A brief introduction to grey systems theory

TLDR

This paper introduces the elementary concepts and fundamental principles of grey systems, outlines its main components, and reviews its rapid progress and broad applications across science and learning. The authors analyze the characteristics of unascertained systems with incomplete and inaccurate data and compare four uncertain theories—probability statistics, fuzzy mathematics, grey system, and rough set theory. The findings show that precise models are ineffective for complex, data‑incomplete problems, and position grey systems theory as a simpler, more suitable method, contrasting it with probability statistics, fuzzy mathematics, and rough set theory across diverse research settings.

Abstract

Purpose The purpose of this paper is to introduce the elementary concepts and fundamental principles of grey systems and the main components of grey systems theory. Also to discuss the astonishing progress that grey systems theory has made in the world of learning and its wide‐ranging applications in the entire spectrum of science. Design/methodology/approach The characteristics of unascertained systems including incomplete information and inaccuracies in data are analysed and four uncertain theories: probability statistics, fuzzy mathematics, grey system and rough set theory are compared. The scientific principle of simplicity and how precise models suffer from inaccuracies are also shown. Findings The four uncertain theories, probability statistics, fuzzy mathematics, grey system and rough set theory are examined with different research objects, different basic sets, different methods and procedures, different data requirements, different emphasis, different objectives and different characteristics. Practical implications The scientific principle of simplicity and how precise models suffer from inaccuracies are shown. So, precise models are not necessarily an effective means to deal with complex matters, especially in the case that the available information is incomplete and the collected data inaccurate. Originality/value The elementary concepts and fundamental principles of grey systems and the main components of grey systems theory are introduced briefly. The reader is given a general picture of grey systems theory as a new method for studying problems where partial information is known, partial information is unknown; especially for uncertain systems with few data points and poor information.