no linkswith other FCMs. Also the current implementationallows:

� easy customization of the function f and easyreconfiguration of the formula Ai

tþ 1 to adaptto the specific characteristics of individualenterprises;

� generation of scenarios for the same skeletonFCM;

� automatic loop simulation until a user-definedequilibrium point has been reached. Alterna-tively, step-by-step simulation (with graphical

output of partial results) is also available to pro-vide a justification for the partial results.

The following sections exhibit sample skeletonmaps for the business and integrated categories,which provide relevance and research interest tothis paper.

Business metrics

The mechanism proposes six different maps, eachconsisting of generic financial knowledge conceptsas follows:

� The ‘differentiation strategy’ map (Figure 10)reasons on the impact of strategic change to thecompetitive identity and financial status of theenterprise.

� The ‘internal cost’ map summarizes concepts,which affect the overall cost of delivering pro-ducts (or services) to the clients of the enterprise(e.g. value chain optimization, staff performance,execution cost).

� The ‘execution cost’ map (Figure 11) exemplifiesconcepts that influence the production cost of theenterprise.

� The ‘structural cost’ map reasons on the impactof concepts like outsourcing, product orientation,economies of scale, etc., to the overall businessmodel.

Figure 10 Differentiation strategy FCM

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� The ‘customers’ appreciation’ map reasons onthe impact of customer satisfaction in the differ-entiation effort and consequent financial resultsof the enterprise.

� The ‘profit overview’ map (Figure 12) sum-marizes the effect of concepts like income anddelivery cost on the overall profitability of thefinancial enterprise.

Concepts denoted by ‘ # ’ expand further tolower-level maps. Similarly, ‘ " ’ denotes bottom-up causal propagation.

Integrated metrics

The proposed integrated category consists of four(4) different maps as follows:

Figure 11 Execution cost FCM accompanied by a sample input/output/alert interface

Figure 12 Profit overview FCM

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� The ‘high-level’ map (Figure 13) essentiallyrelates concepts which fall under more thanone category, as well as top-most concepts.

� The ‘new entrants’ map supports reasoning ofthe impact of business model adjustments tomeet the product standards (e.g. quality, differ-entiated products, price policies) set by newcompetitors.

� The ‘productivity’ map (Figure 14) reasonson the impact of internal efficiency and salesadequacy on the overall profitability of theenterprise.

� The ‘RAROC’ map (Figure 15) summarizes theimpact of internal efficiency and sales adequacyon the risk-adjusted return on capital indicator ofthe enterprise.

All the above-mentioned maps form a genericdomain of FCMs. This knowledge domain servesas the basis of the proposed approach and can bemodified to comply with the requirements of speci-fic knowledge-capturing exercises. For example,further maps in the technical category could relateconcepts that relate the adequacy of the productioncycle with the expected financial performance ofthe enterprise (Irani et al., 2002; Valiris and Glykas,2000).

Infrastructure & HR metrics

The mechanism may also integrate various mapsconsisting of generic HR category concepts suchas staff performance, motivation, carrier prospects,financial rewards and workload, as well as ‘social’metrics which support reasoning of the impact ofknowledge management, training and employeesatisfaction to the financial model. Similarly themechanism may also integrate various maps consis-ting of technical concepts such as centralization/decentralization of IT infrastructure and IS/ITeffectiveness. While the presentation of such con-cepts supports the completeness of the proposedmethodology tool, they add little (if any) signifi-cance to the research activities presented by thispaper.

Assigning linguistic variables to FCM weightsand concepts

In order to define weight value of the associationrules in an adaptive and dynamic manner, the fol-lowing methodology is proposed. Financial man-agers are asked to describe the interconnectioninfluence of concepts using linguistic notions. Influ-ence of one concept over another is interpreted as a

Figure 13 High-level FCM

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Figure 14 Productivity overview FCM

Figure 15 RAROC overview FCM

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linguistic variable in the interval [� 1, 1]. Its termset T(influence) is:

T(influence)¼{negatively very-veryhigh, negatively very high, negativelyhigh, negatively medium, negativelylow, negatively very low, negativelyvery-very low, zero, positively very-very low, positively very low, posi-tively low, positively medium, posi-tively high, positively very high,positively very-very high}.

This paper proposes a semantic rule M to bedefined at this point. The above-mentioned termsare characterized by the fuzzy sets whose member-ship functions � are shown in Figure 16.

