Neuro-Fuzzy Support of Knowledge Management in Social Regulation Sonja Petrovic-Lazarevic, Ken Coghill & Ajith Abraham School of Business Systems, Monash University, Australia email:
[email protected] Governance & Government Unit, Monash University, Australia email:
[email protected] School of Computing and Information Technology, Monash University, Australia email:
[email protected] Abstract The aim of the paper is to demonstrate the neuro-fuzzy support of knowledge management in social regulation. Knowledge, defined as human capability of making data and information useful for decision making processes, could be understood for social regulation purposes as explicit and tacit. Explicit knowledge relates to the community culture indicating how things work in the community based on social policies and procedures. Tacit knowledge is ethics and norms of the community. The former could be codified, stored and transferable in order to support decision making, while the latter being based on personal knowledge, experience and judgments is difficult to codify and store. However, since the tacit knowledge is expressed mainly through linguistic information, it can be stored and, therefore, support the knowledge management in social regulation through the application of fuzzy and neuro-fuzzy logic. Fuzzy logic modeling holds that human values inform the operation of the fuzzy logic by which the outcomes of interactions between interdependent members of any community are determined. With the system simulation where high precision is not required and parameters can be easily estimated for measurement, the fuzzy control model can be applied to estimating the appropriateness of self-organisation of the community. The model incorporates observed behavioral patterns seeking to explain their effects. The neuro-fuzzy approach is based on the integration of artificial neural networks and fuzzy inference systems. Neural network learning algorithms are used to fine tune the parameters of fuzzy inference system. Consequently, the neuro-fuzzy technique provides an ability to handle imprecision and uncertainty from data and to refine them by a learning algorithm. Applied in social regulation the neuro-fuzzy model creates fuzzy rules, which are easy to comprehend because of its linguistic terms and the structure of if-then rules.
Neuro-fuzzy models implementing Takagi-Sugeno Kang if-then rules and Mamdani type fuzzy inference systems are tested with tobacco smoking enforcement efforts. The obtained results demonstrate the relevance of each model to knowledge management in social regulation. Key words: neuro-fuzzy, fuzzy rules, knowledge management, decision-making, social regulation
1. Introduction Knowledge management is a process of managing and leveraging knowledge, or human capacity to request, structure and use information (Laudon, 2001; McKeown, 2001). Three types of knowledge could be classified: national culture (how things work in the nation), social networks (who can do what) and models for solving problems. National culture is related to policies and procedures established through social regulation. But it is also related to ethics and core values of the society. Social networks and problem solving are associated with an individual or social groups. Policies and procedures can be classified as an explicit knowledge or the knowledge that is codified and transferable in order to support decision making. This knowledge relates to a community culture indicating how things work in the community based on social policies and procedures. On the other hand, tacit knowledge - which is personal knowledge, experience and judgement - is difficult to codify. But since it is expressed mainly through linguistic information it appears that it can be stored with a help of fuzzy and neuro-fuzzy modelling. Fuzzy models use knowledge from human experts to present a system based on inputoutput measurements. That is, linguistic information that provides qualitative instructions and descriptions about the system can be usefully applied when the inputoutput measurements are not easy to obtain. In this respect, contemporary literature recognises the use of fuzzy models to represent the explicit knowledge in the form of fuzzy If..then rules with mechanism of reasoning in humanly understandable terms (Yen, Lanagari, 1999). However, since the tacit knowledge can also be expressed through linguistic information it appears that it can, also, be presented in the form of If…then rules and stored with a help of fuzzy and neuro-fuzzy logic. The research aims to evaluate the significance of neuro-fuzzy support in improving social regulation of access to cigarettes by minors. At present tobacco smoking is well established as a major contributor to ill health and premature death. Consequently, there is a general community concern about the uptake of smoking by young people. In this respect, local governments in the western suburban region of Melbourne Victoria conducted a project to enhance social regulation of access to cigarettes by minors. Findings demonstrated that self-organisation by tobacco retailers failed in respect of
societal public policy objectives affecting the sale of tobacco products to minors. The effects of enforcement and compliance on smoking rates amongst minors were not available from the project data (Coghill, Petrovic-Lazarevic, 2001). The paper provides the neuro-fuzzy learning process based on tacit knowledge in order to highlight what specific steps local government should undertake to reach the outcome with an increase in compliance. In this respect, the paper is divided as follows: Part two defines what has been done so far in order to reduce the rate of regular smoking among young people. Part three relates to neuro-fuzzy models application to easily supervise the learning process of adjusting governmental parameters to reach the expected outcomes. Part four illustrates the application of Tagaki-Sugeno Kang neuro-fuzzy models and Mamdani neuro-fuzzy models based on data provided by local governments. The paper ends with concluding remarks.
2. What is known 2.1 Social regulation of access to cigarettes by minors at present Tobacco smoking is associated with addiction to the nicotine content of cigarette smoke. Addiction to cigarettes commences as an uninformed and irrational action. Smoking by adolescents is related to emulating adult roles and is a symbol of belonging (Bachman et al 1997, 13). Ill-health effects are too remote to be of concern (Winstanley et al, 1995, 175). Recruitment of minors as smokers is different from the “rational addiction” of established adult smokers (Becker & Murphy 1988), and decisions by adults to continue or cease smoking. Early commencement of smoking is closely linked to both long-term smoking and heavy smoking (Tutt et al, 2000). Access to cigarettes is a major factor in the high levels of smoking among minors (Winstanley et al, 1995). The extent of social regulation of the community has effects in the particular instance of the regulation of access by minors to cigarettes in pursuit of the societal objective, expressed as public policy, of reduced incidence of smoking related ill-health and premature death, has been studied. The public policy lends itself to study as there has been considerable attention to the issue for at least two decades in several jurisdictions, with a variety of specific policy measures and a range in the enforcement effort applied and compliance levels achieved. This has been extensively reported in the literature, including changes over time following the amendment of public policy and its enforcement (Coghill, Petrovic-Lazarevic, 2001). In a recent paper, Tutt et al (2000) report on a six year project in the Central Coast region north of Sydney in the Australian State of New South Wales. The project commenced in 1993. The relevant legislative provisions (New South Wales 1991), which did not change significantly during the period reported, made it an offence for a person or their employee to sell tobacco to a person under eighteen years of age. Tutt et
al compared the effects of changes in enforcement and compliance with smoking rates amongst minors. The initial intervention relied entirely on publicity and education of both suppliers and minors and others who were potential consumers of tobacco products. A comparative project was conducted in six local government areas (LGAs) of the western suburban region of Melbourne in the Australian State of Victoria in 1998 and 1999. In two LGAs there were programs of education directed both at the community and at retailers specifically and enforcement through prosecution with supporting media reporting of successful prosecutions. In one, there were no educational programs but there was enforcement through prosecution with supporting media reporting of successful prosecution. In the three remaining areas – the control group - no change was made to seek higher levels of compliance. However, the proximity of the six LGAs and the common exposure to metropolitan media reporting meant that the retailers and others in the control areas might have been exposed to news of the successful prosecutions. 2.2 Fuzzy logic applicability in reducing adolescent smoking rates Fuzzy modelling deals with structure specification, parameter estimation, and model validation. Structure specification indicates finding input variables, its membership functions, and fuzzy rules comprising the underlying model. Parameter estimation relates to determination of parameters of the model through some appropriate optimisation or any other method. Model validation is testing the model on its accuracy (Yen, Lanagari, 1999). This type of modelling if applied for a system simulation does not require high precision in determining structure specification and has parameters that can be easily estimated for measurement. Therefore, it can be used for social regulation simulation and testing. A fuzzy control model consists of several steps known as Mamdani controllers (Bezdek et al, 1999). First step, fuzzification, defines linguistic variables that present inputs and outputs of the model. Second step, inference, represents a set of fuzzy rules. Rules evaluation, as a third step, translates real input numbers to parameterised membership functions. Fourth step, conflict resolution, relates to choosing control action as a result of application of a control rule. Fifth step, defuzzification, transforms the output fuzzy set into a crisp value by a defuzzification procedure ( Bojadziev and Bojadziev, 1995) The fuzzy control model was applied in estimating the type of social regulation. That is, the research has been done about the implications of widespread behavioural characteristics and values found in human communities for the operation of fuzzy logic in social organization (Coghill, Petrovic-Lazarevic, 2001). The research distinguishes between community and society, after Nancy (1991). It argues that there are features of human behaviour and values which are so general as to be regarded as fundamental aspects of mankind, notwithstanding some variations in their rankings between and within communities. Amongst these features are mankind's essentially social nature.
