=Paper=
{{Paper
|id=Vol-2362/paper18
|storemode=property
|title=Modeling of Decision Making Ontology
|pdfUrl=https://ceur-ws.org/Vol-2362/paper18.pdf
|volume=Vol-2362
|authors=Anna Bakurova, Elina Tereschenko,Yurii Filei,Mariia Pasichnyk,Hanna Ropalo
|dblpUrl=https://dblp.org/rec/conf/colins/BakurovaTFPR19
}}
==Modeling of Decision Making Ontology==
https://ceur-ws.org/Vol-2362/paper18.pdf
Modeling of Decision Making Ontology
Anna Bakurova1[0000-0001-6986-3769], Elina Tereschenko2[0000-0001-6207-8071],
Yurii Filei3[0000-0001-5919-1129], Mariia Pasichnyk4[0000-0002-5179-4272],
Hanna Ropalo5[0000-0001-5241-6911]
Zaporizhzhya National Technical University, Zaporizhzhya, Ukraine
1abaka111060@gmail.com, 2elina_vt@ukr.net,
3fileyyuriy@gmail.com, 4mary.pasechnik@gmail.com,
5annropalo@gmail.com
Abstract. Making large data decisions requires the development of effective
methods for processing and analyzing information. One possible way in this di-
rection is creation of ontologies. The purpose of the work is to construct a deci-
sion making meta-ontology and to develop on its basis basic objective ontolo-
gies, which are used in the future for the design of systems for supporting deci-
sion making in the social sphere. To assess the quality of the developed ontolo-
gies, a multi-criteria approach is proposed, in which criteria are formed on the
basis of the theory of fuzzy sets and the theory of graphs. The model of meta-
ontology decision making and two basic ontologies of decision making have
been constructed: the court decision making and management of the pharmacies
network development.
Keywords: Decision Making, Decision Support System, Ontology, Multi-
Criteria Quality Assessment, Fuzzy Set, Topological Criteria, Court Decision,
Pharmacy
1 Introduction
Decision making is the main point in human activity, and the decision making pat-
terns remain the same for all subject areas. Difficulties in making decisions arise be-
cause of the uncertainty and/or insufficient knowledge about the problem situation
and the resources available, the weak structure of the task, and the multi-criteria
choice. The formalization of the applied problem, the choice of the decision proce-
dure, the organization of the work of the decision maker and experts are carried out
by the consultant-analyst. Introduction to the decision making process of decision
support systems (DSS) reduces the level of subjectivity by solving the problems of
insufficiency and uncertainty of the initial information.
This paper proposes a method for modeling ontology of decision making, one of
the stages of which is the construction of a multi-criteria assessment of the ontology
quality. The discussion is conducted on two examples: models of the ontology of a
court decision and the ontology of managing the development of a pharmacies net-
work. In these examples, decision areas are distinguished by the initial degree of for-
malization and the level of possible automation.
2 Related Works
The paper [1] proposed a methodology for developing an information system for de-
cision making using the Information Data Bank of high-tech technologies, which is
based on an object-cognitive analysis of the subject area, integrating the methods of
object-oriented analysis, ontological analysis and semantic knowledge representation
network with a goal of describing knowledge used in the management of complex
dynamic objects in problem situations.
The main provisions of the automated development of ontology based on the anal-
ysis of texts in natural languages are set out in the work of the authors V.V. Litvin,
A.B. Demchuk, M.Ya. Gopyak [2], where the criteria optimization of the constructed
ontology are formed in accordance with the quality standard ISO 9126. This theme is
further developed in [3], which is devoted to the adaptation of the characteristics of
the ISO / IEC25012 standard for assessing the quality of knowledge systems ontolo-
gies. These characteristics include: functionality in use, reliability, clarity, conven-
ience, portability, recoverability, confidentiality. By functionality is meant the ability
of a computer system to satisfy functional user requirements and tasks.
The fuzzy-set approach to assessing the quality of ontology, described in [4, 5],
offers an integral criterion for the quality of an ontology fragment, which consists of
three components: fuzzy functionality, fuzzy injectivity, and fuzzy everywhere cer-
tainty. It is applied to individual fragments of the ontology according to the following
formulas.
Defines the prototype of a set of concepts ะก in compliance ะฬ ๐๐ถ :
ะฬโ1 (ะก) = {< ๐ะฬโ1(ะก) (๐ก), ๐ก >|๐ก โ ๐}, (1)
where ๐ะฬโ1(ะก) (๐ก) = โ๐โ๐ถ (๐๐นฬ๐๐ถ < ๐ก, ๐ >), ๐๐นฬ๐๐ถ โ membership function value.
