=Paper=
{{Paper
|id=Vol-2843/shortpaper001
|storemode=property
|title=Soft modeling and expert systems in modern science: development trends (short paper)
|pdfUrl=https://ceur-ws.org/Vol-2843/shortpaper001.pdf
|volume=Vol-2843
|authors=Vladimir Testov,Oleg Golubev,Aleksey Babkin,Olga Panfilova
}}
==Soft modeling and expert systems in modern science: development trends (short paper)==
https://ceur-ws.org/Vol-2843/shortpaper001.pdf
Soft modeling and expert systems in modern science:
development trends*
Vladimir Testov1, Oleg Golubev1, Aleksey Babkin2 and Olga Panfilova2
1
Vologda State University, 15, Lenin str., Vologda, 160000, Russia
2
Vologda Institute of Law and Economics of the Federal Penitentiary Service of Russia, 2,
Shchetinin Str., Vologda, 160002, Russia
oleg_golubev@mail.ru
Abstract. The article examines the use of the potential of soft modeling and
expert systems in modern science in the construction of mathematical models in
various fields. In the scientific community, there is currently a growing under-
standing of the need to apply flexible and fairly soft mathematics based on in-
formation (expert) systems. As a rule, each model reflects the internal organiza-
tion of a system (economic, social, legal, etc.), its essence, which is determined
by the set goals. One of the first embodiments of the ideas of soft modeling was
the creation of methods of fuzzy mathematics and fuzzy logic, which allow ob-
jectifying processes with a low level of formalization. Fuzzy set theory and
fuzzy logic are the basis for creating fuzzy control systems and fuzzy decision-
making systems (expert systems). The ideas of soft modeling can be applied in
various fields, including legal, since soft models are mainly used in the descrip-
tion of crime. The article discusses the decision one of tasks based on the appli-
cation of soft modelling and expert systems: definition of severity of punish-
ment depending on the social danger of the act and the identity of the perpetra-
tor.
Keywords: Scientific picture of the world, Soft modeling expert systems,
Fuzzy mathematics, Fuzzy set theory.
1 Introduction
In recent years, modern science around the world is increasingly discussing the issues
of modeling, formalization of various social processes, including their methodological
foundations. In connection with the above, the topic related to the formalization of
criteria for evaluating human activity, measurement of characteristics, classification
of objects, etc. is relevant.
It should be noted that most of the solved problems and studies of modern scien-
tific schools are related to the very nature of the objects of research in science, their
specific features in the scientific picture of the world. The essence of the scientific
*
Copyright © 2021 for this paper by its authors. Use permitted under Creative Commons License Attribu-
tion 4.0 International (CC BY 4.0).
picture of the world lies in its integrative function, in ensuring the synthesis of indi-
vidual scientific knowledge. The scientific picture of the world introduces certain
restrictions on the formation and nature of new scientific paradigms, directs the
movement of thought and determines the way of seeing the world around us [1].
Constantly changing imaginative ideas about the dynamic world around us are
sometimes difficult and almost impossible to express in the format of stable concepts,
to classify them, etc. At the moment, in our opinion, it is a fuzzy concept and is built
on the basis of their various models suitable for understanding and learning of com-
plex volatile systems, and, no less, and perhaps even more than friends all have long
rigorous models and concepts.
2 Materials and methods
The study used general theoretical methods of scientific knowledge: interdisciplinary
analysis and synthesis of scientific, mathematical and methodological literature, as
well as advanced scientific experience; comparative historical methods; methods of
empirical research: expertise; modeling.
3 Results
Mathematics plays a special, significant role in creating conditions for the formation
of such a modern scientific picture of the world, which is determined by its place in
the system of sciences, the universality of methods and techniques that underlie a
number of fundamental sciences. Representing a general scientific method of cogni-
tion of reality, today mathematics, its methods, technologies, applications create a
kind of generalized, scientifically based system of general ideas, views on the world
and its surrounding details, show the unity of the scientific picture.
Mathematics has been a strictly deterministic science since ancient Greece. How-
ever, in recent decades (the end of the XX – beginning of the XXI century), mathe-
matical science, its methods, mathematical vision of the world are losing the certainty,
the measure of absolute reliability and steadfastness that previously existed in science
[2-3].
At the moment, there is a growing understanding in the scientific community of the
need to introduce flexible and sufficiently soft mathematics. One of the most striking
examples of this understanding was the research of the largest Russian mathematician
V. I. Arnold, which later formed the basis for the adoption of the ideas of "soft model-
ing" by the modern mathematical community. He pointed out "the usefulness of soft
models, in which there is uncertainty, ambiguity of development paths, and the danger
of hard models, for which a single path of development is predetermined "[4]. The
model, as you know, shows with some simplifications the internal structure of the
system, its essence, which in turn is determined by certain goals. We emphasize that
the ideas expressed by V. I. Arnold are mathematically justified and have great gen-
eral philosophical significance.
In the last ten years in science, on the basis of the development of a synergetic
worldview, discoveries in natural science, there have been changes in the entire style
of scientific thinking (consciousness): the transformation to images (figures) of chaos
took place; the mathematical theory of soft models becomes the basis for many new
trends (directions of development) of modern mathematics (for example, the theory of
bifurcations, fractal geometry, asymptotic mathematics, etc.) [5-6].
One of the first embodiments of the ideas of soft modeling was the creation of
methods of fuzzy mathematics and fuzzy logic, which allow objectifying processes
with a low level of formalization. For the first time, these methods were considered in
the work of L. Zadeh called "Fuzzy sets", which was published in 1965. L. Zadeh
tried to describe such phenomena and concepts that have a multi-valued and inaccu-
rate nature. Vagueness, like uncertainty, is opposed to precision. Indistinctness does
not imply consideration of the appearance of an event and refers only to the way the
event itself is described [7].
The mathematical foundations of fuzzy logic, fuzzy sets and their practical applica-
tion are considered in [8-9].
Here are the basic concepts of this theory. Fuzzy set A (subset of ground set U) is
identified as set of pairs { A ( x ), x} ,where x U , and function A : U [0; 1]
is
identifed as membership function fuzzy set A.
Ordinary sets are a subclass of some class of fuzzy sets. Moreover, the membership
function of an ordinary set takes only two values 0 or 1.
By the intersection of fuzzy sets, we mean such a maximal fuzzy set that is con-
tained both in A and in B ( B A ) , with the membership function
A B x min A x , B x , x U .
The union of fuzzy sets A and B ( B A ) is understood as the smallest fuzzy set
that contains both in A and in B, with the membership function
A B x max A x , B x x U
.
Fuzzy logic is a multi-valued logic with special properties designed to model
fuzziness and a number of natural language components.
Note that one of the main concepts of the theory of fuzzy logic is a linguistic vari-
able , T ,U , G, M where is the variable name, T is the set of its
,
meanings (language expressions), U is the universal set, G is a syntactic rule that
can be used to form language expressions, M is a semantic rule by which each lan-
guage expression is assigned its meaning, which will be a fuzzy set in U . Linguistic
variables can be numeric and non-numeric, which is determined by the type of uni-
versal set. A numeric linguistic variable U ; and the base variable is meas-
urable.
Fuzzy set theory and fuzzy logic are the basis for creating fuzzy control systems
and fuzzy decision-making systems. Currently, expert systems that can partially re-
place a specialist expert have gained steady recognition. One of the main advantages
of expert systems is the ability to accumulate, update, and preserve knowledge for a
long time. All this allows you to improve the skills of specialists working in a particu-
lar organization, using the best, proven solutions. Experts use expert systems to be
confident in their knowledge and not forget anything. Expert systems are able to solve
problems from a specific subject area using deductive methods. Such systems are also
used to solve vaguely structured problems. Expert systems are particularly useful in
cases where experts cannot arrive at a specific location to solve a problem. Expert
systems allow you to spread the experience of experts and make it more accessible.
Today, expert systems are used to diagnose diseases, to search for minerals, to buy
goods through the Internet.
The main component of the expert system is the knowledge base (semantic model),
which describes a specific subject area. Artificial intelligence systems are used in
different fields, however, the scope of application of expert systems is limited, they
can be used where the knowledge base exists in a natural form.
One of the types of expert systems is production expert systems, which are now
most widely used, in which the knowledge base is presented in the form of a set of "if,
then" rules. Such a knowledge base is formed in advance by an expert knowledge
engineer (a generalist who knows the methods of knowledge representation). Produc-
tion expert systems are convenient for programming, but quite expensive, due to the
fact that they require a lot of time for programmers and knowledge engineers.
