Fuzzy cognitive maps as a back end to knowledge-based systems in geographically dispersed financial organizations

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 & Research Article Fuzzy Cognitive Maps as a Back End to Knowledge-based Systems in Geographically Dispersed Financial Organizations George Xirogiannis1*, Michael Glykas1 and Christos Staikouras2 1 2 Department of Financial and Management Engineering, University of the Aegean, Greece Department of Accounting and Finance, Athens University of Economics and Business, Greece This paper addresses the problem of designing a knowledge management methodology tool to act as a decision support mechanism for geographically dispersed financial enterprises. The underlying research addresses the problem of information capture and representation in financial 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 Cognitive Maps (FCMs) to generate a hierarchical and dynamic network of interconnected financial performance concepts. By using FCMs, the proposed mechanism simulates the operational efficiency of distributed organizational models with imprecise relationships and quantifies the impact of the geographically dispersed activities to the overall business model. Generic adaptive maps that supplement the decision-making process present a roadmap for integrating hierarchical FCMs into the business model of typical financial sector enterprises. Copyright # 2004 John Wiley & Sons, Ltd. INTRODUCTION Knowledge has been defined by Western philosophy (Russell, 1989) as ‘justified true belief’. However, as long as there is a chance that this belief is mistaken and as long as there is an evolution of technologies, theories, practice and behaviours, this definition invites individuals and groups to develop constantly ‘what they think that they know’ (Nonaka and Takeushi, 1994). This continuous process of creation of new insights and beliefs is what fuels the entire paradigm of knowledge management and even constitutes the fundamental rationale for the existence of an enterprise. Some *Correspondence to: George Xirogiannis, Department of Financial and Management Engineering, University of the Aegean, 31 Fostini Street, Chios, 82 100, Greece. E-mail: g.xirogiannis@fme.aegean.gr Copyright # 2004 John Wiley & Sons, Ltd. argue that instead of merely solving problems, organizations create and define problems, develop and apply new knowledge to solve problems and then develop further new knowledge through the action of problem solving. In this view an enterprise creates continuously new knowledge through action and interaction, not acting simply as an information-processing machine (Nonaka and Takeushi, 1994; Spencer and Grant, 1996). Currently, there is a pressing need for sharing knowledge among the financial managers (e.g. CFO, Head of Accounting, Head of Budgeting, Head of Business Planning). The effect of knowledge attrition for customers and investors is knowledge intensive. Financial enterprises lose (on average) half of their knowledge base every 5–10 years due to the turnover of their employees. The fact is that financial managers are usually more committed to their specialized profession, thus RESEARCH ARTICLE Knowledge and Process Management losing sight of the enterprise as a whole. Without effective sharing and maintenance of knowledge, financial institutions risk losing their crucial knowledge through labour mobility. Moreover, knowledge has the idiosyncrasy that its value can only be realized when it is put in use (i.e. no shelf value). The more knowledge put in use, the more its value is appreciated (e.g. efficient use through the increase in confidence of application and learning), rather than depreciated, as other physical assets of machinery or natural resources. This paper addresses the problem of designing a novel knowledge management (KM) methodology tool to act as a decision support mechanism for geographically dispersed financial organizations (e.g. multi-national enterprises, multi-branch banks). The proposed methodology tool utilizes the fuzzy causal characteristics of fuzzy cognitive maps (FCMs) to generate a hierarchical and dynamic network of interconnected financial performance concepts. By using FCMs, the proposed mechanism simulates the operational efficiency of distributed organizational models with imprecise relationships and quantifies the impact of the geographically dispersed activities to the overall business model. From the KM perspective, it is the belief of this paper that optimal decision-making can be achieved through the creation of a virtuous circle of knowledge flow: creating and adding knowledge, successful searching for the required pieces of knowledge, feedback for impetus to assert quality knowledge again. Primarily, the proposed model targets the principal beneficiaries and stakeholders of KM projects (financial administration, change management leaders, etc.), assisting them to reason effectively about the status of financial performance metrics, given the (actual or hypothetical) implementation of a set of business model changes. Nevertheless, the explanatory nature of the mechanism can prove to be useful in a wider educational setting. This paper consists of seven sections. The next section presents a short literature overview, while the third section addresses the contemporary knowledge capture and representation problem of financial managers and justifies the need for a novel adaptive knowledge management methodology tool. The fourth section presents an overview of the proposed system, the fifth section discusses the new approach to knowledge modelling based on FCMs and the sixth section discusses the major advantages of the proposed tool. The final section concludes this paper and briefly discusses future research activities. LITERATURE OVERVIEW FCMs as a modelling technique FCMs are a modelling methodology for complex decision systems, which originated from the combination of fuzzy logic (Zadeh, 1965) and neural networks. An FCM describes the behaviour of a system in terms of concepts; each concept represents an entity, a state, a variable or a characteristic of the system (Dickerson and Kosko, 1997). FCM nodes are named by such concepts forming the set of concepts C ¼ {C1, C2, . . . , Cn}. Arcs (Cj, Ci) are oriented and represent causal links between concepts; that is how concept Cj causes concept Ci. Arcs are elements of the set A ¼ {(Cj, Ci)ji}
C  C. Weights of arcs are associated with a weight value matrix Wn  n, where each element of the matrix = A then wji 2 [1, . . . , 1]
R such that if (Cj, Ci) 2 wji ¼ 0 else excitation (respectively inhibition) causal link from concept Cj to concept Ci gives wji > 0 (respectively wji < 0). The proposed methodology framework assumes that [1, . . . , 1] is a fuzzy bipolar interval, bipolarity being used as a means of representing a positive or negative relationship between two concepts. In practice, the graphical illustration of an FCM is a signed graph with feedback, consisting of Weight nodes and weighted interconnections (e.g.  !). Signed and weighted arcs (elements of the set A) connect various nodes (elements of the set C) representing the causal relationships that exist among concepts. This graphical representation (e.g. Figure 1) illustrates different aspects in the behaviour 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 138 G. Xirogiannis et al. Knowledge and Process Management Figure 2 Simple FCM Positive or negative sign and fuzzy weights model the expert knowledge of the causal relationships (Kosko, 1991). Concept Cj causally increases Ci if the weight value wji > 0 and causally decreases Ci if wji < 0. When wji ¼ 0, concept Cj has no causal effect on Ci. The sign of wji indicates whether the relationship between concepts is positive ji ji Ci) or negative (Cj w!  Ci), while the value (Cj w! of wji indicates how strongly concept Cj influences concept Ci. The forward or backward direction of causality indicates whether concept Cj causes concept Ci or vice versa (e.g. Figure 2). Simple variations of FCMs mostly used in business decision-making applications may take trivalent weight values [1, 0, 1]. This paper allows FMCs to utilize fuzzy word weights like strong, medium or weak, each of these words being a fuzzy set to provide complicated FCMs. In contrast, Kwahk and Kim (1999) adopted only a simple relative weight representation in the interval [1, . . . , 1]. To this extent, Kwahk and Kim (1999) offered reduced functionality since it does not allow fuzzy weight definitions. Generally speaking, FCM concept activations take their value in an activation value set V ¼ {0, 1} or {1, 0, 1} if in crisp mode or [, 1] with  ¼ 0 or 1 if in fuzzy mode. The proposed methodology framework assumes fuzzy mode with  ¼ 1. At step t 2 N, each concept Cj is associated with an inner activation value ajt 2 V, and an external activation value etaj 2 R. FCM is a dynamic system. Initialization is aj0 ¼ 0. The dynamic obeys a general recurrent relation atþ1 ¼ f (g(eat, WT at)), 8t  0, involving weight matrix product with inner activation, fuzzy logical operators (g) between this result and external forced activation and finally normalization ( f ). However, this paper assumes no external activation (hence no fuzzy logical operators), resulting in the following typical formula for calculating the values of concepts of FCM: 0 1 n X atþ1 wji atj A ð1Þ ¼ f@ i j¼1; j6¼i Fuzzy Cognitive Maps RESEARCH ARTICLE where aitþ1 is the value of concept Ci at step t þ 1, aja the value of the interconnected concept Cj at step t, wji is the weighted arc from Cj to Ci and f : R ! V is a threshold function, which normalizes activations. Two normalization functions are usually used. The unipolar sigmoid function where  > 0 determines the steepness of the continuous function fðxÞ ¼ 1þe1x . When concepts can be negative ( < 0), function fðxÞ ¼ tanhðxÞ can also be used. To understand better the analogy between the sign of the weight and the positive/negative relationship, it may be necessary to revisit the characteristics of the fuzzy relation (Kaufmann, 1975; Lee et al., 2002). A fuzzy relation from a set A to a set B or (A, B) represents its degree of membership in the unit interval [0, 1]. Generally speaking, sets A and B can be fuzzy sets. The corresponding fuzzy membership function is mf:A  B ! [0, 1]. Therefore, mf(x, y) is interpreted as the ‘strength’ of the fuzzy membership of the fuzzy relation (x, y) where x 2 A and y 2 B. Then this fuzzy relation concept can be denoted equivalently as x f ! y and applied to interpret the causality value of FCM, since wji (the causality value of the arc from nodes Cj to Ci) in a certain FCM is interpreted as the degree of fuzzy relationship between two nodes Cj and Ci. Hence, wji in FCMs is the fuzzy membership value mf(Cj, Ci) and can be denoted ji Ci. as Cj w! However, we understand that the fuzzy relation (weight) between concept nodes is more general than the original fuzzy relation concept. This is because it can include negative () fuzzy relations. Fuzzy relations mean fuzzy causality; causality can have a negative sign. In FCMs, the negative fuzzy relation (or causality) between two concept nodes is the degree of a relation with a ‘negation’ of a concept node. For example, if the negation of a concept 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 equipped with capacities of Hebbian learning (Kosko, 1986a, 1998). FCMs are used to represent and to model the knowledge on the examining system. Existing knowledge of the behaviour of the system is stored in the structure of nodes and interconnections of the map. The fundamental difference between FCMs and neural networks is in the fact that all the nodes of the FCM graph have a strong semantic defined by the modelling of the concept, whereas the nor input/nor output nodes of the graph of the neural network have a weak semantic, only defined by mathematical relations. 139 RESEARCH ARTICLE Applications of fuzzy cognitive maps Over the last 10 years, a variety of FCMs have been used for capturing—representing knowledge and intelligent information in engineering applications, for instance, geographical information systems Liu and Satur (1999) and fault detection (Ndouse and Okuda, 1996; Pelaez and Bowles, 1995). FCMs have been used in modelling the supervision of distributed systems (Stylios et al., 1997). FCMs have also been used in operations research (Craiger et al., 1996), web data mining (Hong and Han, 2002; Lee et al., 2000), as a back end to computer-based models and medical diagnosis (e.g. Georgopoulos et al., 2002). Several research reports applying basic concepts of FCMs have also been presented in the field of business and other social sciences. Research in Axelrod (1976) and Perusich (1996) have used FCM for representing tacit knowledge in political and social analysis. FCMs have been successfully applied to various fields such as decision making in complex war games (Klein and Cooper, 1982), strategic planning (Diffenbach, 1982; Ramaprasad and Poon, 1985), information retrieval (Johnson and Briggs, 1994) and distributed decision process modelling (Zhang et al., 1994). Research like that of Lee and Kim (1997) has successfully applied FCMs to infer rich implications from stock market analysis results. Research like that of Lee and Kim (1998) also suggested a new concept of fuzzy causal relations found in FCMs and applied it to analyse and predict stock market trends. The inference power of FCMs has also been adopted to analyse the competition between two companies, which are assumed to use differential games mechanisms to set up their own strategic planning (Lee and Kwon, 1998). FCMs have been integrated with case-based reasoning technique to build organizational memory in the field of knowledge management (Noh et al., 2000). Recent research adopted FCMs to support the core activities of highly technical functions like urban design (Xirogiannis, 2004). Summarizing, FCMs can contribute to the construction of more intelligent systems, since the more intelligent a system becomes, the more symbolic and fuzzy representations it utilizes. In addition, a few modifications have been proposed. For example, the research in Silva (1995) proposed new forms of combined matrices for FCMs, the research in Hagiwara (1992) extended FCMs by permitting non-linear and time delay on the arcs, and the research in Schneider et al. (1995) presented a method for automatically constructing FCMs. More recently, Liu and Satur (1999) have carried extensive research on FCMs, 140 Knowledge and Process Management investigating inference properties of FCMs, proposed contextual FCMs based on the objectoriented paradigm of decision support and applied contextual FCMs to geographical information systems (Liu, 2000). KNOWLEDGE MANAGEMENT IN FINANCIAL ENTERPRISES The decision-making problem Financial management is one of the major areas of business of financial sector institutions. The risks undertaken by fund managers in their investment decisions affect directly the institutions’ business continuity, profitability and reputation. Fund managers’ work allows direct performance measurement, while the rewards based on measured performance affect their career prospects and job security. Junior financial managers are therefore more risk averse in their portfolio management decisions, which they ‘herd’ to follow the market trends in avoiding investment risks above the market objective level, whereas senior managers are given more discretion in their investment decisions. The high monetary rewards, considerations of job security and market-relative measurement of performance induce financial managers’ selfinterests and ownership of critical knowledge, which may create effective investment decisions. Therefore creating an open environment to share analytical skills of market signals, intimate knowledge of clients, or capability to sense political atmosphere and market sentiment among financial managers can minimize any miscalculated risks. The need for knowledge sharing Knowledge can be reused potentially an infinite number of times without wearing off or needing repair. With each subsequent application of information processing, the experience of use and background understanding of environmental settings builds up. This potential to apply knowledge an infinite number of times allows for economies of scale, which may reduce radically the transaction and/or operational costs. Hence the potential value of knowledge can only be fully realized if it is leveraged effectively through sharing and reuse. Intimate, contextual and firm-specific knowledge is an intangible asset that is costly to develop, hard to replace and time consuming to replicate. Possession of intimate knowledge with real value to customers allows enterprises to differentiate themselves from competitors. Coordinated G. Xirogiannis et al. Knowledge and Process Management processing of disparate pieces of information to develop skills and capabilities in a way that helps an enterprise to achieve its goals is a form of intellectual capital and a valuable source of competitive advantage. Individuals with different culture and experiences lack the contextual links associated with the enterprise’s specific knowledge. Communication of knowledge separated from its context hinders thorough understanding and detaches intuitive interpretation through symbolic environmental associations. Knowledge so communicated is inevitably abstract. It consists of generalized analyses of events, and the recipient may find it difficult to comprehend its relevance to a specific situation. Indeed, skilful masters differentiate from novices by the intimate understanding of the tasks and the environment linked together with specific contextual interacting factors that differentiate skillful masters from novice beginners. Sharing, and only communication, of knowledge carries a common context where individuals can interact and engage in a mutual dialogue with common understanding. Effective sharing creates a synergy with value where the sum is more than its parts. Therefore, effective dissemination of specialized contextual knowledge among members of the firm minimizes miscalculation or misperception of risks. KM and transaction costs reduction Sharing of knowledge involves information flows between the distributed organizational entities of an enterprise. The cost—benefit analysis of knowledge flow must consider the enterprise’s specific environmental factors in terms of co-location of decision rights and knowledge. Colocation refers to the delegation of decision-making authority to the party holding necessary knowledge (e.g. discretionary investment decisions made by financial managers within institutional guidelines). The cost of no knowledge sharing can be proportional to the decision-making costs (in practice, the sum of agency and knowledge transfer costs). Agency cost arises from self-interested individuals in conflict with management when decisions are delegated to them. The time and effort spent by management and possibly the need for policy adjustments, remuneration packages and coordination of individual members are all agency costs. The knowledge transfer costs arise from training, practice and experience needed to equip individuals with the necessary knowledge. The distance of decision rights from the CEO office affects the total decision-making costs and causes trade-offs between suboptimal decisions Fuzzy Cognitive Maps RESEARCH ARTICLE and possession of necessary knowledge. The lack of embedded know-how at central management causes suboptimal decisions to be made when the decision-maker is away from sources of knowledge; therefore the knowledge transfer costs owing to poor information sharing is very high. On the other hand, when some knowledge carrier away from central management makes a decision, the need for control and coordination to maintain consistency and integrity incurs high agency costs. There is a cost-optimal point where the sum of the agency and transfer costs is at its minimum. Effective knowledge sharing lowers the costs by shifting the optimal point of total organizational costs downward, i.e. shifting the knowledge transfer cost curve downward. This component identifies the agency and knowledge transfer costs involved in sharing knowledge in the current environment setting to ensure organizational fit. FUNDAMENTALS OF THE METHODOLOGY TOOL The knowledge flow cycle Many financial analysts and investigation reports about multi-million dollar losses at Sumitomo and Barings attribute the losses to the neglect of paying attention to operational risk. Operational risk results in losses due to deficiencies in information, personnel unavailability, human error, and inadequate procedures and control. Also, financial managers who have practical knowledge about trading risks become reluctant to share their knowledge with other organizational entities. By nature, most of these risks are difficult to quantify and therefore are handled arbitrarily. Thus, many analysts recommend that financial enterprises utilize comprehensive systems for capturing and monitoring risk, accompanied by an automated risk-reporting process. These reports should be easily read and understood by top management. Such problems require technology and management tools to motivate financial managers’ willingness to offer information, identify the need for information processing, support top management to deal with multi-attribute problems and achieve balanced and well-informed decisions. It is the view of this paper that optimal decision-making can be achieved through the creation of a virtuous cycle of knowledge flow (Figure 3). This paper adopts this knowledge flow sequence to propose, under the non co-location situation, an adaptive enabling mechanism that will allow a financial enterprise to integrate knowledge capture as a back end to its intelligent decision-making process. 141 RESEARCH ARTICLE Knowledge and Process Management Figure 3 Virtuous circle for knowledge flow Knowledge flow implementation The proposed tool addresses the following KM problems of financial institutions in order to provide an implementation of the virtuous cycle of knowledge flow as presented in Figure 3: the tool aims to become a means for knowledge sharing and capture, as well as distributed KM in financial enterprises. The current implementation of the proposed methodology tool consists of the following modules:  Knowledge capture. This module allows the user to generate graphically adaptive and highly flexible entity relationship diagrams (e.g. influence diagrams, cause- and -effect diagrams) from the information items provided by internal databases as well as external relevant sources. Information items then are linked in FCMs for the assertion of knowledge in a distributed (but cooperative) manner.  FCM hierachy. Knowledge capture allows distributed FCMs to be associated and concepts to be composed/decomposed via node linking. In practice, node linking generates multi-branch FCM hierarchies (as defined in Xirogiannis et al., 2004). FCM hierarchies are twofold: —distributed decomposition of FCMs to encode and analyse specific contexts in their individualistic behaviour; —adaptive synchronization of FCMs on a project level (e.g. major organizational units, functional areas) in the hierarchy.  Knowledge alerts. This module associates specific alerts to the predefined threshold values of knowledge entities and distributes corresponding messages to individual managers. Alerts and real-time data is to be provided via the existing intranet/Internet message-passing technology of the enterprise.  Work flow simulator. This module implements the FCM inference engine based on the FCM 142 value generator algorithms (see next section). The FCM inference engine may interact dynamically with methodology tools, which plan and monitor business performance (such as the Adjust engine also implemented by the research team) to define and measure specialized performance indicators. Moreover, the inference engine can be extended (on demand) with intelligent functions like abductive reasoning (Flach and Kakas, 1998) to integrate intelligent reverse engineering functionality.  Database link module. Future implementation of the system will also provide the user with the capability to interface existing databases of the enterprise directly with the Know Fuz system. These core modules (Figure 4) form the current implementation (also know as ‘Know Fuz’ implementation) of the proposed system, which may associate both quantitatively and qualitatively disperse financial information stored in the internal and external databases to extract meaningful knowledge as a back end to intelligent decision making. FCMs in financial modelling The proposed system extends this typical FCM algorithm (also used in Kwahk and Kim, 1999) by proposing the following new algorithm aiming at modelling more effectively the geographically dispersed nature of the financial enterprise domain: Atþ1 i   n X t t Wj1 Aj ¼ f k1 A i þ k2  ð2Þ j¼1; j6¼1 The coefficient k1 represents the proportion of the contribution of the value of the concept Ai at time t in the computation of the