The degree of fuzzy functionality implies that each ontology concept will have tex-
tual inputs that have a small number of common terms, and is determined by the for-
mula:
๐ฝ(ะฬ ๐๐ถ )๐๐๐ = 1 โ ๐ผ(ะฬ ๐๐ถ )๐๐๐ (2)
1 1
where ๐ผ(ะฬ ๐๐ถ )๐๐๐ = 2 โ๐๐ ,๐๐ โ๐ถ (|๐| โ๐กโ๐ (๐ะฬโ1(๐ ) (๐ก)&๐ะฬโ1 (๐ก))); |C| - the num-
๐ถ|๐ถ| ๐ (๐๐ )
ber of concepts in the group of homogeneous ontology concepts; |T| the number of
2
terms associated with concepts; C|C| - the number of combinations of C in two, corre-
sponding to the number of all possible pairs of concepts.
The greater the value of fuzzy functionality, the higher the quality of the ontology
fragment. Estimates of the degree of injectivity and non-injectivity are found accord-
ing to the following formulas:
๐ฝ(ะฬ ๐๐ถ )๐๐๐ = 1 โ ๐ผ(ะฬ ๐๐ถ )๐๐๐ (3)
1 1
where ๐ผ(ะฬ ๐๐ถ )๐๐๐ = 2 โ๐ก๐,๐ก๐โ๐ (
|๐ถ|
โ๐โ๐ถ (๐ะฬ (๐)&๐ะฬ (๐))).
๐ถ|๐| (๐ก๐ ) (๐ก๐ )
The quality estimates (1-3) presented in [5] are applied to the analysis of ontology
fragments; therefore, to take into account the structure of the entire ontology, we sug-
gest using topological characteristics of the graphs. In the work of J. Tevet [6], the
measurement of a structure is considered in the attributes of the theory of information,
which is based on the internal variety of the structure. The measure of diversity in
absolute terms is the amount of information, and the variety of degrees of vertices of
the graph (elements of the system) determines the degree of topological entropy. Top-
ological entropy HE is calculated through the degree of elements deg ๐๐ :
|๐|
๐ป๐ธ = โ โ๐=1(๐๐๐๐๐ /2|๐ธ|) ร log(๐๐๐๐๐ /2|๐ธ|) (4)
|๐|
where deg ๐๐ - valence of structural element ๐๐ and 2|๐ธ| = โ๐=1 ๐๐๐๐๐ .
For the structure analysis of a complex system, it is advisable to take into account
such graph characteristics: a hierarchy of the structure; the diameter of the graph; the
bandwidth of the structure.
Vitor Basto Fernandes [7] explores the problem of multi-criteria optimization of
ontology quality on such characteristics: usability; functional basis; structural metrics;
semantic.
Despite a fairly representative presentation of ontology modeling and quality as-
sessment of their construction in the scientific literature, there are still unresolved
issues of modeling decision making meta-ontology, problems of automating decision
making in the social sphere, multi-criteria assessment of the quality of decision mak-
ing ontologies. This paper is devoted to the problems of using ontologies in designing
decision support systems in areas related to human activity (i.e., in the social sphere),
and to determining the multi-criteria assessment of the quality of such ontologies
based on non-multiple and topological approaches. As you can see, the intersection of
a set of characteristics proposed by different researchers [2, 3, 5, 7] is traced, accord-
ing to two estimates - functionality and reliability (injectivity), which are also the
main characteristics of the ISO / IEC 25012 standard. Therefore, next, these two crite-
ria include in the construction of multi-criteria evaluation, complementing various
options for topological (structural) criteria.
3 New approach for modeling ontology decision making
In the theory of artificial intelligence, โontologyโ is understood as the formalization of
a certain field of knowledge by a conceptual scheme. We will consider decision mak-
ing as a process taking place according to the scheme shown in Fig. 1, where the sign
"โ" shows the corresponding relationship between superclasses (SC). Define the
ontology of decision making as
๏ป ๏ฝ๏ป ๏ฝ
O ๏ฝ O form , O alternative , O choice (5)
where ๏ปO form ๏ฝ - a set of subject ontologies of task formalization; ๏ปO altern ๏ฝ - subject
ontologies of producing a variety of alternatives (possible solutions); O choice - ontol-
ogy of decision making from a given set of alternatives.