Through expert systems, it is possible to solve many topical problems of modern
science, including, for example, in the legal field [10].
Further, for example, consider the problem of determining the severity of punish-
ment depending on the public danger of the act and the public danger of the person
responsible. In each of these two categories, it is important for experts to identify the
most significant characteristics and evaluate them separately. For simplicity, in the
example the first category we will evaluate in a consistent form, and secondly, high-
light three characteristics: social danger of the person in the past, present and future.
These qualities are evaluated by three experts (judges) independently of each other,
putting any number in the range from 0 to 10, depending on the degree of public dan-
ger. This number is nothing more than a membership function multiplied by 10. The
results of the evaluation are shown in Table 1.
With a large number of characteristics, it is more convenient to perform all the
procedures in the MS Excel program (a variant of the expert system).
Table 1. The results of the evaluation.
The danger The severity
Danger The danger of The danger of
of person- of the pun-
Experts of the personality in personality in
ality in the ishment max
act the past the present
future (min )
А1 7 5 7 6
А2 5 6 7 7
6
А3 6 4 6 5
min (А1,А2,А3) 5 4 6 5
After the experts fill in the table, you need to find the minimum value in each col-
umn and write it in the last line. The meaning of this operation is as follows. The
opinion of each expert on each of the characteristics of the public danger of the crime
and the identity of the perpetrator corresponds to a certain fuzzy set. To find the
common part of these different sets, one must find their intersection, and the intersec-
tion of fuzzy sets forms the membership function. Thus, the value of this function is
equal to the minimum of the values of the membership functions of all three sets.
Next, we need to find the optimal value of the membership function of the fuzzy
set of the linguistic variable "severity of punishment". To do this, we need to find the
union of fuzzy sets corresponding to each of the four characteristics. The value of the
membership function of such a union is found as the maximum of the values of the
membership functions of each of the four fuzzy sets corresponding to the four se-
lected characteristics. In other words, you need to find the maximum value among the
minimum values written in the last line. In this example, this number is 6, i.e. the
desired value of the membership function is 0.6. Thus, the severity of the penalty is
0.6 on a scale from 0 to 1, i.e. "slightly above average". Note that the rule under con-
sideration corresponds to the minimax principle, which is widely used in mathemati-
cal game theory.
4 Discussion
Questions of modeling and formalization of legal processes are related to the very
nature of research objects in various fields of science, their specific features in the
scientific picture of the world. The essence of the scientific picture of the world lies in
its integrative function, in ensuring the synthesis of individual scientific knowledge.
The scientific picture of the world introduces certain restrictions on the formation and
nature of new scientific paradigms, directs the movement of thought and determines
the way of seeing the world around us.
The problems put forward for research by the authors are related to the nature of
the objects of research, including their specific features in the scientific picture of the
world. The diversity of the surrounding world, the absence of clearly defined catego-
ries and strict boundaries in it, justifies the scientific acceptance of fuzzy concepts
with an amorphous set of features (for example, the identity of a criminal, etc.). Non-
strict (soft) representations show themselves to be a more effective means of under-
standing complex, unstable systems. Mathematics plays a special, significant role in
creating conditions for the formation of a modern scientific paradigm, which is de-
termined by the universality of its methods and techniques [11-14].
5 Conclusion
Expert systems today are able to solve problems from a specific area, using various
methods and techniques. Such systems are also used to solve vaguely structured prob-
lems. Expert systems allow you to spread the experience of experts and make it more
accessible.
Thus, using the ideas of soft modeling and using expert systems, it is possible to
objectify processes with a low level of formalization, including, for example, the
processes of determining the danger of crime. Fuzzy set theory and fuzzy logic are the
basis for creating fuzzy control systems and fuzzy decision-making systems.
The undeniable advantages of fuzzy control systems in comparison with others are:
─ The probability of operating with non-strict input data;
─ Formalization of evaluation and comparison criteria based on fuzzy mathematics;
─ Better evaluation of input and output data of research results;
─ Conducting a comparative analysis with a given degree of accuracy, rapid model-
ing of complex dynamic systems [15].
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