Definitions of a system

Definitions of a System — the concept of "system" has many different definitions, used depending on the context, field of knowledge, and research goals. This is due to the interdisciplinary nature of the systems approach and the evolution of the concept of a system itself.

Reasons for Multiple Definitions

The differences in the definitions of a system are due to several factors:

• Duality of the concept: A System is viewed both as an objectively existing phenomenon and as a model or method for studying reality, created by a subject (Objective and subjective in systems analysis).
• Context and discipline: Definitions are adapted to the needs of a specific field (biology, engineering, economics, sociology, computer science).
• Research goals: Depending on the task (analysis of structure, behavior, control, design), the emphasis in the definition shifts.
• Level of abstraction: Definitions can be either broadly philosophical or narrowly specialized and formalized.
• Evolution of the concept: The historical development of systemic concepts has led to the addition of new aspects (goal, environment, observer) to the definitions.

Common Components of Definitions

Despite the differences, an analysis of most formulations allows for the identification of common key components that reflect the essential properties of systems:

• Elements (components, parts): The constituents of a system.
• Links (relationships): Interactions between elements.
• Structure: The organization of elements and links.
• Integrity (wholeness): A system as a unified whole, whose properties are not reducible to the properties of its parts.
• Boundaries: The separation of the system from its environment.
• Interaction with the environment: Exchange via inputs and outputs (Open system).
• Goal or Function: The purpose or directionality of the system's behavior.

Different definitions may emphasize one or more of these components.

Classification of Approaches to Definition

Definitions of a system can be broadly classified according to their primary emphasis:

• Descriptive: Focus on the objective description of composition (elements) and interconnections. Characteristic of the early stage of systems theory.
• Constructive (Goal-oriented): Emphasize the goal or function of the system, its organization for achieving a result, and often include the role of an observer or designer.
• Functional (Cybernetic): View the system as a transformer of inputs into outputs, focusing on behavior and control.
• Structural-functional: Combine a description of the structure with an indication of the functions of the elements or the system as a whole.

Examples of System Definitions

The table below presents various definitions of the "system" concept, indicating their authors (if known) and an analysis of the key ideas and emphasis of each formulation. This illustrates the diversity of approaches to understanding this fundamental concept.

Comparison of Definitions for the Concept of "System"