Fig. 1. Decision making scheme.
Filling in subject ontologies O form and O altern requires working with a specific sub-
ject area, researching specific tasks. Each representative O form of the set ๏ปO form ๏ฝ
of ontologies of formalization of the tasks of the subject areas includes the super-
classes "Situation" and "Formal Task", which are in the relation of Formalization.
Each representative O altern of a multitude ๏ปO altern ๏ฝ of ontologies for producing a set
of alternatives to subject areas includes the superclasses "Formal Task" and "Set of
Alternatives" that are in the relation "Production". The ontology O choice of decision
making from a given set of alternatives includes the superclasses โSet of alternativesโ,
โSolverโ and โDecision madeโ, relations โAnalysisโ, โDecision choiceโ. To provide
feedback in decision making, lets define an additional relation
Adjustment : Solver ๏ฎ Formal Task . The superclass "Situation" includes many classes
containing information from a specific subject area and describes the situation in
which a decision must be made. The โFormal Problemโ superclass consists of a set of
classes that carrying information on the construction of formalizations, mathematical
models in a particular subject area. At this stage, the decision making task is present-
ed as a tuple X , opt _ rule where X is a set of alternatives, opt _ rule is the crite-
rion of the quality of the alternative. The superclass "A set of alternatives" contains
many classes, which include methods for generating multiple alternatives X in a
particular subject area. The โSolverโ superclass includes a set of classes containing
exact and heuristic methods for constructing decision rules solv _ rule on a set of
alternatives, as well as the class โDecision making subjectโ with the subclasses โDeci-
sion makerโ and โAutomaticโ. The โDecision Makingโ superclass consists of a set of
classes that contain information on the decision made in a particular subject area.
To describe ontologies and work with them, the freely distributed editor Protรฉ-
gรฉ 5.5.0 was used [8]. Fig. 2 shows the decision ontology as an ontograph using the
GraphViz graphical module of the Protรฉgรฉ editor.
Vector objective function (VOF) includes criteria of functionality and injectivity,
defined on the basis of fuzzy sets, as well as topological criteria TG, which character-
ize the structure and information capacity of the ontograph:
Q(O' ) ๏ฝ ( F , I , {TG}) ๏ฎ max (6)
where F - the functionality of the ontology fragment, which is calculated by the for-
mula (2); I - the injectivity of the ontology fragment, calculated by the formula (3);
{TG} - topological criteria, from which in this case, those whose values are maxim-
ized are selected. For example, in the examples discussed below, bandwidth is used.
Fig. 2. Ontology of decision making in the form of ontograph.
The calculation of the ontology fragments estimates is performed on the fuzzy-
weighted parts of the ontograph, whose weights are determined by an expert method.
VOF (6) establishes a relation of either dominance or partial order on the set of alter-
native ontologies O' ๏ฝ {O'1 , O' 2 ,...}. If for all criteria F , I , TG with i ๏น j inequalities
F (O'i ) ๏ณ F (O' j ) , I (O'i ) ๏ณ I (O' j ) , TG(O'i ) ๏ณ TG(O' j ) and at least one inequality
is strict, then they say that the alternative O'i dominates the alternative O' j , i.e.
O' i ๏ฆ O' j .
Thus, the general algorithm for constructing an ontology of decision making,
which is followed in this work, consists of the following steps:
1. building a decision meta-ontology;
2. the construction of a basic ontology manually based on the analysis of the texts of
documents;
3. multi-criteria assessment of the quality of the basic ontology;
4. automating the expansion of the base ontology by acquiring new knowledge from
various sources with the help of the Protรฉgรฉ editor;
5. integration of ontology with other related ontologies.
4 Experiments
Next, we consider the construction of a basic ontology of decision making on the
example of two subject areas.
4.1 Example 1. The ontology of a court decision.
Court decisions are made in accordance with Art. 65 of the Criminal Code of Ukraine
(ะกะก of Ukraine) [9], the court imposes penalties within the limits established in the
sanction of the article of the Special Part, which provides for responsibility for the
committed crime, in accordance with the provisions of the General Part, taking into
account the degree of gravity of the crime, the person guilty and the circumstances ,
softening and aggravating punishment. When choosing a sentence the judge must
assess all elements of the crime and all the circumstances of its implementation in
order to determine the extent of liability of the defendant and the appointment of him
a co-sentence. The degree of punishment, depending on the composition of the crime
is regulated by the rules of law, which allows formally determine the limits of maxi-
mum and minimum penalty. In addition to the objective factors in this process, there
is also subjectivity, the so-called judicial oversight.
