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Design+

ARTICLE
Modern interpretations of probability

2
Yuri F. Zinkovsky 1 and Leonid O. Uryvsky *
1 Department of Applied Radio Electronics, Faculty of Radio Engineering, National Technical
University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine
2 Department of Electronic Communications and Internet of Things, Institute of Telecommunication
Systems, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv,
Ukraine

Abstract

Probability, along with logic and fuzziness, has become an essential framework for
studying and managing complex, uncertain, and dynamic processes across science,
engineering, and society, particularly in an era marked by globalization, incomplete
information, and rapid technological change. The present work continues and
further develops the exploration of the category of “probability” in its application
to the technical field, particularly in radio engineering and electronics, as previously
explored by the authors. In this interpretation, the concept of “probability” is
examined across various areas of human activity, rendering it relevant to a broad
range of specialists engaged with random processes in their respective fields. This
study analyzes the varying interpretations underlying the theoretical foundations
and practical applications of probability, logic, and fuzzy systems. This variability
arises from differing understandings of the philosophical meaning of probability
*Corresponding author: and logic, the objective principles governing the interconnection of probabilistic and
Leonid O. Uryvsky logical reasoning, and the formation of fuzzy set theories and associated engineering
(leonid_uic@ukr.net)
tools. These tools have become increasingly useful in implementing the life cycle
Citation: Zinkovsky YF, of structurally complex long-range technical systems, particularly in fields such as
Uryvsky LO. Modern interpretations
of probability. Design+. energy, telecommunications, military, and space technology. Moreover, the theory
2025;2(2):6387. of fuzzy multitudes and related engineering approaches has gained relevance in
doi: 10.36922/dp.6387 studying climate change and the environmental ecology surrounding humans. They
Received: November 21, 2024 help establish the current state and predict future trends in social systems, wildlife
populations, and other complex, dynamic environments.
Revised: February 5, 2025
Accepted: April 14, 2025
Keywords: Probability; Logic; Multitude; Fuzziness; Incomplete information; Engineering
Published online: May 13, 2025 activities
Copyright: © 2025 Author(s).
This is an Open-Access article
distributed under the terms
of the Creative Commons
AttributionNoncommercial License, 1. Introduction
permitting all non-commercial use,
distribution, and reproduction in any Probability, as a mathematical category, is a numerical characteristic of the degree of
medium, provided the original work possibility of a random event occurring under certain specified conditions that can be
is properly cited. repeated an unlimited number of times. Probability theory is a branch of mathematics
Publisher’s Note: AccScience that focuses on determining the probabilities of events related to given random events.
Publishing remains neutral with Based on the given probabilities of individual random events, the probabilities of
regard to jurisdictional claims in
published maps and institutional other events related in any way to the primary events can be determined. This theory
affiliations. also studies random variables and random processes. The mathematical apparatus of

Volume 2 Issue 2 (2025) 1 doi: 10.36922/dp.6387