A model abstracted from a grey system. Grey system is a system that contains both known information and unknown or unascertained information, and such a system is ubiquitous. An important content of studying grey system is how to abstract and establish a model from a fuzzy system with insufficient overall information, so that the factors of grey system can be changed from fuzzy to clear, and the less knowledge can provide research basis. Grey system theory is the product of the extension of cybernetics viewpoint and method to social and economic fields, and also the result of the combination of automatic control science and mathematical methods of operational research.
Paste mathematics
Mathematical theory and method to study and deal with fuzziness. 1965, the American cybernetic scholar L.A. Zadeh published the paper Fuzzy Sets, which marked the birth of this new discipline. Modern mathematics is based on set theory. A set of objects determines a set of attributes, and people can explain concepts by specifying attributes or objects. The sum of the objects that conform to the concept is called the extension of the concept, and the extension is actually a set. All realistic theoretical systems may be included in the mathematical framework of set description. Classical set theory only limits its expressive force to those concepts and things with clear extension. It clearly stipulates that every set must be composed of certain elements, and the subordinate relationship of elements to the set must be clear. The mathematical treatment of fuzziness is based on the extension of classical set theory to fuzzy set theory, and the fuzzy subset in product space gives the fuzzy relationship between a pair of elements. On this basis, the fuzzy phenomenon is dealt with mathematically.
From the point of view of pure mathematics, the expansion of the concept of set has added new contents to many branches of mathematics. Such as fuzzy topology, fuzzy linear space, fuzzy measure and integral, fuzzy group, fuzzy category, fuzzy graph theory and so on. Some of these areas have been thoroughly studied.
The mainstream of fuzzy mathematics development lies in its application. Because the concept of fuzziness finds the description of fuzzy sets, the process of people's judgment, evaluation, reasoning, decision-making and control by using concepts can also be described by fuzzy mathematics. Such as fuzzy cluster analysis, fuzzy comprehensive evaluation, fuzzy decision-making, fuzzy control and so on. These methods constitute the embryonic form of fuzzy system theory and speculative mathematics, and have made concrete research achievements in the fields of medicine, meteorology, psychology, economic management, petroleum, geology, environment, biology, agriculture, forestry, chemical engineering, language, control, remote sensing, education and sports. The most important application field of fuzzy mathematics should be computer intelligence. It has been used in expert system and knowledge engineering.
Neural network means that there are two different basic ways of thinking: logic and intuition.
The research content of neural network is quite extensive, which embodies the characteristics of interdisciplinary technology field. At present, the main research work focuses on the following aspects:
(1) biological prototype research. This paper studies the biological prototype structure and functional mechanism of nerve cells, neural networks and nervous systems from the aspects of physiology, psychology, anatomy, brain science and pathology.
(2) Establish a theoretical model. Through the study of biological prototype, the theoretical models of neurons and neural networks are established. It includes conceptual model, knowledge model, physical and chemical model, mathematical model and so on.
(3) Research on network model and algorithm. On the basis of theoretical model research, a concrete neural network model is constructed to realize computer simulation or hardware preparation, including the study of network learning algorithm. This work is also called technology model research.
(4) Artificial neural network application system. Based on the research of network model and algorithm, practical application systems are formed by using artificial neural network, such as completing some signal processing or pattern recognition functions, constructing expert systems, manufacturing robots, etc.
Throughout the development history of contemporary emerging technologies, mankind has gone through a bumpy road in the process of conquering space, elementary particles, the origin of life and other scientific and technological fields. We will also see that the study of exploring human brain function and neural network will change with each passing day with the overcoming of many difficulties.
Logical thinking refers to the process of reasoning according to logical rules; First, it transforms information into concepts and represents them with symbols. Then, logical reasoning is carried out in serial mode according to symbolic operation. This process can be written as a serial instruction for the computer to execute. Intuitive thinking is to synthesize distributed information, and the result is a sudden idea or a solution to the problem. The fundamental point of this way of thinking lies in the following two points: 1. Information is stored on the network through the distribution of excitation patterns on neurons; 2. Information processing is accomplished through the dynamic process of simultaneous interaction between neurons.