Author: Zen and the Art of Computer Programming
1 Introduction
Fuzzy System Modeling (Fuzzy System Modeling) refers to adding some assumptions or knowledge, concepts and other constraints in the description of the fuzzy system, so as to establish a model that can process real-world information but cannot accurately predict the real results, so as to serve as an actual One of the important tools in the application. Its purpose is to abstract the complex and imprecise real-world modeling and give it rationality and limitations, thereby improving the reliability and robustness of the model, so that it can better adapt to real-world changes and input conditions, And has a certain degree of self-learning ability, with a wide range of application value.
In the field of fuzzy system modeling, the most basic concepts and terms are fuzzy set, fuzzy quantity, fuzzy boundary, fuzzy definition, fuzzy input, fuzzy output, fuzzy rule, fuzzy reasoning and fuzzy simulation. Among them, fuzzy set, fuzzy quantity, fuzzy boundary and fuzzy definition are respectively used to represent entities, attributes and their value ranges in the fuzzy system; fuzzy input and fuzzy output are used to represent the external input and output of the fuzzy system. