Growing role of intellectual capital within organizations is affecting new strategies related to knowledge management and competence development. Among different aspects related to this field, knowledge diffusion has become one of the interesting areas from both practitioner and researcher’s perspectives. Several models were proposed with main goal of simulating diffusion and explaining the nature of these processes. Existing models are focused on knowledge diffusion and they assume diffusion within a single layer using knowledge representation. From the organizational perspective connecting several types of knowledge and modelling changes of competence can bring additional value. In this paper we extended existing approaches by using multilayer diffusion model and focused on analysis of competence development process. The proposed model describes competence development process in a new way through horizontal and vertical knowledge diffusion in multilayer network. In the network, agents collaborate and interchange various kinds of knowledge through different layers and these mutual activities affect the competencies in a positive or negative way. Taking into consideration worker’s cognitive and social abilities and the previous level of competence the new competence level can be estimated. The model is developed to support competence management in different organizations.
Employees’ competence becomes the main part of organization’s intellectual capital [
Competence is an observable or measurable ability of an actor to perform a necessary action(s) in a given context(s) to achieve a specific outcome(s) [
In our work the modelling of the competence development process is based on the knowledge diffusion model that extends current solutions. The approach is new and required special characteristics of diffusion model. We developed a multilayer diffusion model based on the multilayer graph reflecting organisation’s network. In the graph each layer represents competence’s component (some kind of knowledge). There is an interaction between layers defined as a vertical diffusion. The horizontal diffusion occurs on every layer’s level and relates to the diffusion of one type of knowledge between knowledge workers. Moreover, every node of organisation’s network represents knowledge worker with individual set of knowledge and own cognitive and social potentials for learning (self-learning) and teaching (training). The knowledge worker, in every step of simulation, is looking for best source of knowledge. In addition, depending on node’s neighbourhood, the knowledge can be forgotten.
The existing diffusion models from the literature were not suitable for competence modelling due to their limitations. The most important drawback is the lack of simultaneous support of vertical and horizontal diffusion. Moreover, diffusion logic proposed in the literature does not reflect the competence development process. In our approach the diffusion logic is set to search for best teacher (source of knowledge) in node’s neighbourhood. The best teacher is a node with the highest value of knowledge and teaching ability. The diffusion result is affected by the learning/teaching abilities of nodes, initial value of knowledge, vertical diffusion form other layers (relation between knowledge), and forgetting process. Similarly constructed diffusion model cannot be found in the literature.
The rest of the paper is organized in the following way. Section
In the literature we can find different definitions of competence linked with three fundamental characteristics: resources, context, and objectives [
Competence-based approaches have proved to be a critical tool in many organizational functions, such as employment planning, recruitment, trainings, raising work efficiency, personal development, and managing key competencies [ Competence-based approach can provide identification of the skills, knowledge, behaviours, and capabilities needed to meet current and future personnel selection needs, in alignment with the differentiations in strategies and organizational priorities. Competence-based approach can focus on the individual and group development plans to eliminate the gap between the competencies requested by a project, job role, or enterprise strategy and those available.
The important way of competence developing is a community of practice because a growing number of people and organizations in various sectors are now focusing on communities of practice as a key to improving their performance [
From a pragmatic point of view competence is a combination of components, usually related to knowledge, experiences, and skills/abilities. It is important to notice that it is not possible to directly develop another person’s competence. It is just possible to set the scene, to provide the tools, and to act like a catalyst [
There are some challenging issues with competence-based approach [
In order to overcome this challenging issue the following attributes had to be identified and analysed [
From observation of the organization we can observe that in any organization the competencies are considered at the following levels [
The literature proposed some content of particular levels [ individual competence (e.g., result orientation, role commitment, continuous learning, networking, creativity, intelligence, behavioral traits (including such aspects as honesty and maturity), motivation, and communication capabilities); team competence (e.g., knowledge sharing, cultural integration, resources utilization, innovation, and management/leadership); organizational competence (e.g., knowledge landscape, knowledge assets, information sharing, push/pull power balance, and synergy creation).