Walkman, Hala [10] developed the basic ontology for the legal domain, where the
formation of a court decision is indicated by a binary relation:
listened_courtโcourt_process. The proposed ontology of the court decision proposed
by the authors of this article allows us to extend the basic ontology for the system of
law from the work [10] by introducing the formalization of this binary relation. The
ontology of the court decision is a structure that reflects the connection between the
classes of input data (the participants in the process, the personality of the defendant,
the personality of the judge, the circumstances burdening and mitigating the crime)
necessary for the decision, and the measure of punishment, which is represented by
many elements: a fine, restriction and imprisonment (real and conditional), public
works. When imposing a punishment determine the circumstances that mitigate the
punishment specified in Art. 66 of the ะกะก of Ukraine [9]. There are eleven such cir-
cumstances. Circumstances that burden a punishment are specified in Art. 67 [9].
These circumstances are determined by 14. The mechanism for making a court deci-
sion is determined by the relations schematically shown in Fig. 3.
Fig. 3. The scheme of the court decision.
The court decision ontology allowed to develop a general DSS court model in form [13]:
(Fine,Years,RF,PW,Cond)=F(Severity,Mitigation,Personality,Burden,Lawyer) (7)
where F is the corresponding output algorithm, PW โ public work, Cond โ condition,
Severity- characterizes the severity of the crime; Personality - characterizes the guilty
person; Mitigation - mitigating circumstances; Burden - circumstances that burden the
punishment; Lawyer - the level of neutrality of a court's decision and takes value with
the term -small {loyal, neutral, strict}; Fine - the size of the fine, Years - the number
of years of imprisonment, RF - restriction of freedom.
PW, Cond - determines the actual or conditional entry into action.
Let's evaluate the efficiency of introducing into the ontology class "Judgment Solu-
tion", which will have three representatives โ neutral (N), strict (H) and loyal (L),
within the limits allowed by the rule of law. There are factors shaping the court deci-
sion: B - burdening circumstances, M - mitigating circumstances, P+ -positive proper-
ties of the defendant's personality, P- - negative qualities of the defendant. Calculate
the estimates for the three situations Var1 , Var2 , Var3 . The initial data of the first
situation Var1 are presented in Table 1, which is the matrix of adjacency of the fuzzy
graph of the fragment of the ontology.
Table 1. Initial data of the first situation (Example 1).
Var1 L N H
P+ 0,8 1 0,1
P- 0,2 1 0,9
B 0,1 1 0,9
M 0,7 1 0,1
The second situation Var2 corresponds to the automated decision making process
(Table 2).
Table 2. The second situation (Example 1).
Var2 N
P+ 1
P- 1
B 1
M 1
Situation three Var3 describes the initial data presented in Table 3.
Table 3. The third situation (Example 1).
Var3 L N H
P+ 1 1 0
P- 0 1 1
B 0 1 1
M 1 1 0
This is an idealized option in which soft solutions take into account all positive and
mitigating factors, and rigid ones are all negative and aggravating factors.
For the automatic ontology construction, such topological criteria TG as topological
entropy (4) of work [6] and bandwidth are of interest. The results of the calculations
of the VOF (6) for the three decision making situations are presented in Table 4.
Comparing the results, we get a ranking Var3 ๏ป Var1 ๏ฆ Var2 .
Table 4. The results of the calculations(Example 1).
Indicator Var1 Var2 Var3
Functionality 0,64 0 0,67
Injectivity 0,51 0 0,56
Bandwidth 0,25 0,25 0,25
Topological entropy 2,824 2,824 2,824
4.2 Example 2. Ontology of decision making on managing the development of
a pharmacy network
The choice of the most preferred pharmacy development strategy is the task of making
marketing decisions and management. Unlike a court decision based on structured legal
documents, this task refers to unstructured, requiring selection of criteria for evaluating
the decision, as well as the construction of methods for their initialization. In this case,
the source of data for building a basic ontology is mainly the texts of scientific articles
and practical publications from scientific journals and the Internet. An example of such
a publication is the article by an international group of researchers [11] representing a
medical ontology for the care of chronically ill patients, which helps health care provid-
ers to detect abnormal circumstances such as irregular diagnoses, unobservable concom-
itant illnesses, missing information, unobserved associated illnesses or preventive ac-
tions. Another example is the work of Thomas Puschmann [12]. An ontological ap-
proach is used to harmonize conceptual descriptions of subject areas compiled by
various specialists (medicine, pharmacy, commerce).