value of Ai at time t þ 1. In practice, this is equivalent to assuming that G. Xirogiannis et al. Knowledge and Process Management RESEARCH ARTICLE Figure 4 Know Fuz functional overview Wii ¼ k1. The incorporation of this coefficient results in smoother variation of concept values during the iterations of the FCM algorithm. The coefficient k2 expresses the ‘influence’ of the interconnected concepts in the configuration of the value of the concept Ai at time t þ 1. In practice, it indicates the centralized or decentralized importance (e.g. decentralization distance) of the concept Ai in comparison to other concepts of the map. Also, it may indicate the sufficiency of the set of concepts Aj j 6¼ i, in the estimation of the value of the concept Ai. This paper also assumes that k1 and k2 can be fuzzy sets, extending previous relevant research. To demonstrate financial modelling using FCMs, consider Figure 5, which depicts a graphical example of fuzzy relationships with no feedback loops, followed by sample numerical calculations using formula (2), with k1 ¼ k2 ¼ 1 and  ¼ 5 as the steepness of the normalization function. Figure 5 Sample FCM calculations with no feedback loop Fuzzy Cognitive Maps 143 RESEARCH ARTICLE Knowledge and Process Management Figure 6 Sample FCM calculations with feedback loop Setting the input value of ‘sales volume’ to 0.5 (1st scenario) triggers the FCM formula. The formula then calculates the current values of all related concepts. A ‘zero’ concept value indicates that the concept remains neutral, waiting for causal relationships to modify its current value. A generic interpretation of the first scenario indicates that if sales volume increases by 50% then the income may increase by 88.07% and the profitability by 95.61%. In contrast, if the sales volume increases by 20% (2nd scenario), then the income and profitability may increase by 59.86% and 89.04% respectively. Figure 6 presents a typical example of a feedback loop. Similarly to Figure 5, changing the input value of ‘sales volume’ triggers the FCM formula. However, the feedback loop dictates that calculations stop only when an equilibrium state for all affected concepts has been reached, modifying all input values accordingly. istics, local economy principles such as interest rates, etc.).  Integrated category: essentially all top-most concepts (e.g. a concept Ai with no backward causality such that 8j : wji ¼ 0), or concepts which may fall under more than one main categories. This categorization is compatible both with either the ‘process view’ or the ‘organizational view’ (as adopted by Kwahk and Kim, 1999) of the enterprise to allow greater flexibility in modelling dispersed knowledge flows. The hierarchical decomposition of knowledge concepts generates a set of dynamically interconnected hierarchical FCMS IN KNOWLEDGE MODELLING FCM categories The current implementation of the proposed system encodes generic maps that can supplement the knowledge modelling of typical geographically dispersed financial organizations. The proposed FCMs may store concepts under different map categories (Figure 7); for example:  Business category: all concepts relating to core financial activities.  Technical category: all infrastructure-related concepts, with emphasis on technology infrastructure.  Social category: all HR-related concepts, accompanied by external stimuli (e.g. market character- 144 Figure 7 Map categories G. Xirogiannis et al. Knowledge and Process Management RESEARCH ARTICLE Figure 8 Alignment of the organizational hierarchy with the FCM knowledge hierarchy maps. Each map analyses further the relationships among concepts at the same hierarchical level. Consider, for example, a generic organizational chart of a typical bank (Figure 8). A simple rule of thumb for generating hierarchies is by aligning FCMs with 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 than 250 concepts, forming a hierarchy of more than 15 maps. Its dynamic interface allows its users to utilize a subset of these 250 concepts by setting the value of the redundant concepts and/or the value of the associated weights to zero. The proposed system can portray the financial model following either a holistic or a scalable Figure 9 Sample FCM hierarchy Fuzzy Cognitive Maps 145 RESEARCH ARTICLE Knowledge and Process Management approach. This is analogous to seeing the enterprise either as a single, ‘big bang’ event or as an ongoing activity of targeting successive tasks of selected sub-processes. The proposed mechanism can accommodate both approaches. Essentially, the implementation can decompose concepts to their constituent parts (sub-concepts) on demand and let the user reason about lower-level hierarchies of FCM before it passes values to the higherlevel hierarchies. The proposed mechanism also allows the user to specify the degree of FCM decomposition during the map traversal. Instead of waiting for a lower-level FCM to traverse its nodes and pass its value to higher-level map hierarchies, the user may assign directly an external value to nodes which link hierarchies. In practice, the simulation is carried out as if there are no links with other FCMs. Also the current implementation allows:  easy customization of the function f and easy reconfiguration of the formula Ati þ 1 to adapt to the specific characteristics of individual enterprises;  generation of scenarios for the same skeleton FCM;  automatic loop simulation until a user-defined equilibrium point has been reached. Alternatively, step-by-step simulation (with graphical output of partial results) is also available to provide a justification for the partial results. The following sections exhibit sample skeleton maps for the business and integrated categories, which provide relevance and research interest to this paper. Business metrics The mechanism proposes six different maps, each consisting of generic financial knowledge concepts as follows:  The ‘differentiation strategy’ map (Figure 10) reasons on the impact of strategic change to the competitive identity and financial status of the enterprise.  The ‘internal cost’ map summarizes concepts, which affect the overall cost of delivering products (or services) to the clients of the enterprise (e.g. value chain optimization, staff performance, execution cost).  