The dichotomy between definitions of competence that target individual workers and definitions that target the results of their work is a complex issue [
For the propose of model designing it is required to identify the structure of competence. Competencies are considered as a union of different components (see Table
List of main competence components.
Competence components (categories of resources) | Base references |
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(i) Knowledge |
Treasury Board of Canada Secretariat ( |
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(i) Knowledge |
HR-XML ( |
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(i) Input competencies |
[ |
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(i) Know-what |
[ |
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(i) Knowledge |
[ |
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(i) Knowledge (what you learn in education) |
[ |
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(i) Knowledge (theoretical knowledge, knowledge of the existing, and knowledge of procedures) |
[ |
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(i) Knowledge (includes theoretical knowledge and procedural knowledge) |
[ |
After the presentation of the components of competence it is crucial to understand what the relationship between them is. A good way of understanding the relationship is use of competence ontology structures, which can be found in the literature [ define an organization-wide role structure based on the competencies required by job functions and organizational positions; identify the competencies required in order to perform the various activities involved in each business process and assignment of roles to process activities based on these competencies; identify the competencies acquired in the organization and assignment of users to roles through competence matching.
Moreover, the competence ontology is the most important part of an effective competence management system [
Diffusion of knowledge can be analysed in several dimensions. Knowledge diffusion, treated as a part of an innovative process, is the process by which an innovation is communicated through certain channels over time among the members of a social system [
In the area of scientific research knowledge diffusion can be defined as the adaptations and applications of knowledge documented in scientific publications and patents [
Technology diffusion is a complex social communication process. According to [
In a learning organisation knowledge diffusion is a process of knowledge communication and learning [
It is important to say that tracing knowledge diffusion is a challenging issue due to the extreme complexity of diffusion processes [
From the economic point of view the knowledge diffusion process is related to the transfer of intellectual capital. Knowledge diffusion takes place through worker mobility [
At cognitive level the research of knowledge diffusion is related to the problem of [
The next important issue, related to knowledge transfer, is homophily, defined as tendency of people to associate relatively more with those who are similar to them than with those who are not [
Knowledge diffusion must be based on efficient communication channels between all actors. The importance of such efficient channels is empirically supported by MacGarvie [
The process of diffusion of knowledge is based on several communication mechanisms [
From one point of view knowledge diffusion is intended by the organization. According to Canals [
The problem of knowledge diffusion is an important element of complex network theory application. Based on the literature analysis we can recognise two approaches to problem modelling [
When discussing the knowledge diffusion modelling we should keep in mind two dimensions of this problem: network topology and design of interaction rules driving knowledge transmission. Many studies show that the effectiveness of the diffusion mainly depends on the network structure and the seeding strategy used [
The main concepts of knowledge transmission mechanism, according to [
The complex nature of knowledge diffusion problem is difficult to conceptualise and formalize. However, there are some propositions in the literature. In [
A number of papers studied a model of a population of agents whose interaction network coevolves with knowledge diffusion and accumulation. General idea of the proposed model is based on the Cowan and Jonard model (CJ) [ agents are arranged in one-dimensional space; each agent occupies one vertex and may interact with their the population of individuals is endowed with different levels of initial knowledge; a small number of agents are “experts” and are endowed with a high level of knowledge in at least one value of the vector; all individuals interact among themselves, exchanging information; knowledge is a nonrival good and can be transferred without decreasing the level of knowledge possessed by each trader.
In our work we extended the classical CJ model to multidimensional vertical and horizontal diffusion scheme. Moreover, new mechanism of knowledge processing was introduced including self-learning and forgetting processes. Some authors noticed the importance of these factors (e.g., dissemination ability and knowledge forgetting in Geng and Mao work [
In [
The paper [
The key factors that affect the speed and the distribution of knowledge diffusion are identified by Morone et al. [
The diffusion of different kinds of knowledge in an organisation can be interpreted as a multilayers network (share the same set of nodes connected with many links grounded on different layers). In the literature the main emphasis is placed on multilayered diffusion processes through a multilayered material for a wide range of applications, including industrial, biological, electrical, and environmental areas [
So far there has been no work combining the competence with knowledge diffusion. Moreover, the proposed model with vertical and horizontal diffusion for multilayer organisation graph with self-learning and forgetting processes is a new approach to the problem of knowledge diffusion.
