The adaptation of automated organizational management systems (ASOM) is closely related to the concept of distributed systems. In this context, adaptation involves modifying structural relationships between information blocks, adjusting processing algorithm parameters, and incorporating reflective elements. Currently, the field of ASOM adaptation within complex distributed systems has emerged, where specialized mathematical models and methods are employed. This paper presents an analysis of the scientific and methodological framework for ASOM adaptation, including examples of successful applications of ontology synthesis and conceptual structure synthesis using degree-based structural typologies. Limitations of current approaches in addressing adaptation challenges, particularly with respect to conceptual changes, are identified. Further development directions are suggested, focusing on enhancing the scientific and methodological framework through tensor transformations in electrical multicoil networks.
System The emergence of new means and methods of their
application Designed automated organizational management system
System model Description of functioning
and management processes
Logical database model
Source data system (axioms
of management) System of information processing procedures The problem is that: introducing new settings or changing software leads to conflict situations. It is easier to develop a new automated control system than to adapt its current version. Such adaptation ideally should occur without a complete redesign or the need for new automation tools, instead relying on transformative procedures that require minimal time and resources. Therefore, when designing new ASOM, it is advisable to integrate adaptability features, preferably in an automated manner.
To address ASOM adaptation, several key research directions should be emphasized. The organization management process operates in three modes (Figure 2):
The problem of adaptation of AOMS to conceptual changes in management
processes Adjustment Mode (target management):
1) transformation of the area of controlled parameters;
2) changing the boundaries and dimensions of the zones of permissible and boundaryachievable parameters.
Operational Management Mode:
1) adaptation of algorithms for restoring the current state of the system in relation to current management criteria;
2) adaptation of algorithms for diagnosing functional deviations, risks, threats, etc. management).
Planning or Programming Mode:
1) adaptation of the control object model (structure and behavior);
2) adaptation of algorithms for predicting the state of the system under given control and conditions;
3) adaptation of algorithms for selecting optimal control for a given terminal state of the system.
Achieving ASOM adaptation to a new management concept during the planning mode requires mechanisms that transform: 1. Management Object Model: Restructures the management process to align with a new conceptual framework, including functional relationships and responses to external influences. 2. Prediction Algorithms: Adjusts ASOM software to predict the system's state under the new management model and external conditions. 3. Optimal Management Algorithms: Updates decision-support algorithms to plan for the organization’s functioning under the modified model and performance criteria. For the adjustment mode of previously created plans, transformation mechanisms include: 1. Controlled Parameter Areas: Expands the parameters, dimensionality, and structure of inter-parameter relationships. 2. Acceptable and Limit-Reachable States: Adapts criteria for achieving established goals.
1. Current State Algorithms: Reflects observed parameters in the cognitive model of the management process.
3. Decision Support Algorithms: Provides real-time support for current management decisions.
This detailed breakdown of the adaptation problem highlights the importance of developing mathematical and software solutions for ASOM. Targeted research in these areas will lay the theoretical groundwork for adaptive ASOM development. Some scientific advancements have already been made in synthesizing structures with defined properties and in the conceptual design of complex systems. 2. Mathematical Models and Methods for Constructing Adaptive
In constructing adaptive Automated Systems of Organizational Management (ASOM), two primary
approaches, closely linked through ontology application, can be identified (Figure 3):
System Algebra Framework: Utilizes Boolean functions, predicate calculus, and logical
inference [
The system algebra framework combines mathematical logic with algebraic structures, such as groups and rings, which serve as models for processes, and lattices, which model structural relationships. The set degree framework similarly employs algebra but focuses on set degree formation and logical procedures. Together, these approaches support the development of adaptive mechanisms for systems, with multiple successful implementations already demonstrated.
As proposed in [
Algebra, algebraic structures (groups,
rings, lattices). | | | |
Apparatus of stages of sets (kinds of structures).
Conceptual design.
Ontological approach
The following types of confinement models are identified (Figure 4): Conceptual CM (CCM): Connects elements through "causes/depends on" relationships, with a specific case being the triadic CM (TCM) (Figure 4a).