Definition	Author(s)	Analysis / Key Idea	Emphasis
A complex of interacting components.	L. von Bertalanffy	A foundational definition emphasizing interaction as the basis of a system.	Interaction, Components
A set of elements in certain relationships with each other and with the environment.	L. von Bertalanffy	Adds relationships and interaction with the environment to the elements.	Elements, Relationships, Environment
A whole composed of many parts. An ensemble of features.	C. Cherry	Emphasizes the integrity and composite nature of a system.	Integrity, Parts/Features
A set of interconnected elements, separate from its environment and interacting with it as a whole.	F. I. Peregudov, F. P. Tarasenko	A classic definition that combines key attributes: elements, links, boundaries, interaction with the environment, and integrity.	Elements, Links, Environment, Integrity
An arrangement, a set, or a collection of things connected or related in such a manner as to form a unity or whole; an arrangement of physical components...	DiStefano	Emphasis on the unification (arrangement) of components (including physical ones) into a single whole.	Unity, Integrity, Components (physical)
A combination of interacting elements organized to achieve one or more stated purposes.	ISO15288	A constructive definition from the systems engineering standard. Explicitly introduces purpose and organization.	Elements, Interaction, Organization, Goal
A finite set of functional elements and the relationships between them, distinguished from the environment in accordance with a specific goal within a specific time interval.	V. N. Sagatovsky	A constructive definition that includes functional elements, relationships, goal, environment, and time constraints.	Elements (functional), Relationships, Goal, Environment, Time
A reflection in the mind of a subject (researcher, observer) of the properties of objects and their relationships in solving a research or cognition task.	Yu. I. Chernyak	A subject-oriented definition. A system as a mental model dependent on the observer.	Subject/Observer, Cognition, Model
A system S on an object A with respect to an integrative property (quality) is a collection of such elements, in such relationships, that generate this integrative property.	E. B. Agoshkova, B. V. Akhlibininsky	Emphasis on the emergence of integrative (emergent) properties from the interaction of elements and their relationships.	Emergence, Integrative properties
A collection of integrated and regularly interacting or interdependent elements, created to achieve certain goals, where the relationships between elements are defined and stable, and the overall performance or functionality of the system is better than that of a simple sum of the elements.	PMBOK	A definition from project management. Combines integration, interaction, goal, and emergence (performance > sum).	Integration, Interaction, Goal, Emergence/Synergy
A device that accepts one or more inputs and generates one or more outputs.	Drenick	A cybernetic definition. A system as a transformer, a "black box" model.	Inputs, Outputs, Transformation
A device, process, or scheme... whose function... is to operate on... information and/or energy and/or matter...	D. Ellis, F. Ludwig	A functional definition that extends the cybernetic one; points to the handling of flows.	Function, Process, Transformation (of information/energy/matter)
A mathematical abstraction that serves as a model of a dynamic phenomenon.	H. Freeman	A mathematical perspective. A system as a mathematical model of dynamics.	Model, Mathematics, Dynamics
An integrated assembly of interacting elements, designed to carry out cooperatively a predetermined function.	R. Gibson	Emphasis on the cooperation of elements to perform a common function.	Integration, Interaction, Cooperation, Function
A set of objects together with relationships between the objects and between their attributes.	A. Hall, R. Fagen	A formal, set-theoretic definition that includes the attributes of objects.	Objects, Relationships, Attributes
A collection of entities... which receives... inputs and acts... to produce... outputs, pursuing... a goal of maximizing certain functions of the inputs and outputs.	R. Kershner	A cybernetic definition that includes a goal as the optimization of the transformation function for inputs/outputs.	Inputs, Outputs, Goal (function optimization)
A region of space-time in which parts-components are connected by functional relationships.	J. Miller	Emphasizes spatio-temporal boundaries and functional links between parts.	Boundaries (space/time), Functional relationships
From a mathematical perspective... a collection of relations among... units. The more closely intertwined the relations, the more organized the system...	A. Rapoport	A mathematical/structural view, focusing on relationships and the degree of organization.	Relationships, Organization
A set of actions (functions), linked in time and space by a set of practical tasks for decision-making and performance evaluation...	S. Sengupta, R. Ackoff	An activity-based approach. A system as a set of functions/actions for solving control tasks.	Actions/Functions, Tasks, Decision making, Control
A term... used to denote... a regular... arrangement... or a collection of... elements... necessary to perform some operation.	A. Wilson, M. Wilson	Indicates two meanings: an ordered whole (structure) and a set of elements for an operation (function).	Arrangement/Order, Operation/Function
A non-empty set of elements... where the elements... are in certain... relationships, connections with each other.	G. Kröber	A minimalist structural definition.	Elements, Relationships/Links
An abstract system... a partially connected set of abstract objects...	L. Zadeh, C. Desoer	A formal definition of an abstract system.	Abstraction, Objects, Partial connectivity
A set of related acting elements.	O. Lange	A concise definition emphasizing the activity/action of elements.	Elements, Links, Action
Any form of activity distribution in a network that is considered regular by some observer.	G. Pask	A behavioral/cybernetic approach with an emphasis on observed regularity and the role of the observer.	Activity, Regularity, Observer
A set of related... components... ordered by relationships... characterized by a unity that is expressed in integral properties and functions...	V. S. Tyukhtin	Combines components, relationships, orderliness, unity, and integrative properties/functions.	Components, Relationships, Orderliness, Unity, Integrative properties
The diversity of relationships and links among the elements of a set, constituting an integral unity... an organized set...	A. D. Ursul	Emphasis on the diversity of links, integrity, and organization.	Relationships/Links, Diversity, Integrity, Organization
A complex of selectively involved components whose interaction... acquires the character of mutual assistance... to obtain a focused, useful result.	P. K. Anokhin	A biological/functional approach. Emphasis on the "mutual assistance" of components to achieve a "useful result" (Goal/Function).	Components, Mutual Assistance, Useful Result (Goal/Function)
	L. A. Blyumenfeld	A detailed operational definition including links, indivisibility of elements, integrity of interaction with the environment, and preservation of identity during evolution.	Elements, Links, Indivisibility, Integrity, Environment, Evolution/Identity
A set of objects on which a relationship is realized... Its dual will be the definition... of a set of objects that possess... properties with fixed... relationships.	A. I. Uyemov	A logical-philosophical approach. Proposes two dual definitions via objects/relationships and objects/properties.	Objects, Relationships, Properties (logical structure)
A composition of parts (elements) that jointly produce behavior or meaning that is absent in its individual components.	International Council on Systems Engineering (INCOSE)	A modern definition from systems engineering, emphasizing the emergence of behavior or meaning.	Parts/Elements, Joint action, Emergent behavior/meaning

Reasons for the Lack of a Single Definition of a System

• Evolution of understanding: Over time, the concept of a system became more complex: from early interpretations as an "organized set" to the inclusion of goals, the role of the observer, and methods of system representation.
• Context and research goals: The definition of a system depends on the purpose of the analysis, the level of consideration, and the research task. At different stages of analysis, different "working" definitions are formulated that emphasize the most significant aspects.
• Diversity of objects and approaches: Systems differ in their nature (e.g., well-organized, poorly organized, self-organizing), which requires different models and approaches. In some cases, a system's goal may be absent from the definition (e.g., for natural objects).
• The system as a cognitive construct: A system is a means of consciously simplifying and representing reality. Different tasks of perceiving and analyzing reality require the construction of different system models.
  

External links

• System — Wikipedia

See also

• Concept of a system
• System
• System structure
• Formalization of system models
• System element