Modelling of the competence development based on the knowledge diffusion process requires a new approach. There are a couple of reasons for that. Competence cannot be changed directly; we can only influence its components. The value of the components of competence (see Table
In the proposed model, the components of competence are represented by the layers in the multilayer graph. From the point of view of the diffusion process, the content of layers is invalid and the diffusion process is focused on knowledge flow and not their content or meaning. We define only the relationship between their elements, which may be damping (weakening) or forcing (strengthening). This approach is similar to Shannon’s information theory where content of the messages has no meaning. However, there is an opinion in the competence literature that the process of competence computing should be understood as enabling the use of competence databases for inference and combination of competencies for different functions and processes, not as a reductionist account of competencies to numeric models [
Proposition of 3-class layers model for diffusion model for competence development [ Class 1: know-how—practical, hands-on forms of knowledge gained through incremental improvements to products and processes. Class 2: know-why—theoretical forms of understanding that enable the creation of new kinds of products and processes. Class 3: know-what—a strategic form of understanding about the value creating purposes to which available know-how and know-why forms of knowledge may be applied.
We assume that one layer in our model is dedicated to one kind of knowledge, which belongs to one class of competence’s components. The question arises: can each component of competence be called knowledge? The works [ Knowledge can be explicitly formalized—texts, documents multimedia. Knowledge can be a practice—it rests on the accumulation of experiments. Knowledge can be tacit—all cannot be formalized. Its transmission requires suitable means: conversation, training, joint work, and so forth. Knowledge can be social—the technical know-how of a company does not rest on an individual but on the interaction of all the members of its technical community. It is while collaborating, by confronting their points of view, that these technicians create and finally hold new knowledge. Knowledge is dynamic and evolves/moves in time.
In our approach the term
Every node in the network represents single knowledge worker. According to [
The organization
The knowledge domain in organisation
The methods of knowledge modelling mainly focus on the formally representation of relationship between different areas/element/types of knowledge. The best way to do is to use the ontological approach. Ontology is a formal, explicit specification of a shared conceptualization [
In our approach the competence acquisition is a result of combination of different competence’s components [
Based on the knowledge space theory let
Let
For
In a knowledge network the node actively processes knowledge and edges represents channels for knowledge relocation [
The knowledge network for organisation
Every layer in
For any node from
Based on the multilayer graph
In order to distinguish personal abilities for communication on knowledge level, two parameters are introduced: cognitive abilities for node social abilities for node
Competence can get gradually stronger, in a situation where surroundings affect and stimulate its components. For example, we acquire new skills in a training session or while working (e.g., software developers programming every day). Competence (its level) can also degrade. The most common reason for this is not using the given competence in everyday work. The other is thanks to technology progress which makes the components of competence outdated. We can distinguish different relations between competencies which affect the interaction between them. Increasing competence in a certain competence group (e.g., communication) can affect the increase of other competencies (e.g., sales of products). Next issues regarding competence processing in an organisation start to show up when we take a look from a company’s perspective. From the company’s point of view, certain competencies are created only by combining the competencies of a greater number of employees. The complexity of these combined competencies is too great for a single person to obtain this kind of competence.
In this approach we do not analyse the content of knowledge included in competence. In our case we are interested in the competence’s level, which allows us to analyse the knowledge and competencies growth and dynamics in the organization. In the presented method the competence value will be normalized to range
Linking competence value with expertise level.