8 9 8 7 1
Is a part 7 6 9 5 6 1 4 a 2 c 2 3 4 5 3 7 9 8
Is 8 9 6 1 5 b 7 d Has the property
2 6 4 1 3 4 2 5 3
Through CMs, knowledge structuring can be achieved using interrelated cognitive models of a specialized kind, setting a standard for ontology detailing by various researchers. This approach facilitates the development of formal methods for operating and transforming ontology structures.
In [
, , … , , where each object is classified as an instance of a corresponding concept. These object sets serve as the basis for n many-sorted algebras.
Each set , defines an abstract data type: = (
, Σ, ), where
denotes the type name (e.g., circle); Σ is the signature of the many-sorted algebra (circle parameters like center coordinates, radius);
is the defining relations of the type (circle equations).
= ( , … , , … , ).
Process CM (PKM): Structures processes by identifying life cycle stages with "is of" relationships.
property." input/output for" relationships.
o o o
species relations, expressed as "is." Meronymic (MKM) (Figure 4c): Analyzes subsystems systematically with "is part Attributive (AKM) (Figure 4d): Classifies properties using the relation "has a (1) (2) where is the attribute identifier (for example, "x"); - its value (real number). Operations such as merge, substitute, delete, and interpret (merge, substitute, delete, enterp) are defined for this domain. In addition to these operations, various functions are defined, for example, the value selection function of the domain:
, } with variables from other domains. It includes Boolean operations "AND," "OR," "otherwise" and simplifies conditions via the interpretation operation (=). elements are constraints (conditions).
Entity Domain with Attributes, , represented by tuples { ,
} , ( , ) →
; , , ∗ , where for each i there is only one j, that forms an element of the T:
∀ ∃ : , , each condition (constraint) belonging to the subset ∗, is an expression with operands belonging to the domain . Operations on elements of this domain are the union or division (merge, split) of entities. The union operation is interpreted as the synthesis of a new entity with a compatible set of properties and constraints (conditions) of operand entities. The division operation is the reverse. Instances of the domain of entities with attributes are tuples of corresponding facts; Relation Domain, RI, on structures:
, × … × , , , ∗ , where , × … × , is a Cartesian product of algebraic data types from the domain (attribute space related to the i-th structure); - types of relation attributes; ∗ - constraints (conditions) defining the relation. Operations such as union, separation, substitution (merge, split, substitute) are performed on relations.
The ontology itself is a tuple of concept domains with attributes, relations, and constraints: = ( , , ∗). (3)
= 〈 , ∗ , ∗ 〉 , (4) where is the problem ontology according to the construction rules (3); ∗ is the task ontology; ∗ is the set of additional constraints (conditions). Each action is an entity within the domain, serving as a command to external services or other ontological models. Parameters are attributes from or constants.
The transformation of algorithms depending on changes in conditions and constraints is carried out using the parameter initialization function (InstPar), which is given as a set of mappings between the action attribute and the attribute values of entities and relations in the ontology model: : , , , → , , , , (5) , ∈ , , ∈ ∈ , where is the ontological model of the considered task; is the task’s ontology.
The software system based on the ontological model of tasks is presented in Figure 5 [
Knowledge base Semantic interpretation of facts.
Ontology
Fact base Establishing the fact of the process.
Extensions to the description of ontology classes and relations.
Description of models using ontology.
Web sites Document repositories
Log files Database
Web services
Simulation system
Services and modeling systems
Model execution
manager
Information service provider Model interaction broker
Interpreting facts, solving tasks, establishing
relationships.
Requests to the provider during
model execution.
Semantic interpretation of events.
Events
Models Using operations by calling external services.
External services
The management process in the intelligent control system generates events, which are interpreted using the ontology of the corresponding subject area. Based on the interpretation of the event, models and algorithms necessary for implementing the computational process for management in current conditions are activated. Using the ontology of models and algorithms, a new computation schedule is created. The synthesis of the schedule is carried out using the apparatus of mathematical logic (logical inference).
Depending on the context of the occurring events, either one or another ontological model is
activated. The initiator of activation is the ontological model being executed (Figure 6) [
Activator model Activated model Defining the Goal
Initializing the General Model
Model selection
Initialization Identifying Relevant Models
Context
Execution in a specific context.
