=Paper=
{{Paper
|id=Vol-2744/short13
|storemode=property
|title=Detecting Errors in Cognitive Models Using Visualization Metaphors of Fuzzy Cognitive Maps (short paper)
|pdfUrl=https://ceur-ws.org/Vol-2744/short13.pdf
|volume=Vol-2744
|authors=Ruslan Isaev,Aleksandr Podvesovskii
}}
==Detecting Errors in Cognitive Models Using Visualization Metaphors of Fuzzy Cognitive Maps (short paper)==
https://ceur-ws.org/Vol-2744/short13.pdf
Detecting Errors in Cognitive Models Using Visualization
Metaphors of Fuzzy Cognitive Maps *
Ruslan Isaev [0000-0003-3263-4051] and Aleksandr Podvesovskii [0000-0002-1118-3266]
Bryansk State Technical University, Bryansk, Russia
ruslan-isaev-32@yandex.ru, apodv@tu-bryansk.ru
Abstract. Verification of cognitive models is one of the most important stages in
their construction, since reliability of results of subsequent modeling largely de-
pends on the successful implementation of verification. The paper considers the
problem of verifying cause-and-effect relationships in cognitive models based on
the use of fuzzy cognitive maps. It is noted that increasing the effectiveness of
cognitive model verification is possible by activating analyst's cognitive poten-
tial. The most natural way of such activation is to increase cognitive clarity of the
model through the use of visualization capabilities. For this purpose, a number of
metaphors for visualizing fuzzy cognitive maps have been proposed, aimed at
increasing their cognitive clarity during verification. Each of the metaphors is
focused on the visualization of a certain type of fragments of a fuzzy cognitive
map potentially containing errors, redundancy or incompleteness and therefore
of interest from the point of view of verification. The first considered visualiza-
tion metaphor is intended to display the cycles that are part of a cognitive graph.
The second metaphor focuses on the mapping of transitive paths between con-
cepts. Finally, the third metaphor is aimed at eliminating cognitive model incom-
pleteness, which consists in the lack of relationships between some concepts. Ex-
amples are given of applying the proposed visualization metaphors to increase
cognitive clarity of the visual image of the verified fuzzy cognitive map.
Keywords: Cognitive Modeling, Fuzzy Cognitive Map, Visualization
Metaphor, Cognitive Clarity, Verification.
1 Introduction
This paper continues a series of publications of the authors’ research materials in the
field of visualization of cognitive models based on fuzzy cognitive maps (FCM).
An FCM reflects a researcher’s subjective idea of a system in the form of a set of se-
mantic categories (called factors or concepts) and a set of causal relationships between
them [1]. Thus, an FCM can be visualized in the form of a weighted directed graph the
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
* The reported study was funded by RFBR, project number 19-07-00844.
2 R. Isaev and A. Podvesovskii
vertices of which correspond to concepts and the edges – to cause-and-effect relation-
ships.
One of the conditions for effective work with a cognitive model is to ensure its visual
representation. In [2, 3], the authors proposed an approach to FCM visualization based
on the visualization metaphor concept. Visualization metaphor traditionally includes
two components: spatial metaphor and representation metaphor [4].
The spatial metaphor defines general principles of transferring a visualized object
into the visual model space. With regard to an FCM, such a metaphor is based on graph
visualization algorithms and formalized criteria of cognitive clarity [3]. These criteria
describe requirements for the FCM visual image quality. Observing these requirements
simplifies visual perception of the cognitive model by the analyst. This leads to a gen-
eral increase in the speed of working with the model, and also helps to reduce the num-
ber of errors made at various stages of modeling.
The representation metaphor used below is responsible for finalizing the resulting
visual image in order to identify its components that are most important in the context
of the problem being solved. A number of different representation metaphors are used
in the visualization of the FCM taking into account the analyst’s needs at different
stages of cognitive modeling.
The paper investigates capabilities of FCM visualization when solving one of the
important tasks of cognitive modeling – namely, cognitive model verification. The re-
search is based on the hypothesis of an increase in the efficiency of FCM verification
by increasing cognitive clarity of its visual image.
2 The task of verifying cognitive models
The task of verifying a cognitive model is an important task solved at the stage of model
building and is aimed at identifying a possible discrepancy between the model and the
modeled system itself. This discrepancy can be expressed in the following basic forms.
1. The cognitive model may lack concepts that reflect important parameters of the mod-
eled system, or, conversely, there may be redundant concepts that are not important
in relation to the modeling goal.
2. A set of cause-and-effect relationships given on a set of concepts can be character-
ized by both incompleteness and redundancy.
3. Errors can be made when setting parameters of cause-and-effect relationships (di-
rection, sign, intensity).
Search techniques and eliminating inconsistencies of the first type require highly qual-
ified experts and deep understanding of the subject area and, as a rule, are the most
difficult to formalize. One of the possible approaches here may be ontological engi-
neering [5].