Communities are comprised of individuals who are interdependent on each other and who interact with each other. The interactions occur according to fundamental patterns of human behaviour and values, notwithstanding the capacity for the exercise of free will and independent action. This understanding of the nature of communities stands in contra-distinction to perspectives that treat people as autonomous individuals. For estimating the type of social regulation of smoking among minors it is assumed that social regulation occurs in many forms, including the informal social customs which govern interpersonal relationships, systems of belief and behaviour mediated through religious and similar social institutions, constitutional arrangements and formal regulation established through legislative processes. The applied model considers three variables. These are: the baseline condition (compliance rate by retailers' obedience), maximum enforcement according to protocol, enforcement community education (no retailer education). Variables are presented in a membership form expressing explicit expert systems knowledge. Then, If…then enforcement effort rules are introduced following the fuzzy control procedure. The applied fuzzy control model demonstrates an estimate of the outcomes of social regulation given its formal provision of the social regulation regime ( Coghill, PetrovicLazarevic, 2000). Although the model is based on expert systems, it has limitations. Firstly, it only covers explicit knowledge based on social policies and procedure. Secondly, it does not reflect tacit knowledge of community based on local ethics and norms that can significantly reduce adolescent smoking rates. Thirdly, the model does not provide government representatives with the answer to what extent to concentrate on available social regulation measures in anticipating smoking enforcement efforts.
3. Neuro-fuzzy support of social regulation Neuro-fuzzy modelling is based on combination of neural networks and fuzzy models. It is a way to create a fuzzy model "from data by some kind of learning method that is motivated by learning procedures used in neural networks" (Bezdek et al, 1999). A Fuzzy Inference System (FIS) can utilize human expertise by storing its essential components in rule base and database, and perform fuzzy reasoning to infer the overall output value. The derivation of if-then rules and corresponding membership functions depends heavily on the a priori knowledge about the system under consideration. However there is no systematic way to transform experiences of knowledge of human experts to the knowledge base of a FIS. There is also a need for adaptability or some learning algorithms to produce outputs within the required error rate (Abraham 2001).
On the other hand, Artificial Neural Network (ANN) learning mechanism does not rely on human expertise. Due to the homogenous structure of ANN, it is hard to extract structured knowledge from either the weights or the configuration of the ANN. The weights of the ANN represent the coefficients of the hyper-plane that partition the input space into two LGAs with different output values. If we can visualize this hyper-plane structure from the training data then the subsequent learning procedures in an ANN can be reduced. However, in reality, the a priori knowledge is usually obtained from human experts and it is most appropriate to express the knowledge as a set of fuzzy if-then rules and it is not possible to encode into an ANN. Table 1 summarizes the comparison of FIS and ANN. Table 1. Complementary features of ANN and FIS ANN Black box Learning from scratch
FIS Interpretable Making use of linguistic knowledge
To a large extent, the drawbacks pertaining to these two approaches seem complementary. Therefore it is natural to consider building an integrated system combining the concepts of FIS and ANN modeling. A common way to apply a learning algorithm to a FIS is to represent it in a special ANN like architecture. However the conventional ANN learning algorithms (gradient descent) cannot be applied directly to such a system as the functions used in the inference process are usually non differentiable. This problem can be tackled by using differentiable functions in the inference system or by not using the standard neural learning algorithm (Abraham & Nath, 2000). In our research we used Adaptive Network Based Fuzzy Inference System (ANFIS) that implements a Takagi Sugeno Kang (TSK) fuzzy inference system (Jang J.S.R, 1991) and an Evolving Fuzzy Neural Network (EFuNN) implementing a Mamdani fuzzy inference system (Kasabov, 1998). In a TKS fuzzy inference system the conclusion of a fuzzy rule is constituted by a weighted linear combination of the crisp inputs rather than a fuzzy set. For a first order TSK model, a common rule set with two fuzzy if-then rules is represented as follows: Rule 1: If x is A1 and y is B1, then f1 = p1x + q1y + r1 Rule 2: If x is A2 and y is B2, then f2 = p2x + q2y + r2 where x and y are linguistic variables and A1, A2,, B1,, B2 are corresponding fuzzy sets and p1 , q1, r1 and p2, q2, r2 ,are linear parameters.