Approximate value of |
Expertise level | Description (based on [ |
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0–0,2 | Novice | Minimal exposure to the domain. |
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0,2–0,4 | Initiate | Began introductory instruction to the domain. |
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0,4–0,6 | Apprentice | Undergoing a program of domain learning beyond the introductory level. Traditionally the apprentice is immersed in the domain by a more experienced employee. |
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0,6–0,8 | Journeyman | Person who can perform a day’s labor unsupervised, although working under orders. |
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0,8–1 | Expert | The distinguished or brilliant journeyman, highly regarded by peers, whose judgments are uncommonly accurate and reliable, whose performance shows consummate skill and economy of effort, and who can deal effectively with rare or “tough” cases. Also an expert is one who has special skills or knowledge derived from extensive experience with subdomains. |
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Master | Master is any journeyman or expert who is also qualified to teach those at a lower level. Traditionally, a master is one of an elite group of experts whose judgments set the regulations, standards, or ideals. |
The competence set for organization
There relationships between competence and knowledge in organization
Relation mash for competencies and knowledge relation.
Based on the matrix
In order to analyse the competence development in an organization in addition to the structure of the network, which represents the relationships that exist between staff, we also need to describe the processes associated with the competence development. Let us introduce the time index:
In the proposed model the knowledge diffusion process takes place in two directions: vertical (
Horizontal knowledge diffusion occurs only between active nodes. There are two possible methods of knowledge diffusion between nodes: broadcast: the node transfers knowledge to all connected nodes; multicast: the node transfers knowledge to a selected set of nodes; the set of receiving nodes may be selected randomly or based on some strategies.
In our approach we focus on the multicast scheme for horizontal knowledge diffusion. Every node on selected layer of multilayer graph
Horizontal knowledge diffusion is calculated for node
The interpretation of knowledge diffusion function depends on the purpose and goals of the organization. In addition, the final function form depends on the specific nature and structure of knowledge networks and knowledge resources in an organization. For the purposes in the paper we have proposed functions ((
Let us propose some form of function
Let us define the vertical diffusion matrix for worker
Vertical knowledge diffusion for nodes
Let us propose some form function for vertical knowledge diffusion:
The function (
Over time employee competencies (knowledge) are reduced if they are not stimulated by the workers from surrounding and the work itself. From the formal point of view knowledge forgetting model can be found in [
Let us introduce a formula for average knowledge transfer potential for node neighbourhood calculation:
If for node
In proposed function
If the knowledge value for node
One of the forgetting formula propositions is the following:
Due to the rapid obsolescence of knowledge and the requirements of increasingly complex processes there is a need to continuously acquire new knowledge by employees. Lifelong learning philosophy [
If for node
The function
For
Competence development based on the knowledge diffusion involves various processes: horizontal knowledge diffusion, vertical knowledge diffusion, knowledge forgetting, and self-learning. In addition, knowledge diffusion is a two-dimensional process. In this section we will develop the main points of procedure for knowledge diffusion calculation in multilayer networks.
Layer selection is based on layer’s ranking
Node selection is based on node’s ranking
FOR all subsequent element FOR all subsequent element Execute horizontal knowledge diffusion process: Execute vertical knowledge diffusion process: Calculation average knowledge transfer potential for node neighbourhood If Execute vertical knowledge diffusion process: If Execute vertical knowledge diffusion process:
The logic of horizontal diffusion refers to the analysis of components’ values on single level. Because we operate on single layer the problem of granularity scales of competence’s component is not a crucial one. The problem could arise in terms of relations between layers (which represent competence components). Mutual vertical relations between layers can be nonlinear and based on own logic. In presented approach the matrix
The presented approach, from the methodical point of view, is an agent based simulation. This kind of simulation is adequate for such systems with complex interaction. In our simulation we based on the NetLogo framework [
The model of knowledge diffusion is used to analyze the development of competencies in an organization. However, its final application is competence management. Keeping in mind main management axioms [ Axioms of management 1: the object is suitable for observations and measurements. The presented model gives ability to observe and measure every component of competence. Moreover, all knowledge flow between actors can be tracked and analysed. Axioms of management 2: at the interval of observation object can change its state. The dynamics of knowledge flows on different levels of network is noticeable. The process of knowledge diffusion is based on the continuously changing value of actors (workers) knowledge. Axioms of management 3: the predetermined target defined expected object’s state. In the organization the target is set on the strategic level and concerns for expected values of competencies. Axioms of management 4: there are alternative ways to influence the behaviour of an object. Any types of knowledge, components of competence, can be changed by training (increase of knowledge level), expert’s mentoring (direct diffusion of knowledge), or team building (network reconfiguration). Axioms of management 5: there is a predefined criterion of management efficiency. The criterion determines the degree of matching acquired competencies to market or company requirements. Axioms of management 6: there are resources for the execution of the decision. The network consists of nodes which represents knowledge workers (actors).