Ontology for managing the pharmacies network is a mechanism for describing the
subject area, including the basic concepts of this area, their properties and the connec-
tions between them. Such connections are a type of interaction between the concepts of
the subject domain. The ontology of decision making on managing the development of
the pharmacy network is a structure that describes the relationship between input classes
(the class of target management objects: Buying Capacity - CA, Internet Pharmacy - E,
Assortment - As, Traffic - T) needed for decision making, and class A set of control
strategies: S1, S2, S3, ..., Si, by introducing the formalization of the binary relationship:
Selection: ManagerโPreferred strategy. The mechanism of decision making on man-
aging the development of the pharmacy network is determined by the relationships
shown schematically in Fig. 4.
Fig. 4. The scheme for decision making the pharmacy network development.
The construction of ontology has allowed us to formulate a general model of DSS
management by the development of a pharmacy network, which has the form:
S ๏ฝ f( CA, As, E, T) , (8)
where S is the most preferred management strategy.
In addition, the elements can be included in the ontology: the quality of the pedes-
trian flow, the type of district, the competitive environment, the distance to the medi-
cal institutions. More detailed DSS for the situation of opening a new pharmacy is
considered in article [14].
Let's evaluate the effectiveness of different decision making situations with the
help of the VOF (6). The first situation Var1 corresponds to the decision of the man-
ager (PDM). The second situation Var2 corresponds to the automatic choice of the
decision using DSS. The first situation Var1 corresponds to the manager's choice of
the most preferred of three different strategies: S1 - oriented to the development of
an online pharmacy; S 2 - aimed at increasing the purchasing power (loyalty pro-
gram) and increasing the range, S 3 - select a place with high traffic for pharmacy
placement. The second situation is represented by one strategy, which includes con-
sideration of all criteria for increasing the efficiency of pharmacies, corresponding to
the classes of ontology. The results of the calculations of the estimates for the two
decision making situations are presented in Table 5. From the calculations we get that
the second situation of decision making is not worse than the first, Var1 ๏ป Var2 .
Table 5. The results of the calculations (Example 2).
Indicator Var1 (manager) Var2 ( DSS)
Functionality 0,958 0,783
Injectivity 0,917 0,822
Bandwidth 0,33 0,33
Topological entropy 0,985 0,985
5 Discussions and Conclusions
The proposed algorithm for constructing a decision making ontology was used to
create meta-ontology and two basic decision making ontologies in the social sphere.
Conceptualization of decision making (5) defined the need for the construction of
objective ontologies for the formalization of problems O form and the production of
alternatives O altern in the presence of a common for all areas of human activity ontol-
ogy of choosing solutions from a given set of alternatives O choice . The introduction of
the "Adjustment" relationship raises the question of the possibility and level of deci-
sion making automation for various areas. In the presence of a representative of
"PDM "class "Solver", the decision is subjective, since a person is involved in the
decision.
The introduction of the "Automaton" representative of the class "Solver" makes the
decision to be formalized. For example, the court decision making ontology belongs
to a strictly structured area. The ontology of decision making on managing the devel-
opment of the pharmacy network belongs to a weakly structured area. Experiments
were conducted to determine the effectiveness of the introduction of automation of
decision making. The criterion of effectiveness is the VOF (6), which consists of non-
commensurate indicators reflecting the degree of functionality and injectivity, as well
as topological criteria characterizing the throughput and topological entropy of the
ontographs. The introduction of a full formalization of the sentence resulted in an
assessment of the functionality of the system, demonstrating the need for a judge
(PDM).
6 Future Works and Acknowledgment
The emphasis in decision making meta-ontology (5) on the ontologies of formaliza-
tion of tasks O form and on the production of alternatives O altern emphasizes the need
for integration between content-related ontologies. Decision making in the social
sphere requires the formation of new knowledge from documents available in the
semantic web of different nature, which is impossible without the automatic detection
of latent knowledge.
The ontological knowledge bases of the consolidated linguistic resources of the
syntactic processing of Ukrainian-language texts in the work [15] opens the possibili-
ties for further automated development of ontologies of decision making, in particu-
lar, in the social sphere. The work was carried out within the research work "Mathe-
matical modeling of socio-economic processes and systems" at the Department of
System Analysis and Computational Mathematics of Zaporizhzhya National Tech-
nical University.