� M(negatively very-very high)¼ the fuzzy set for‘an influence close to 90%’ with membershipfunction �nvvh.

� M(negatively very high)¼ the fuzzy set for ‘aninfluence close to 80%’ with membership func-tion �nvh.

� M(negatively high)¼ the fuzzy set for ‘an influenceclose to 65%’ with membership function �nh.

� M(negatively medium)¼ the fuzzy set for ‘aninfluence close to 50%’ with membership func-tion �nm.

� M(negatively low)¼ the fuzzy set for ‘an influ-ence close to 35%’ with membership function �nl.

� M(negatively very low)¼ the fuzzy set for ‘aninfluence close to 20%’ with membership func-tion �nvl.

� M(negatively very-very low)¼ the fuzzy set for‘an influence close to 10%’ with membershipfunction �nvvl.

� M(zero)¼ the fuzzy set for ‘an influence close to0’ with membership function �z.

� M(positively very-very low)¼ the fuzzy set for‘an influence close to 10%’ with membershipfunction �pvvl.

� M(positively very low)¼ the fuzzy set for ‘aninfluence close to 20%’ with membership func-tion �pvl.

� M(positively low)¼ the fuzzy set for ‘an influ-ence close to 35%’ with membership function �pl.

� M(positively medium)¼ the fuzzy set for ‘aninfluence close to 50%’ with membership func-tion �pm.

� M(positively high)¼ the fuzzy set for ‘an influ-ence close to 65%’ with membership function�ph.

� M(positively very high)¼ the fuzzy set for ‘aninfluence close to 80%’ with membership func-tion �pvh.

� M(positively very-very high)¼ the fuzzy set for‘an influence close to 90%’ with membershipfunction �pvvh.

The membership functions are not of the samesize since it is desirable to have a finer distinctionbetween grades at the lower and higher ends ofthe influence scale. As an example, three financialmanagers proposed different linguistic weightsfor the interconnection Wij from concept Ci to con-cept Cj: (a) positively high, (b) positively very high,(c) positively very-very high. The three suggestedlinguistics are integrated using a sum combinationmethod and then the defuzzification method ofcentre of gravity (CoG) is used to produce a weightwij¼ 0.77 in the interval [� 1, 1]. This approach hasthe advantage that experts do not have to assignnumerical causality weights but to describe thedegree of causality among concepts. The samesemantic rule and term set can be used to definethe coefficients k1 and k2.

A similar methodology can be used to assignvalues to concepts. The financial managers arealso asked to describe the measurement of each con-cept using, once again, linguistic notions. Measure-ment of a concept is also interpreted as a linguistic

Figure 16 Membership functions of linguistic variable influence

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variable with values in the interval [� 1, 1]. Its termset T(Measurement)¼T(Influence). A new seman-tic rule M2 (analogous to M) is also defined andthese terms are characterized by the fuzzy setswhose membership functions �2 are analogous tomembership functions �.

PRELIMINARY EXPERIMENTS

The nature of the experiments

Two informal experiments were conducted byutilizing metrics from actual (though random)knowledge-based decision support exercises intwo major financial sector enterprises. For eachexperiment, a team of experts was engaged to:

� provide linguistic variables for the causalweights, the concept values and the coefficientsvalues to let the FCM algorithm reason aboutthe impact of potential financial performancechanges;

� provide their independent expert estimates(using similar linguistic variables) of the impactof geographically dispersed activities to the over-all business model.

In both cases, the proposed tool iterated a subsetof approximately 150 concepts spread over 10 sam-ple hierarchical maps in order to calculate theirequilibrium values. Both cases run on a typicalbusiness PC with a 2.4GHz Pentium processorand 512MB RAM. As far as the number of itera-tions is concerned, lower-level maps iterated10 times on average. The average number of itera-tions increased to 25 for middle and upper-levelmaps. Only the topmost map increased the averagenumber of iterations to approximately 80 (depend-ing on the initial concept and weight values) due tothe volume of map links. In practice, the actual pro-cess time was negligible on such a typical PC.