This framework also supports the creation of new ontologies. This involves the following steps: 1. Analyzing the problem and identifying relevant entities, relations, constraints, and operations. 2. Constructing the ontological model using available components, supplemented with any newly identified elements.
The ontology-based tool for building software systems offers functionalities including: Ontology Operations: Creation and modification of ontology classes, relationships, and attribute constraints. Fact Operations: Creation and modification of individual facts, constraint verification, and fact validation. Ontological Model Management: Creation and editing of models using classes and facts, defining constraints, operations, and service links. Execution of Models: Testing models on a factual base and verifying outcomes.
The system is implemented in Python with PyQt for its graphical interface, and includes components such as an ontology editor, fact editor, model editor, and simulation programs. Future development will focus on expanding model interactions, implementing logical inference, enabling multi-variant computations, and addressing contextual dependencies.
2.3. Deployment of Security Domain Ontology Based on Conceptual Schemes of Abstract Security Relations
In [
A subject's interests nominally constitute a subset of its possibilities (the subject is interested in realizing these possibilities).
Any possibility that blocks possibilities from the subject's area of interest represents a threat to the subject's interests.
An action to realize a possibility is a possibility that is formative for the subject related to that possibility.
Since threats and actions regarding the realization of possibilities can also define threats and measures, it can be said that there are first, second, third, etc., order threats and measures.
The ontology construction process involves iteratively breaking down the factors in a structuretree format within this set of possibilities. This breakdown involves: Concept Elaboration: Specification and detailing of initial concepts. Inter-branch Relations: Formation of relations between ontology branches by integrating hierarchical levels and factor-based relationships.
Using conceptual schemes of abstract security relation structures [
Relationship of genetic connection of possibilities or set of pairs: possibility possibility, which proves to be a necessary condition for the realization of the considered possibility. of 1.2 1.0 1.1 1.2 ⋮ ( ⊂ 1.0)&( ⊂ ) ⇒ ( ⊂ 1.1) ∨ ( ⊂ 1.2) ⇒: ( = ∅) ¬ ( ( ( ∈ ℬ( 1 × 1) & ∈ ) ⊃ ( ⊂ 1.1) & ∈ Pr )&( ∈ Pr )& (Pr \ = Pr \ ) ⇒ ∈ ℬ( 1 × 1)&( ∈ ) ⇒ ( ⊂ 1.2)&( ∈ Pr )&(Pr \ ⋮ ∈ Pr )& = Pr \ )
⋮ { ⊂ ℬ( 1 × 1)|Pr = Pr }
Constituents presented in Table 1 are types of abstract security relation structures synthesized
using formal rules of transforming text structure when applying set degree formation operations [
The handbook of theoretical constructs [
The scientific results presented are an example of a fairly successful solution to the problem of adapting ASOM. However, it cannot be claimed that the problem is fully solved. There are limitations and drawbacks to the methods that do not allow concluding the completion of creating a conceptual transformation apparatus for management systems.
Therefore, when adapting the computational procedures' regulations (see section Помилка! Джерело посилання не знайдено.), the ontology of models and algorithms is used, which is preformed and entered into the knowledge base. The task of expanding and developing the ontology based on the interpretation of facts and events remains unresolved. This leads to the need, once again, to create a new version of the mathematical and software when there are conceptual changes in the management process for which the ASOM is created. The adaptation or "learning" of ASOM under a new management concept has not yet been implemented.
For the method of using conceptual schemes of structure types (see section Помилка! Джерело
посилання не знайдено.), the bottleneck is the interpretation of the created abstract schemes. For
higher set degrees (which are significant in practice), the generated constituents are expressions with
a very large dimension. Their size exceeds human capabilities to operate with data blocks. In [
As a method for synthesizing new structures, tensor transformation of networks developed by
Gabriel Kron [
An electrical network is convenient for a formalized description of structural connections of various kinds. Unlike other types of non-electric networks, an electrical network is always surrounded by a dynamic electromagnetic field created by itself, extending to infinity in all directions. By using the model of induction and self-induction in the branches of an electrical network, it is convenient to describe various intra-system connections between elements of the analyzed structure (organizational topology).
