Making large data decisions requires the development of effective methods for processing and analyzing information. One possible way in this direction is creation of ontologies. The purpose of the work is to construct a decision making meta-ontology and to develop on its basis basic objective ontologies, which are used in the future for the design of systems for supporting decision making in the social sphere. To assess the quality of the developed ontologies, 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 metaontology decision making and two basic ontologies of decision making have been constructed: the court decision making and management of the pharmacies network development.
Decision making is the main point in human activity, and the decision making patterns remain the same for all subject areas. Difficulties in making decisions arise because 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 procedure, 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 network. In these examples, decision areas are distinguished by the initial degree of formalization and the level of possible automation. 2
The paper [1] proposed a methodology for developing an information system for decision 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 analysis 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 ontologies. These characteristics include: functionality in use, reliability, clarity, convenience, 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 certainty. It is applied to individual fragments of the ontology according to the following formulas.
Defines the prototype of a set of concepts С in compliance Г̃ :
Г̃−1(С) = {< Г̃−1(С)( ), >| ∈ }, where Г̃−1(С)( ) = ⋁ ∈ ( ̃ < , >), ̃ – membership function value.
The degree of fuzzy functionality implies that each ontology concept will have
textual inputs that have a small number of common terms, and is determined by the
formula:
(Г̃ )
= 1 − (Г̃ )
(
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
according to the following formulas:
(Г̃ )
= 1 − (Г̃ )
(
( ))). ( )
The quality estimates (
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 assessment 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 making 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, according to two estimates - functionality and reliability (injectivity), which are also the main characteristics of the ISO / IEC 25012 standard. Therefore, next, these two criteria include in the construction of multi-criteria evaluation, complementing various options for topological (structural) criteria. 3
In the theory of artificial intelligence, “ontology” is understood as the formalization of a certain field of knowledge by a conceptual scheme. We will consider decision making as a process taking place according to the scheme shown in Fig. 1, where the sign "→" shows the corresponding relationship between superclasses (SC). Define the ontology of decision making as
O O form , O alternative , O choice
(
Filling in subject ontologies O form and O altern requires working with a specific subject area, researching specific tasks. Each representative O form of the set O form of ontologies of formalization of the tasks of the subject areas includes the superclasses "Situation" and "Formal Task", which are in the relation of Formalization. Each representative O altern of a multitude O altern 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 “Set of alternatives”, “Solver” and “Decision made”, relations “Analysis”, “Decision choice”. To provide feedback in decision making, lets define an additional relation Adjustment :Solver 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 “Formal Problem” 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 presented as a tuple X , opt _ rule where X is a set of alternatives, opt _ rule is the criterion 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 “Solver” 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 “Decision making subject” with the subclasses “Decision maker” and “Automatic”. The “Decision Making” 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 Protégé 5.5.0 was used [8]. Fig. 2 shows the decision ontology as an ontograph using the GraphViz graphical module of the Protégé 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 characterize the structure and information capacity of the ontograph:
Q(O' ) (F, I ,{TG}) max (
The calculation of the ontology fragments estimates is performed on the
fuzzyweighted parts of the ontograph, whose weights are determined by an expert method.
VOF (
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 Protégé editor; 5. integration of ontology with other related ontologies. 4
Next, we consider the construction of a basic ontology of decision making on the example of two subject areas. 4.1
Court decisions are made in accordance with Art. 65 of the Criminal Code of Ukraine (СС 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 maximum 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_court→court_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 СС of Ukraine [9]. There are eleven such circumstances. Circumstances that burden a punishment are specified in Art. 67 [9]. These circumstances are determined by 14. The mechanism for making a court decision is determined by the relations schematically shown in Fig. 3.
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)
(
PW, Cond - determines the actual or conditional entry into action.
Let's evaluate the efficiency of introducing into the ontology class "Judgment Solution", which will have three representatives – neutral (N), strict (H) and loyal (L), within the limits allowed by the rule of law. There are factors shaping the court decision: B - burdening circumstances, M - mitigating circumstances, P+ -positive properties 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.
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 providers to detect abnormal circumstances such as irregular diagnoses, unobservable concomitant illnesses, missing information, unobserved associated illnesses or preventive actions. Another example is the work of Thomas Puschmann [12]. An ontological approach 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
connections 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: Manager→Preferred strategy. The mechanism of decision making on
managing the development of the pharmacy network is determined by the relationships
shown schematically in Fig. 4.
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 f( CA, As, E, T) ,
(
In addition, the elements can be included in the ontology: the quality of the pedestrian flow, the type of district, the competitive environment, the distance to the medical 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 (
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
development 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 (
The emphasis in decision making meta-ontology (
The ontological knowledge bases of the consolidated linguistic resources of the syntactic processing of Ukrainian-language texts in the work [15] opens the possibilities for further automated development of ontologies of decision making, in particular, in the social sphere. The work was carried out within the research work "Mathematical modeling of socio-economic processes and systems" at the Department of System Analysis and Computational Mathematics of Zaporizhzhya National Technical University. 9. Kriminalniy kodeks Ukrayini. Vidomosti Verhovnoyi Radi Ukrayini, № 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 proektirovaniya, № 2(12), pp. 19-39 (In Russian) (2014) 11. Riaño, D., Real, F., López-Vallverdú, J.A., Campana, F., Ercolani, S., Mecocci, P., Annicchiarico, R., Caltagirone, C.: An ontology-based personalization of health-care knowledge to support clinical decisions for chronically ill patients. In: Journal of Biomedical Informatics, pp. 429–446 (In English) (2012) 12. Puschmann, T., Alt, R.: Customer Relationship Management in the Pharmaceutical Industry 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., Pasіchnyk, M.S.: Algoritm Sugeno u sistemі pіdtrimki prijnyattya sudovih rіshen'. Informatsiyni tehnologiyi ta komp’yuterne 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, №19, p.2, Ekonomichni nauki pp. 5–13 (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, № 3, pp. 157 (In English) (2018)