Moreover, in the discussed context, competence management is a process of tracking changes in the content of knowledge related to the competencies.
All the concepts of knowledge diffusion models require validation. In real conditions only few models can be checked due to the limitation of data. As a result, a number of simulation network models are used. The description of models can be found in [
At the beginning the network generated by the Watts-Strogatz model is a regular network, and it can rewire from the regular network to the random network by adjusting the parameter
The analyzed simulation model contains 500 nodes (agents). The network is generated based on the Watts-Strogatz model for
Hierarchical structure for knowledge.
Due to high stochastic nature of competence development process and multidimensionality of the proposed model the deep simulation analysis is very difficult to maintain. In order to illustrate the different aspects of the proposed model, in the context of competence management, we will discuss a number of case studies.
The proposed model was verified during simulations in terms of multilayer diffusion and development of competence. Simulations were performed on Watts-Strogatz network with 0.1 rewiring probability. Initial knowledge to each worker was assigned randomly from the range (0,5) and maximal expert knowledge was assigned to the level of 30. The number of experts was assigned to 3% of all network nodes. Simulations were performed at model parameters with assigned values
Symmetric settings for vertical diffusion.
1 | 2 | 3 | 4 | |
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1 | 0 | 0,4 | 0,4 | 0,4 |
2 | 0,4 | 0 | 0,4 | 0,4 |
3 | 0,4 | 0,4 | 0 | 0,4 |
4 | 0,4 | 0,4 | 0,4 | 0 |
Matrix based setting for vertical diffusion.
1 | 2 | 3 | 4 | |
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1 | 0 | 0,6 | 0 | 0 |
2 | 0,1 | 0 | 0,5 | 0,5 |
3 | 0 | 0,2 | 0 | 0 |
4 | 0 | 0,2 | 0 | 0 |
Results for model with disabled vertical diffusion similar to earlier models are presented in Figure
Results of simulation with disabled vertical simulation.
Results of simulation with symmetric vertical simulation.
Simulation model allows tracking incoming and outgoing knowledge for each component. Results for incoming and for outgoing knowledge at each layer are visible in Figures
Knowledge incoming form vertical diffusion based on symmetric relations.
Knowledge outgoing from vertical diffusion based on symmetric relations.
Combining between model knowledge components and building metric for competencies makes possible tracking different competence development over time. In Figure
Development of competencies based on four layers.
In the next step simulation is based on the asymmetric settings for vertical diffusion and results for knowledge in each layer are shown in Figure
Knowledge diffusion based on asymmetric settings.
Knowledge outgoing from vertical diffusion based on asymmetric relations.
Parameters used for different relations between layers can be changed over time and they are related to the situation with emerging technologies and innovations. Obtained results showed diffusion processes between different layers. Dynamics of processes was simulated using both vertical and horizontal diffusion. Effect of deterioration was simulated as well as self-learning which results in changes over the time.
In the next step the role of experts within the network was modelled using asymmetric relations between knowledge components. Using the proposed model it is possible to simulate changes after adding experts with assigned knowledge higher than all network members. In the first stage of the simulation shown in Figure
Multilayer knowledge diffusion improved by adding experts.