If we interpret the organizational-functional structure in the form of a multi-coil electrical
network, tensor synthesis of Kron [
For an existing multi-coil electrical network, there is a connection tensor or in other words, a primitive network transformation tensor. A primitive network is a set of node pairs (an electric coil with an input and output point) and elementary circuits that form a specific network but are not connected to each other. The transformation tensor is such that the corresponding electrical network functions in a defined manner:
( , , ) = 0 , where is the impedance tensor (electrical resistances of node pairs and network circuits, taking into account the resistance of inductance and self-induction in mutual influence of coils), is the current tensor;
is the voltage tensor; ( , , ) = 0 is the formalized representation of the network's behavior.
is derived from the impedance tensor of the
primitive network ′ using the transformation tensor ( ) [
The synthesis tensor
is derived to transform the impedance tensor of the output network into the impedance tensor of another network , without changing the network's behavior: = ( ) ′ . = (
) , ( , , ) = ( , , ) = 0 , where ( ) is the transposed synthesis tensor .
depends on the form of the formalized description
of the system behavior ( , , ). The result of this derivation is a compound tensor (a tensor whose
elements are also tensors) [
In [
– is the set of electrical networks obtained by transforming from the output network { , , } using the synthesis tensor , determined based on the formalized condition (6). (6) (7) (8) (9)
The choice of a specific network { , , }∗ from the variety Ω is made using an established criterion :
{ , , }∗ ≻ ⋯ ≻ { , , } ≻ ⋯ ≻ { , , } , (10) where is the number of alternative electrical networks forming the set Ω .
Thus, solving the problem of synthesizing structures with specified properties and addressing the adaptation problem of ASOM to conceptual changes in the control process can be implemented by introducing the following intermediate scheme (Figure 7).
Determination of the synthesis tensor from the conditions
defining the domain of existence of the transformed
network.
Procedure for transforming a
conceptual diagram using the Kron network synthesis tensor
A new conceptual diagram that meets the selection criterion Conceptual diagram 1
Conceptual ...
diagram 2 Bank of interpreted conceptual diagrams for specific systems
This scheme involves using a pre-interpreted bank of conceptual schemes for specific systems. Conceptual schemes are presented as multi-coil electrical networks with a corresponding formalized description of the desired behavior. In other words, defining the boundaries of the region of permissible state parameters or the existence area of the system.
In case of changes in the control loop that cannot be adapted by adjusting parameters within the existing control structure: the conceptual schema that is relevant to the initial state of the ASOM is retrieved from the database. Each conceptual schema has a formalized representation of its domain of existence and a pre-formed synthesis tensor to determine alternative schemes within that domain; using the synthesis tensor, a transformation of the original conceptual schema results in a set of alternative conceptual schemes; a criterion for establishing preference is formulated for comparing these alternative conceptual schemes; the criterion previously established is used to determine and choose a new conceptual scheme that best meets the needs of adapting the ASOM to the changes that have occurred in the management process.
Therefore, to address the adaptation problem in this context, progress should be made in the following directions: creating a database of pre-interpreted conceptual schemes for specific systems in relevant subject areas; developing a procedure for transforming conceptual schemes based on the use of the tensor transformation procedure for electrical networks.
Methods and models designed to solve adaptation and self-organization problems of Automated Control Systems (ACS) belong to the field of conceptual ontology design and transformation.
confinement models for ontological networks; algebraic systems apparatus; set theory apparatus of N. Bourbaki.
The main practical challenge in implementing these approaches is the issue of dimensionality. To construct adaptive control systems with complexity corresponding to real processes, the problem of creating a specialized language for interpreting (representing) the results of conceptual design needs to be addressed.
As an intermediate step in solving the adaptation problem, it is advisable to address the design task by transforming previously created conceptual schemes of specific systems.
creating and accumulating a database (bank) of pre-interpreted conceptual schemes for specific systems; developing a procedure for transforming conceptual schemes based on the use of the tensor transformation procedure for electrical networks.