The ‘execution cost’ map (Figure 11) exemplifies concepts that influence the production cost of the enterprise.  The ‘structural cost’ map reasons on the impact of concepts like outsourcing, product orientation, economies of scale, etc., to the overall business model. Figure 10 Differentiation strategy FCM 146 G. Xirogiannis et al. Knowledge and Process Management RESEARCH ARTICLE Figure 11 Execution cost FCM accompanied by a sample input/output/alert interface  The ‘customers’ appreciation’ map reasons on the impact of customer satisfaction in the differentiation effort and consequent financial results of the enterprise.  The ‘profit overview’ map (Figure 12) summarizes the effect of concepts like income and delivery cost on the overall profitability of the financial enterprise. Concepts denoted by ‘ # ’ expand further to lower-level maps. Similarly, ‘ " ’ denotes bottomup causal propagation. Integrated metrics The proposed integrated category consists of four (4) different maps as follows: Figure 12 Profit overview FCM Fuzzy Cognitive Maps 147 RESEARCH ARTICLE Knowledge and Process Management Figure 13 High-level FCM  The ‘high-level’ map (Figure 13) essentially relates concepts which fall under more than one category, as well as top-most concepts.  The ‘new entrants’ map supports reasoning of the impact of business model adjustments to meet the product standards (e.g. quality, differentiated products, price policies) set by new competitors.  The ‘productivity’ map (Figure 14) reasons on the impact of internal efficiency and sales adequacy on the overall profitability of the enterprise.  The ‘RAROC’ map (Figure 15) summarizes the impact of internal efficiency and sales adequacy on the risk-adjusted return on capital indicator of the enterprise. All the above-mentioned maps form a generic domain of FCMs. This knowledge domain serves as the basis of the proposed approach and can be modified to comply with the requirements of specific knowledge-capturing exercises. For example, further maps in the technical category could relate concepts that relate the adequacy of the production cycle with the expected financial performance of the enterprise (Irani et al., 2002; Valiris and Glykas, 2000). 148 Infrastructure & HR metrics The mechanism may also integrate various maps consisting of generic HR category concepts such as staff performance, motivation, carrier prospects, financial rewards and workload, as well as ‘social’ metrics which support reasoning of the impact of knowledge management, training and employee satisfaction to the financial model. Similarly the mechanism may also integrate various maps consisting of technical concepts such as centralization/ decentralization of IT infrastructure and IS/IT effectiveness. While the presentation of such concepts supports the completeness of the proposed methodology tool, they add little (if any) significance to the research activities presented by this paper. Assigning linguistic variables to FCM weights and concepts In order to define weight value of the association rules in an adaptive and dynamic manner, the following methodology is proposed. Financial managers are asked to describe the interconnection influence of concepts using linguistic notions. Influence of one concept over another is interpreted as a G. Xirogiannis et al. Knowledge and Process Management Figure 14 RESEARCH ARTICLE Productivity overview FCM Figure 15 RAROC overview FCM Fuzzy Cognitive Maps 149 RESEARCH ARTICLE Knowledge and Process Management linguistic variable in the interval [  1, 1]. Its term set T(influence) is: T(influence) ¼ {negatively very-very high, negatively very high, negatively high, negatively medium, negatively low, negatively very low, negatively very-very low, zero, positively veryvery low, positively very low, positively low, positively medium, positively high, positively very high, positively very-very high}. This paper proposes a semantic rule M to be defined at this point. The above-mentioned terms are characterized by the fuzzy sets whose membership functions  are shown in Figure 16.  M(negatively very-very high) ¼ the fuzzy set for ‘an influence close to 90%’ with membership function nvvh.  M(negatively very high) ¼ the fuzzy set for ‘an influence close to 80%’ with membership function nvh.  M(negatively high) ¼ the fuzzy set for ‘an influence close to 65%’ with membership function nh.  M(negatively medium) ¼ the fuzzy set for ‘an influence close to 50%’ with membership function nm.  M(negatively low) ¼ the fuzzy set for ‘an influence close to 35%’ with membership function nl.  M(negatively very low) ¼ the fuzzy set for ‘an influence close to 20%’ with membership function nvl.  M(negatively very-very low) ¼ the fuzzy set for ‘an influence close to 10%’ with membership function nvvl.  M(zero) ¼ the fuzzy set for ‘an influence close to 0’ with membership function z.  M(positively very-very low) ¼ the fuzzy set for ‘an influence close to 10%’ with membership function pvvl.  M(positively very low) ¼ the fuzzy set for ‘an influence close to 20%’ with membership function pvl.  M(positively low) ¼ the fuzzy set for ‘an influence close to 35%’ with membership function pl.  M(positively medium) ¼ the fuzzy set for ‘an influence close to 50%’ with membership function pm.  M(positively high) ¼ the fuzzy set for ‘an influence close to 65%’ with membership function ph.  M(positively very high) ¼ the fuzzy set for ‘an influence close to 80%’ with membership function pvh.  