Discussion

Theoretical valueVarious aspects of the proposed modellingmechanism are now commented on. As far as thetheoretical value is concerned, the proposedmechanism extends previous research attempts by:

� allowing fuzzy node and weight definitions inthe cognitive maps;

� introducing a specific interpretation mechanismof linguistic variables to fuzzy sets;

� proposing an updated FCM algorithm to suit bet-ter the KM domain of geographically dispersedorganizations;

� supporting node linking to establish map hier-archies and dynamic map selection duringsimulation;

� concentrating on the actual KM activity and theassociated business model;

� allowing dynamic map decomposition andreconfiguration;

� integrating three modes of FCM simulation,namely bivalent (with a crisp activation set{0, 1}), trivalent (with a crisp activation set{� 1, 0, 1}) and linear (with an activation set inthe fuzzy interval [�1, . . . , 1]);

� supporting the user with appropriate interfacewindows when loops, cycles and node conflictsare identified.

Practical valueAs far as the practical value of the proposedmechanism is concerned:

� When compared to the expert estimates, themechanism does not provide a fundamentallydifferent ‘diagnosis’. On the contrary, it providesreasonably good approximations of the expertestimates.

� The justification of the ‘diagnosis’ (essentially themetrics decomposition) proved extremely help-ful in comprehending the sequence of complexconcept interactions (essentially the knowledgeroadmap).

� The concept-based approach did not restrict theinterpretation of the financial impact of geogra-phically dispersed activities to the overall busi-ness model. The fuzzy interpretation of conceptand weight values served as indications ratherthan precise arithmetic calculations.

� The hierarchical (or partial) traversal of financialmetrics improved the distributed knowledgemonitoring throughout the geographical levelsof the enterprise and stipulated targeted commu-nication of the associated financial performance.

� The realism of impact estimation depended onthe number of concepts and weights, as well ason the estimation of their fuzzy characteristics(weights values, input values, coefficients, etc).However, the complexity and the length of theknowledge domain did not discourage the main-tenance of the mechanism. Irrelevant and/orunnecessary knowledge maps could be isolatedon demand to reduce the reasoning effort.

� The adaptive nature of the proposed mechanismis also worth mentioning. For instance:—the tool can portray either a holistic or a scal-

able approach to financial modelling to com-ply with the knowledge modelling approachof the enterprise;

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—knowledge categorization is compatible witheither the ‘process view’ or the ‘organizationalview’ of the enterprise;

—hierarchical (and/or decentralized) compo-sition/decomposition of knowledge conceptscouples effectively with the hierarchical(and/or decentralized) structures of anenterprise;

—skeleton FCMs accompanied by business cases(scenarios) improve the flexibility of the toolby allowing the user to generate alternativeknowledge-based decision roadmaps with lit-tle extra effort;

—maps can expand/retract on demand, allow-ing the user to utilize only the necessary subsetof knowledge concepts;

—maps are dynamic; further knowledge con-cepts may be added to encapsulate furtherknowledge interactions;

—the FCM value calculation formula maychange on demand to adapt better to thecharacteristics of the knowledge interactionsof the enterprise.

Added valueHaving established the theoretical and practicalvalue of the proposed mechanism, it is useful todiscuss also the added value of incorporatingsuch a mechanism into KM exercises. It is the beliefof this paper that the resulting tool provides realvalue to the principle beneficiaries and stake-holders of KM projects. For example:

� The mechanism eases significantly the complex-ity of deriving knowledge-based decisions. Infor-mal experiments indicated that the time requiredby experts to estimate manually the extensiveimpact of major changes to geographically dis-persed business models could pose a consider-able overhead. On the other hand, the elapsedtime for automated knowledge-based decisionsupport using FCM can be insignificant, oncethe map hierarchies have been set up.

� To extend further this syllogism, realisticknowledge-based decision support should in-volve continuous argument of change options(e.g. application of best practices, alternative stra-tegic scenarios) until an equilibrium solutionaccepted by all stakeholders has been agreedupon. Informal discussions with the principalbeneficiaries and stakeholders of the two finan-cial sector enterprises revealed that the proposedknowledge-based support can reduce signifi-cantly the impact estimation overheads, lettingthe stakeholders focus on the actual financialmanagement exercise while exploring in depth

all alternatives and effectively controlling majorchange initiatives.

� The proposed mechanism can also assist thefinancial performance evaluation of the enter-prise on a regular basis. FCMs may serve as aback end to performance score cards (Bourneet al., 2000; Kaplan and Norton, 1996, 2001) toprovide holistic strategic performance evaluationand management. However, a detailed analysisof this extension is beyond the scope of thispaper.