Figure 1. TSK type fuzzy inference system Figure 1 illustrates the TSK fuzzy inference system when two membership functions each are assigned to the two inputs (x and y). TSK fuzzy controller usually needs a smaller number of rules, because their output is already a linear function of the inputs rather than a constant fuzzy set.
Figure 2. Architecture of the ANFIS Figure 2 depicts the five layered architecture of ANFIS and the functionality of each layer is as follows: Layer-1 Every node in this layer has a node function
Oi1 = µ Ai ( x ) , for i =1, 2 or Oi1 = µ Bi − 2 ( y ) , for i=3,4,….
is the membership grade of a fuzzy set A ( = A1, A2, B1 or B2) and it specifies the degree to which the given input x (or y) satisfies the quantifier A. Usually the node function can be any parameterized function. A Gaussian membership function is specified by two parameters c (membership function center) and σ (membership function width) Oi1
2 1 − æç x − c ö÷ Guassian (x, c, σ) = e 2 è σ ø
Parameters in this layer are referred to premise parameters. Layer-2 Every node in this layer multiplies the incoming signals and sends the product out. Each node output represents the firing strength of a rule.
Oi2 = wi = µ Ai ( x ) × µ Bi ( y ), i = 1,2...... . In general any T-norm operators that perform fuzzy AND can be used as the node function in this layer. Layer-3 Every i-th node in this layer calculates the ratio of the i-th rule’s firing strength to the sum of all rules firing strength.
Oi3 = wi =
wi , i = 1,2.... . w1 + w2
Layer-4 Every node i in this layer is with a node function
O14 = wi f i = wi ( pi x + qi y + ri ) , where wi is the output of layer3, and {pi , qi , ri } is the parameter set. Parameters in this layer will be referred to as consequent parameters. Layer-5 The single node in this layer computes the overall output as the summation of all incoming signals:
O15 = Overall output = å wi f i = i
åi wi f i . åi wi
ANFIS makes use of a mixture of backpropagation to learn the premise parameters and least mean square estimation to determine the consequent parameters. A step in the
learning procedure has two parts: In the first part the input patterns are propagated, and the optimal conclusion parameters are estimated by an iterative least mean square procedure, while the antecedent parameters (membership functions) are assumed to be fixed for the current cycle through the training set. In the second part the patterns are propagated again, and in this epoch, backpropagation is used to modify the antecedent parameters, while the conclusion parameters remain fixed. This procedure is then iterated. Evolving Fuzzy Neural Network (EFuNN) implements a Mamdani type FIS and all nodes are created during learning. EFuNN has a five-layer structure as shown in Figure 4. Figure 3 illustrates a Mamdani FIS combining two fuzzy rules using the max-min method. According to the Mamdani FIS, the rule antecedents and consequents are defined by fuzzy sets and has the following structure:
if x is A1 and y is B1 then z1 = C1 where A1 and B1 are the fuzzy sets representing input variables and C1 and is the fuzzy set representing the output fuzzy set. In EFuNN, the input layer is followed by the second layer of nodes representing fuzzy quantification of each input variable space. Each input variable is represented here by a group of spatially arranged neurons to represent a fuzzification of this variable. Different membership functions can be attached to these neurons (triangular, Gaussian, etc.). The nodes representing membership functions can be modified during learning. New neurons can evolve in this layer if, for a given input vector, the corresponding variable value does not belong to any of the existing membership functions to a degree greater than a membership threshold. The third layer contains rule nodes that evolve through hybrid supervised/unsupervised learning. The rule nodes represent prototypes of input-output data associations, graphically represented as an association of hyper-spheres from the fuzzy input and fuzzy output spaces. Each