M(positively very-very high) ¼ the fuzzy set for ‘an influence close to 90%’ with membership function pvvh. The membership functions are not of the same size since it is desirable to have a finer distinction between grades at the lower and higher ends of the influence scale. As an example, three financial managers proposed different linguistic weights for the interconnection Wij from concept Ci to concept Cj: (a) positively high, (b) positively very high, (c) positively very-very high. The three suggested linguistics are integrated using a sum combination method and then the defuzzification method of centre of gravity (CoG) is used to produce a weight wij ¼ 0.77 in the interval [  1, 1]. This approach has the advantage that experts do not have to assign numerical causality weights but to describe the degree of causality among concepts. The same semantic rule and term set can be used to define the coefficients k1 and k2. A similar methodology can be used to assign values to concepts. The financial managers are also asked to describe the measurement of each concept using, once again, linguistic notions. Measurement of a concept is also interpreted as a linguistic Figure 16 Membership functions of linguistic variable influence 150 G. Xirogiannis et al. Knowledge and Process Management variable with values in the interval [  1, 1]. Its term set T(Measurement) ¼ T(Influence). A new semantic rule M2 (analogous to M) is also defined and these terms are characterized by the fuzzy sets whose membership functions 2 are analogous to membership functions . PRELIMINARY EXPERIMENTS The nature of the experiments Two informal experiments were conducted by utilizing metrics from actual (though random) knowledge-based decision support exercises in two major financial sector enterprises. For each experiment, a team of experts was engaged to:  provide linguistic variables for the causal weights, the concept values and the coefficients values to let the FCM algorithm reason about the impact of potential financial performance changes;  provide their independent expert estimates (using similar linguistic variables) of the impact of geographically dispersed activities to the overall business model. In both cases, the proposed tool iterated a subset of approximately 150 concepts spread over 10 sample hierarchical maps in order to calculate their equilibrium values. Both cases run on a typical business PC with a 2.4 GHz Pentium processor and 512 MB RAM. As far as the number of iterations is concerned, lower-level maps iterated 10 times on average. The average number of iterations increased to 25 for middle and upper-level maps. Only the topmost map increased the average number of iterations to approximately 80 (depending on the initial concept and weight values) due to the volume of map links. In practice, the actual process time was negligible on such a typical PC. Discussion Theoretical value Various aspects of the proposed modelling mechanism are now commented on. As far as the theoretical value is concerned, the proposed mechanism extends previous research attempts by:  allowing fuzzy node and weight definitions in the cognitive maps;  introducing a specific interpretation mechanism of linguistic variables to fuzzy sets;  proposing an updated FCM algorithm to suit better the KM domain of geographically dispersed organizations; Fuzzy Cognitive Maps RESEARCH ARTICLE  supporting node linking to establish map hierarchies and dynamic map selection during simulation;  concentrating on the actual KM activity and the associated business model;  allowing dynamic map decomposition and reconfiguration;  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 in the fuzzy interval [1, . . . , 1]);  supporting the user with appropriate interface windows when loops, cycles and node conflicts are identified. Practical value As far as the practical value of the proposed mechanism is concerned:  When compared to the expert estimates, the mechanism does not provide a fundamentally different ‘diagnosis’. On the contrary, it provides reasonably good approximations of the expert estimates.  The justification of the ‘diagnosis’ (essentially the metrics decomposition) proved extremely helpful in comprehending the sequence of complex concept interactions (essentially the knowledge roadmap).  The concept-based approach did not restrict the interpretation of the financial impact of geographically dispersed activities to the overall business model. The fuzzy interpretation of concept and weight values served as indications rather than precise arithmetic calculations.  The hierarchical (or partial) traversal of financial metrics improved the distributed knowledge monitoring throughout the geographical levels of the enterprise and stipulated targeted communication of the associated financial performance.  The realism of impact estimation depended on the number of concepts and weights, as well as on the estimation of their fuzzy characteristics (weights values, input values, coefficients, etc). However, the complexity and the length of the knowledge domain did not discourage the maintenance of the mechanism. Irrelevant and/or unnecessary knowledge maps could be isolated on demand to reduce the reasoning effort.  The adaptive nature of the proposed mechanism is also worth mentioning. For instance: —the tool can portray either a holistic or a scalable approach to financial modelling to comply with the knowledge modelling approach of the enterprise; 151 RESEARCH ARTICLE —knowledge categorization is compatible with either the ‘process view’ or the ‘organizational view’ of the enterprise; —hierarchical (and/or decentralized) composition/decomposition of knowledge concepts couples effectively with the hierarchical (and/or decentralized) structures of an enterprise; —skeleton FCMs accompanied by business cases (scenarios) improve the flexibility of the tool by allowing the user to generate alternative knowledge-based decision roadmaps with little extra effort; —maps can expand/retract on demand, allowing the user to utilize only the necessary subset of knowledge concepts; —maps are dynamic; further knowledge concepts may be added to encapsulate further knowledge interactions; —the FCM value calculation formula may change on demand to adapt better to the characteristics of the knowledge interactions of the enterprise. Added value Having established the theoretical and practical value of the proposed mechanism, it is useful to discuss also the added value of incorporating such a mechanism into KM exercises. It is the belief of this paper that the resulting tool provides real value to the principle beneficiaries and stakeholders of KM projects. For example:  The mechanism eases significantly the complexity of deriving knowledge-based decisions. Informal experiments indicated that the time required by experts to estimate manually the extensive impact of major changes to geographically dispersed business models could pose a considerable overhead. On the other hand, the elapsed time for automated knowledge-based decision support using FCM can be insignificant, once the map hierarchies have been set up.  