References
1. Chernyahovskaya, L. R., Shkundina, R. A., Nugaeva, K. R.: Ontologicheskiy podhod k
razrabotke sistem podderzhki prinyatiya resheniy. In: Vestnik UGATU (In Russian)
http://journal.ugatu.ac.ru/index.php/Vestnik/article/view/2027.
2. Litvin, V. V., Gopyak, M. Ya., Demchuk, A. B.: Metod avtomatizovanoyi rozbudovi ta
otsinyuvannya yakostั ontologiy baz znan. In: Vseukrayinskiy. naukovo-tehnichniy zbir-
nik. Harkiv, โ161, pp. 62โ69 (In Ukrainian) (2012)
3. Demchuk, A. B., Gopyak, M. Ya.: Metod otsinyuvannya yakosti ontologiy baz znan intel-
ektualnih sistem na osnovi ISO/IEC 25012. In: Visnik Natsionalnogo universitetu. Lvivska
politehnika, Informatsiyni sistemi ta merezhi, โ 805, pp. 80-86 (In Ukrainian) (2014)
4. Bershteyn, L.S., Bozhenyuk, A.V.: Nechetkie grafyi i gipergrafyi. M., Nauchnyiy mir,
p. 256 (In Russian) (2005).
5. Afanaseva, T. V., Moshkin, V. S., Namestnikov, A. M., Timina, N. I., Yarushkina, A. G.:
Ontologicheskiy i nechetkiy analiz slabostrukturirovannyih informatsionnyih resursov. Ul-
yanovsk, UlGTU, p. 130 (In Russian) (2016)
6. Tevet, J.: Structure of the Graphs and Graphs of the Structure. S. E. R. R., Tallinn, p. 76
(In English) (2003)
7. Basto Fernandes, V.: Ontologies Quality Assessment and Optimization University Institute
of Lisbon (ISCTE-IUL).
https://www.researchgate.net/publication/308646484_An_Ontology_of_Preference-
Based_Multiobjective_Metaheuristics.
8. New Protege Short Course. Stanford Center for Biomedical Informatics Research. Stan-
ford Univ., California, USA. http://protege.stanford.edu/.
9. Kriminalniy kodeks Ukrayini. Vidomosti Verhovnoyi Radi Ukrayini, โ 25-26, p. 131. (In
Ukrainian) (2001) http://zakon4.rada.gov.ua/laws/show/2341-14.
10. Valkman, Yu.R., Hala, E.A.: Proektirovanie ontologii dlya pravovoy predmetnoy oblasti
na osnove tekstovogo kontenta s ispolzovaniem nechyotkoy logiki. In: Ontologiya proek-
tirovaniya, โ 2(12), pp. 19-39 (In Russian) (2014)
11. Riaรฑo, D., Real, F., Lรณpez-Vallverdรบ, J.A., Campana, F., Ercolani, S., Mecocci, P., An-
nicchiarico, R., Caltagirone, C.: An ontology-based personalization of health-care
knowledge to support clinical decisions for chronically ill patients. In: Journal of Biomedi-
cal Informatics, pp. 429โ446 (In English) (2012)
12. Puschmann, T., Alt, R.: Customer Relationship Management in the Pharmaceutical Indus-
try Institute of Information. Management University of St. Gallen St. Gallen, Switzerland.
(In English) https://www.researchgate.net/publication/
44938144_Customer_Relationship_Management_in_the_Pharmaceutical_Industry.
13. Bakurova, A.V., Tereshchenko, E.V., Pasัchnyk, M.S.: Algoritm Sugeno u sistemั pัd-
trimki prijnyattya sudovih rัshen'. Informatsiyni tehnologiyi ta kompโyuterne
modelyuvannya. In: Mizhnarodnoyi naukovo-praktichnoyi konferentsiyi, Ivano-Frankivsk,
p. GolIney, O.M., pp. 81-84 (In Ukrainian) (2018)
14. Bakurova, A.V., Ropalo, H.M.: Sistema pidtrimki priynyattya rishennya pro
rozmischennya aptek na osnovi nechitkoyi logiki. In: Upravlinnya proektami, sistemniy
analiz i logistika, K., Natsionalniy transportniy universitet, โ19, p.2, Ekonomichni nauki
pp. 5โ13 (In Ukrainian) (2017)
15. Lytvyn, V. V., Vysotska, V. A., Hrendus, M. H.: Method of data expression from the
ukrainian content based on the ontological approach. In: Radioelektronika, informatika,
upravlinnya, โ 3, pp. 157 (In English) (2018)