rule node, e.g. rj, represents an association between a hyper-sphere from the fuzzy input space and a hyper-sphere from the fuzzy output space; W1(rj) connection weights representing the co-ordinates of the center of the sphere in the fuzzy input space, and W2 (rj) – the co-ordinates in the fuzzy output space. The radius of an input hyper-sphere of a rule node is defined as (1- Sthr), where Sthr is the sensitivity threshold parameter defining the minimum activation of a rule node (e.g., r1, previously evolved to represent a data point (Xd1,Yd1)) to an input vector (e.g., (Xd2,Yd2)) in order for the new input vector to be associated with this rule node. Two pairs of fuzzy input-output data vectors d1=(Xd1,Yd1) and d2=(Xd2,Yd2) will be allocated to the first rule node r1 if they fall into the r1 input sphere and in the r1 output sphere, i.e. the local normalised fuzzy difference between Xd1 and Xd2 is smaller than the radius r and the local normalised fuzzy difference between Yd1 and Yd2 is smaller than an error threshold Errthr. The local normalised fuzzy difference between two fuzzy membership vectors d1f and d2f that represent the membership degrees to which two real
values d1 and d2 data belong to the pre-defined membership function, are calculated as D(d1f,d2f) = sum(abs(d1f - d2f ))/sum(d1f + d2f ). If data example d1 = (Xd1,Yd1), where Xd1 and Xd2 are correspondingly the input and the output fuzzy membership degree vectors, and the data example is associated with a rule node r1 with a centre r11 , then a new data point d2=(Xd2,Yd2), will also be associated with this rule node through the process of associating (learning) new data points to a rule node. The centres of this node hyper-spheres adjust in the fuzzy input space depending on a learning rate lr1, and in the fuzzy output space depending on a learning rate lr2, on the two data point's d1 and d2. The adjustment of the centre r11 to its new position r12 can be represented mathematically by the change in the connection weights of the rule node r1 from W1( r11 ) and W2( r11 ) to W1( r12 ) and W2( r12 ) according to the following vector operations:
W2 ( r12 ) = W2( r11 ) + lr2 . Err(Yd1,Yd2) . A1( r11 ) W1( r12 )=W1 ( r11 ) + lr1 . Ds (Xd1, Xd2) where Err(Yd1,Yd2)= Ds(Yd1,Yd2)=Yd1-Yd2 is the signed value rather than the absolute value of the fuzzy difference vector; A1( r11 ) is the activation of the rule node r11 for the input vector Xd2. While the connection weights from W1 and W2 capture spatial characteristics of the learned data (centres of hyper-spheres), the temporal layer of connection weights W3 captures temporal dependencies between consecutive data examples. If the winning rule node at the moment (t-1) (to which the input data vector at the moment (t-1) was associated) was r1=inda1(t-1), and the winning node at the moment t is r2=inda1(t), then a link between the two nodes is established as follows:
W3(r1,r2) (t) = W3(r1,r2) (t-1) + lr3. A1(r1) (t-1) A1(r2)) (t), where: A1(r) (t) denotes the activation of a rule node r at a time moment (t); lr3 defines the degree to which the EFuNN associates links between rules (clusters, prototypes) that include consecutive data examples (if lr3=0, no temporal associations are learned in an EFuNN structure). The learned temporal associations can be used to support the activation of rule nodes based on temporal, pattern similarity. Here, temporal dependencies are learned through establishing structural links. The ratio spatial-similarity/temporal-correlation can be balanced for different applications through two parameters Ss and Tc such that the
activation of a rule node r for a new data example dnew is defined as the following vector operations:
A1 (r) = f ( Ss . D(r, dnew) + Tc .W3(r (t-1), r)) where f is the activation function of the rule node r, D(r, dnew) is the normalised fuzzy distance value and r (t-1) is the winning neuron at the previous time moment. The fourth layer of neurons represents fuzzy quantification for the output variables. The fifth layer represents the real values for the output variables.