To extend further this syllogism, realistic knowledge-based decision support should involve continuous argument of change options (e.g. application of best practices, alternative strategic scenarios) until an equilibrium solution accepted by all stakeholders has been agreed upon. Informal discussions with the principal beneficiaries and stakeholders of the two financial sector enterprises revealed that the proposed knowledge-based support can reduce significantly the impact estimation overheads, letting the stakeholders focus on the actual financial management exercise while exploring in depth 152 Knowledge and Process Management all alternatives and effectively controlling major change initiatives.  The proposed mechanism can also assist the financial performance evaluation of the enterprise on a regular basis. FCMs may serve as a back end to performance score cards (Bourne et al., 2000; Kaplan and Norton, 1996, 2001) to provide holistic strategic performance evaluation and management. However, a detailed analysis of this extension is beyond the scope of this paper. Preliminary usability evaluation Senior managers of the two major financial sector enterprises have evaluated the usability of the proposed tool and have identified a number of benefits that can be achieved by its utilization. Detailed presentation of the usability evaluation results are beyond the scope of the paper. However, a summary of major business benefits (as identified by senior managers) is provided to improve the autonomy of this paper:  Shared goals: —Concept-driven KM pulls individuals together by providing a shared direction and determination of internal change. —Shared KM and financial performance measurement enable business units to realize how they fit into the overall business model and what is their actual contribution. —Senior management receives valuable input from the business units (or the individual employees) who really comprehend the weaknesses of the current business model as well as the opportunities for performance-driven changes.  Shared culture: —All business units feel that their individual contribution is taken into consideration and provide valuable input to potential business model changes. —All business units and individuals feel confident and optimistic; they realize that they will be the ultimate beneficiaries of any potential business model changes. —The information and knowledge-sharing culture supports the enterprise’s competitive strategy and provides the energy to sustain this by exploiting fully the group and the individual 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. G. Xirogiannis et al. Knowledge and Process Management —The entire enterprise becomes increasingly receptive to internal changes, since the benefit can be easily demonstrated to individual business units.  Shared information: —All business units and individuals have the necessary information needed to set clearly their objectives and priorities. —Senior management can control effectively all aspects of business model changes. —The enterprise reacts rapidly to threats and opportunities fully utilizing benefits from KM. —It reinforces trust and respect throughout the enterprise. —It becomes easier for financial managers to retrieve and share pieces of knowledge. —Top management improves its capacity to integrate all incoming information for decision making (e.g. time restrictions, other managerial engagements, information given with a high/low level of detail). —Top management can review more frequently the firm’s risk measurement methodologies, models and assumptions for various types of risk (including operational risk). Summarizing, preliminary experimental results showed that FCM-based knowledge management can be an effective and realistic back end to decision support. This is considered to be a major contribution of the proposed methodology tool to actual KM exercises. Moreover, ex ante reasoning of the impact of geographically dispersed activities to the overall business model can be estimated with a moderate start-up effort. Scenario building, on the other hand, can be trivial once the skeleton FCMs have been established. RESEARCH ARTICLE cial institutions in order to provide an implementation of the cycle of knowledge flow. The proposed methodology tool utilized the fuzzy causal characteristics of FCMs to generate a hierarchical and dynamic network of interconnected financial performance concepts. Generic maps that supplement the knowledge-based decision process presented a roadmap for integrating hierarchical and FCMs into the business model of typical financial sector enterprises. The proposed mechanism should not be regarded only as an effective business modelling support tool. Its main purpose is to drive financial change activities rather than limit itself to qualitative simulations. Moreover, the proposed mechanism should not be seen as a ‘one-off’ decision aid. It should be a means for setting a course for continuous improvement (Langbert and Friedman, 2002). Future research will focus on conducting further real-life experiments to test and promote the usability of the tool, and also to identify potential pitfalls. Furthermore, future research will focus on the automatic determination of appropriate fuzzy sets (e.g. utilizing pattern recognition, mass assignments, empirical data) for the representation of linguistic variables to suit each particular financial domain. Finally, further research will focus on implementing backward map traversal, a form of adbuctive reasoning (Flach and Kakas, 1998). This feature offers the functionality of determining the condition(s) Cij that should hold in order to infer jk Ck. the desired Cj in the causal relationship Cij w! Incorporating performance integrity constraints reduces the search space and eliminates combinatory search explosion. Backward reasoning has been tested extensively in other applications and its integration in the proposed framework may prove beneficial. CONCLUSION This paper presented a knowledge management methodology tool to act as a decision support mechanism for geographically dispersed financial enterprises. The proposed decision aid may serve as a back end to adaptive KM by supporting ‘intelligent’ reasoning of the anticipated financial behaviour. 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