Preliminary usability evaluationSenior managers of the two major financial sectorenterprises have evaluated the usability of the pro-posed tool and have identified a number of benefitsthat can be achieved by its utilization. Detailed pre-sentation of the usability evaluation results arebeyond the scope of the paper. However, a sum-mary of major business benefits (as identified bysenior managers) is provided to improve the auton-omy of this paper:

� Shared goals:—Concept-driven KM pulls individuals together

by providing a shared direction and determi-nation of internal change.

—Shared KM and financial performance mea-surement enable business units to realizehow they fit into the overall business modeland what is their actual contribution.

—Senior management receives valuable inputfrom the business units (or the individualemployees) who really comprehend the weak-nesses of the current business model as well asthe opportunities for performance-drivenchanges.

� Shared culture:—All business units feel that their individual

contribution is taken into considerationand provide valuable input to potential busi-ness model changes.

—All business units and individuals feel confi-dent and optimistic; they realize that theywill be the ultimate beneficiaries of any poten-tial business model changes.

—The information and knowledge-sharing cul-ture supports the enterprise’s competitivestrategy and provides the energy to sustainthis by exploiting fully the group and the indi-vidual potential.

� Shared learning:—The enterprise realizes a high return from its

commitment to its human resources.—There is a constant stream of improvement

within the enterprise.

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—The entire enterprise becomes increasinglyreceptive to internal changes, since the benefitcan be easily demonstrated to individual busi-ness units.

� Shared information:—All business units and individuals have the

necessary information needed to set clearlytheir objectives and priorities.

—Senior management can control effectively allaspects of business model changes.

—The enterprise reacts rapidly to threats andopportunities fully utilizing benefits from KM.

—It reinforces trust and respect throughout theenterprise.

—It becomes easier for financial managers toretrieve and share pieces of knowledge.

—Top management improves its capacity to inte-grate all incoming information for decisionmaking (e.g. time restrictions, other manage-rial engagements, information given with ahigh/low level of detail).

—Top management can review more frequentlythe firm’s risk measurement methodologies,models and assumptions for various types ofrisk (including operational risk).

Summarizing, preliminary experimental resultsshowed that FCM-based knowledge managementcan be an effective and realistic back end to deci-sion support. This is considered to be a major con-tribution of the proposed methodology tool toactual KM exercises. Moreover, ex ante reasoningof the impact of geographically dispersed activitiesto the overall business model can be estimated witha moderate start-up effort. Scenario building, onthe other hand, can be trivial once the skeletonFCMs have been established.

CONCLUSION

This paper presented a knowledge managementmethodology tool to act as a decision supportmechanism for geographically dispersed financialenterprises. The proposed decision aid may serveas a back end to adaptive KM by supporting ‘intel-ligent’ reasoning of the anticipated financial beha-viour. By using FCM, the proposed mechanismdrew a causal representation of financial perfor-mance principles; it simulated the operational effi-ciency of distributed organizational models withimprecise relationships and quantified the impactof the geographically dispersed activities to theoverall business model.

The underlying research addressed the problemof information capture and representation in finan-

cial institutions in order to provide an implementa-tion of the cycle of knowledge flow. The proposedmethodology tool utilized the fuzzy causal charac-teristics of FCMs to generate a hierarchical anddynamic network of interconnected financial per-formance concepts. Generic maps that supplementthe knowledge-based decision process presented aroadmap for integrating hierarchical and FCMsinto the business model of typical financial sectorenterprises.

The proposed mechanism should not beregarded only as an effective business modellingsupport tool. Its main purpose is to drive financialchange activities rather than limit itself to qualita-tive simulations. Moreover, the proposed mechan-ism should not be seen as a ‘one-off’ decision aid. Itshould be a means for setting a course for continu-ous improvement (Langbert and Friedman, 2002).

Future research will focus on conducting furtherreal-life experiments to test and promote the usabil-ity of the tool, and also to identify potential pitfalls.Furthermore, future research will focus on theautomatic determination of appropriate fuzzy sets(e.g. utilizing pattern recognition, mass assign-ments, empirical data) for the representation of lin-guistic variables to suit each particular financialdomain. Finally, further research will focus onimplementing backward map traversal, a form ofadbuctive reasoning (Flach and Kakas, 1998). Thisfeature offers the functionality of determining thecondition(s) Cij that should hold in order to inferthe desired Cj in the causal relationship Cij�!wjk Ck.Incorporating performance integrity constraintsreduces the search space and eliminates combina-tory search explosion. Backward reasoning hasbeen tested extensively in other applications andits integration in the proposed framework mayprove beneficial.

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