Errors made in the parametric identification of the model (the third type of discrep-
ancy) are the least obvious for detection and most often can be detected directly from
the results of modeling, based on the analysis of their plausibility [6]. At the same time,
certain reliability control of parameters of FCM relationships can be performed within
the framework of the identification methods themselves [7].
Detecting Errors in Cognitive Models Using Visualization Metaphors of Fuzzy… 3
The proposed research focuses on the second type of discrepancy as the easiest one
to apply formal verification methods. In addition, as will be shown below, in this case
it becomes possible to effectively combine formal methods with methods based on the
activation of the analyst's cognitive capabilities.
It should be noted here that when identifying the redundancy of a set of relation-
ships, two types of elements of cognitive graph structure are most important for analy-
sis: oriented cycles and pairs of transitive paths. The importance of oriented cycles
stems from the fact that they, representing feedback loops, in some cases can lead to a
violation of cognitive model stability in the course of its scenario analysis. Pairs of
transitive paths describe alternative mechanisms of concept interaction which must be
assessed by the analyst, on the one hand, for mutual consistency, and on the other hand,
for the need to be reflected in the model in general.
The problem of search for oriented cycles and pairs of transitive paths in an FCM
belongs to common problems in graph theory. Therefore, further we describe how to
process and present the results of such a search using visualization capabilities.
3 Application of visualization metaphors of fuzzy cognitive
maps in the process of cognitive model verification
Let us consider some FCM visualization metaphors that can be used in the process of
verifying cognitive models. The use of these and other similar metaphors increases cog-
nitive clarity of verified models, which will help to activate the analyst's cognitive abil-
ities when solving a number of specific tasks during verification. To illustrate the results
of applying the proposed metaphors, we will use the FCM shown in Fig. 1.
Fig. 1. Example of an FCM subject to verification
4 R. Isaev and A. Podvesovskii
3.1 Visualization of oriented cycles
Let us consider a visualization metaphor designed to display oriented cycles found
within an FCM. Suppose one of the cycles is set for the visualization. The essence of
the spatial component of this metaphor consists in depicting the FCM in such a way
that the criterion of unidirectionality of successive edges is maximized on the set of
edges included in a given cycle. Less formally, the metaphor seeks to place the vertices
of the cognitive graph in such a way as to provide a unidirectional image of as many
edges within the cycle as possible. It has been noted [8] that such placement contributes
to the cycle coverage “at a glance”. In this case, it is advisable to choose the direction
“left-to-right” or “top-down” as the priority direction (that is, the direction of most
edges). This is due to the criterion of optimizing edge directions which is also taken
into account [3].
The corresponding representation metaphor is characterized by the concentration of
the analyst's attention directly on the cycle under consideration. A simple solution to
this problem could be complete absence of images of “excess” sections of the FCM.
However, this approach has an obvious disadvantage of removing the context useful
for verification from the analyst's perception. Therefore, it seems more rational to de-
pict all the FCM elements that are not included in the cycle semi-transparent. It should
also be noted that it is advisable to individually adjust the degree of transparency taking
into account peculiarities of a particular analyst’s perception.
Fig. 2 shows an example of application of this metaphor to the test FCM when vis-
ualizing the cycle “1-5-7-6-4-1”. It is easy to see that restructuring the FCM image is
much better (compared to the original metaphor) in attracting the analyst's attention to
the selected cycle. This allows us to speak of an increase in cognitive clarity of the
model in the context of the problem under consideration.
Fig. 2. Example of applying the cycle visualization metaphor
Detecting Errors in Cognitive Models Using Visualization Metaphors of Fuzzy… 5
Let us note that if an FCM includes several cycles, it becomes necessary to specify the
order of their presentation to the analyst. At the same time, it is advisable to take into
account that the risk of FCM stability disruption is primarily due to the presence of
cycles with a positive weight (the weight of a cycle refers to the product of the weights
of influences included in it): concepts in such a cycle tend to intensify their own
changes. Therefore, if there are several such cycles, priority should be given to the cy-
cles with the highest weight.
3.2 Visualization of pairs of transitive paths
The next visualization metaphor is intended to depict pairs of transitive paths between
concepts. As in the previous case, the spatial component of this metaphor takes into
account the criterion of the unidirectionality of successive edges, but additionally max-
imizes the symmetry of the subgraph subject to visualization [3]. By analogy with the
previous case, the representation metaphor uses the effect of a semi-transparent image
of “excess” graph sections to focus the analyst's attention on the selected transitive
paths.
Fig. 3 shows an example of this metaphor application when visualizing a pair of
paths “1-3-6-4” and “1-5-7-4”. Due to equal path lengths, it was possible to ensure the
symmetry of the target subgraph about the horizontal axis.