Figure 3. Mamdani fuzzy inference system
Figure 4. Architecture of EFuNN
4. Neuro-Fuzzy model evaluation and experimentation results Simulations are done with the data provided from the Victoria government for the six LGAs of the state. Each data set was represented by three input variables and two output variables. The input variables considered were compliance rate by retailers, enforcement according to protocol and community education. The corresponding output variables were compliance rate by retailers and compliance rate by retailers projected as estimated rate of smoking uptake by minors. 70 per cent (random) of each data for training and 30 per cent (random) for testing were used. That is, the neuro-fuzzy models ANFIS and EFuNN were first trained on 70 per cent data. Then it is tested on 30 per cent data. 4.1 ANFIS Training Two Gaussian membership functions attached to each input variables were applied. Six rules were learning based on the training data for each of the six LGAs. The training was terminated after 1000 epochs. Training performance is reported in Table 2. The developed inference system is depicted in the Figures 5-16 of the Neuro-Fuzzy test Results using ANFIS. 4.2 EFuNN Training Three Gaussian membership functions for each input variable were used as well as the following evolving parameters: sensitivity threshold Sthr=0.99, error threshold Errthr=0.001 and learning rates for first and second layer = 0.01. EFuNN uses a one pass training approach. The network parameters were determined using a trial and error approach. Online learning in EFuNN resulted in creating 20 rule nodes. Training results are summarized in Table 2. 4.3 Test results The test results for all six LGAs using ANFIS and EFuNN are depicted in Table 2. As evident from the results, ANFIS performed better than EFuNN in terms of performance error. However, EFuNN has outperformed ANFIS in terms of computational time.
Table 2 LGA Time
ANFIS Training Trg RMSE Test RMSE O/P 1 O/P 2 O/P 1 O/P 2
Time
EFuNN Training Trg RMSE Test RMSE O/P 1 &2 O/P 1 &2
1
58
1.2E-4
5.0E-5
0.034
2E-4
4
7.3E-3
0.2201
2 3 4 5 6
54 54 52 50 56
0.0011 0.0011 3.3E-4 3.1E-4 8.0E-4
1.9E-4 1.9E-4 1.6E-4 1.5E-4 5.1E-3
0.058 0.058 0.044 0.027 3E-5
0.032 0.032 0.031 0.010 0.040
3 3 3 4 4
9.2E-3 9.2E-3 5.2E-3 0.0317 0.045
0.421 0.421 0.429 0.653 0.566
Neuro-Fuzzy Test Results (developed rules) using ANFIS
Figure 5. Output 1 (LGA 1)
Figure 7. Output 1 (LGA 2 &3)
Figure 6. Output 2 (LGA 1)
Figure 8. Output 2 (LGA 2 &3)
Figure 9. Output 1 (LGA 4)
Figure 10. Output 2 (LGA 4)
Figure 11. Output 1 (LGA 5)
Figure 12. Output 2 (LGA 5)
Figure 13. Output 1 (LGA 6)
Figure 14. Output 2 (LGA 6)
5. Conclusions In this paper the neuro-fuzzy support of knowledge management in social regulation was investigated. That is, the explicit knowledge based on social policies and procedures to reduce smoking among youngsters, but also the tacit knowledge expressed through the applied membership functions. Empirical results show the dependability of the proposed techniques. Neuro-fuzzy systems make use of linguistic knowledge of fuzzy inference system and the learning capability of neural networks. Thus we are able to precisely model the uncertainty and imprecision within the data as well as to incorporate the learning ability of neural networks. Compared to neural networks, an important advantage of neurofuzzy systems is its reasoning ability (if-then rules) of any particular state.
ANFIS performed better than EFuNN in terms of performance error with a compromise on time. EFuNN performed approximately 12 times faster than ANFIS. Hence where performance speed is the criteria EFuNN sounds to be the ideal candidate. As EFuNN uses a one pass training approach it is also suitable for online learning of new data sets. Depending on governmental requests it is possible to compromise between performance error and computational time. An important disadvantage of ANFIS and EFuNN are the determination of the network parameters like number and type of membership functions for each input variable, membership functions for each output variable and the optimal learning parameters. However, selection of optimal parameters may be formulated as an evolutionary search to make the neuro-fuzzy systems fully adaptable and optimal according to government representatives requests by providing the answer to what extent to concentrate on available social regulation measures in anticipating smoking enforcement efforts.
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