Knowledge transferred with vertical diffusion to other layers resulted in a stable increase. In the next stage, 5 experts were added with maximal knowledge at layer one at the level of 25 and it was repeated after step 300. Adding continuously experts with smaller knowledge delivered better results than one time action based on experts with knowledge much higher than average knowledge within network. Activity for incoming and outgoing knowledge is shown in Figures
Knowledge incoming from vertical diffusion based on asymmetric relations.
Knowledge outgoing from vertical diffusion based on asymmetric relations.
Using this approach it is possible to evaluate a better strategy to add a smaller number of experts with high knowledge or add higher number of experts with smaller knowledge. In the simulated conditions adding experts with high knowledge delivered worse results because of observed deterioration process.
Proposed model can be used for simulating situations of reduction of employment or job quitting. It was simulated in the next step and results are shown in Figure
Multilayer knowledge diffusion with changes of employment.
Even though experts were added to single layer vertical diffusion helped to recover average knowledge at layer number two. Changes in employment are resulting in different activity within incoming and outgoing knowledge at each layer which is illustrated in Figures
Knowledge diffusion based on asymmetric settings.
Knowledge outgoing from vertical diffusion based on asymmetric relations.
Competence has a dynamic nature and can be represented by the set of its states variables values. The state variables represent different pieces of a person’s competence; thus the competence can be seen as a function of several time-based arguments, such as [ The model has several properties that allow managing the competence on an operational level. Current trend in the literature is that competence management can be organized according to four kinds of mutual related processes [
competence identification: in order to create competence matrix all competence components have to be identified; as a result all competence’s component are recognized and measured; moreover, based on each layer analysis, the trends related to the competence are observable and can be predicted; competence assessment: due to all layers identification and description the assessment tools can be selected effectively; competence acquisition: the diffusion mechanism supports the competence acquisition and help with the selection process of employee for training; competence knowledge usage: the analysis of structure and content of network, behind the multilayer graph, give possibility to recognising the communities of practice. The model of knowledge diffusion process, which is based on vertical and horizontal diffusion and forgetting/self-learning processes, gives a better picture of knowledge processing in an organization than the models from the literature. The proposed diffusion model allows checking what happens with competence value in an organization if, for example, the following scenario happens: base knowledge of all employees or only a few (experts) is increasing, some employees are removed from the organisation, and some employees are transferred to other parts of the organisation structure (new location in network). Moreover, we can use dedicated algorithms (e.g., [ Application of the theory of the knowledge spaces allows estimating the level of knowledge in the context of existing and required competencies and relations between knowledge layers. We can precisely determine what part of worker’s knowledge has to be increasing in order to achieve the required level of personal competence. The same problem for organisation required some optimisation approach. The optimisation problem is the following: how to maximise the competence level on worker or organisation level regarding to social and cognitive personal worker’s abilities, knowledge distribution, and domain’s structure whereas the constraints are time and cost of training? In the presented model, only two workers’ roles are distinguished regarding knowledge level: expert and normal worker. However, it is possible to recognise more roles in order to model complex organisation structure. In the work [ In future approach to the modelling of the discussed issue it will be possible to change the relationship between the layers based on time-dependent function or semantic relations reflecting business rules. In the presented approach, there are linear relationships between the layers described by vertical diffusion matrix. When the network of knowledge, competence, and links are large the complexity of proposed approach is growing. The computational complexity depends on formulas for horizontal and vertical diffusion and self-learning/forgetting processes (( The notation of upper and lower shadow for worker’s knowledge set gives opportunity to develop a cost estimation method for commencing development. The cost estimation algorithm in the form of a group competencies expansion algorithm is proposed in [
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was partially supported by fellowship cofinanced by the European Union within European Social Fund, by European Union’s Seventh Framework Programme for research, technological development, and demonstration under Grant Agreement no. 316097 (ENGINE) and by the National Science Centre, the Decision no. DEC-2013/09/B/ST6/02317.