Fig. 3. Example of metaphor application for visualizing pairs of transitive paths
By analogy with the previous metaphor, the priority direction of the edges can be either
“left-to-right” or “top-down”, depending on the analyst's preferences.
3.3 Visualization of a missing relationship between concepts
If the two previous visualization metaphors were aimed at eliminating the redundancy
of a cognitive model, then this metaphor, on the contrary, is aimed at eliminating the
incompleteness of the model. In this case, incompleteness means lack of relationships
between some concepts.
6 R. Isaev and A. Podvesovskii
It should be noted here that absence of oriented paths between some pairs of concepts
in a cognitive graph is a typical situation when building a cognitive model. As a conse-
quence, even in the long term, changes in the states of some concepts will not affect the
states of a number of other concepts. From the point of view of object interpretation,
this means cause-and-effect independence of the corresponding parameters of the mod-
eled system from each other; this is quite admissible. Nevertheless, in a number of
cases, a missing relationship occurs by mistake during the FCM construction, and such
situations require detection and correction.
Pairs of concepts which lack oriented paths between them can be easily identified
based on the operation of transitive closure of a cognitive matrix corresponding to the
FCM under study. The sign of the absence of a path between the concepts is the equality
to zero of the corresponding element of the transitively closed matrix.
In general, there are many unrelated pairs of concepts in an FCM. Thus, in addition
to detecting such pairs, it is also necessary to determine the order of their presentation
to the analyst for the purpose of determining whether it is expedient to add a relation-
ship. It is advisable to give the highest priority to such pairs of concepts the addition of
a relationship between which will have the most significant impact on the modeling
results.
Let the FCM in Fig. 1 initially lack relationship directed from Concept 6 to Con-
cept 4. It is easy to see that this leads to the absence of oriented paths from Concept 3
to all concepts except Concept 6, as well as from Concept 6 to all concepts.
Let us suppose that a relationship is added from Concept 6 to any of the concepts
numbered 1, 2, 4, 5. Obviously, this will lead to the emergence of oriented paths from
Concept 6 itself to all concepts, as well as from Concept 3 to all concepts. If such a
relationship is added from Concept 3, then Concept 6 will remain isolated. Therefore,
it is advisable to assign a higher priority to considering Concept 6 as a concept-cause.
Further, it is required to determine the order of presentation of potential concept-
consequences, that is, concepts with numbers 1, 2, 4, 5. A possible solution here may
be to focus on the intensity of influences exerted by these concepts on the other FCM
concepts. This information can also be obtained from a transitively closed matrix. The
greatest total influence on the concepts within the FCM is exerted by Concept 1.
An example of using a visualization metaphor taking into account the above reason-
ing is shown in Fig. 4. The analyst is invited to add a relationship from Concept 6 to
Concept 1, and he can either agree with this proposal or refuse it. If the analyst agrees
to add a relationship, then he needs to set its parameters, which, in turn, requires the
use of methods of FCM parametric identification [7].
An important feature of the proposed visualization metaphor is the possibility of
adjusting its spatial component in order to increase cognitive clarity of the visual image
of the FCM. So, if the concepts presented to the analyst in order to add a relationship
are situated far from each other and are separated by other elements of the FCM, then
visual image rebuilding is performed, aimed simultaneously at the spatial convergence
of these concepts and at maintaining the usual location of the remaining FCM elements.
Fig. 5 exemplifies how the metaphor works in such a situation. It should be noted that
from the point of view of automating visual image correction, an approach based on the
simulated annealing method proposed in [9] is of interest.
Detecting Errors in Cognitive Models Using Visualization Metaphors of Fuzzy… 7
Fig. 4. Example of using a visualization metaphor to eliminate a missing relationship
between concepts (the case of preserving the original spatial metaphor)
Fig. 5. Example of using a visualization metaphor to eliminate a missing relationship
between concepts (the case of spatial metaphor correction)
4 Conclusion
The paper presents possibilities of applying the approach to FCM visualization based
on visualization metaphors for verification of fuzzy cognitive models. Examples of vis-
ualization of situations that may characterize the incompleteness or redundancy of a set
of cause-and-effect relationships between concepts are considered. It is shown that the
effectiveness of cognitive model verification can be increased by increasing cognitive
clarity of the visual image of the FCM underlying it.
8 R. Isaev and A. Podvesovskii
Areas for further research include:
• Development and research of other visualization metaphors useful in FCM verifica-
tion.
• Development of a general verification methodology that allows combining formal
mathematical methods with subsequent visual processing of the results obtained
on the basis of visualization metaphors.
• Software implementation of the developed methodology in the form of a cognitive
model verification subsystem as part of IGLA DSS [10], as well as its performance
evaluation in the construction and study of fuzzy cognitive models of real applied
problems.
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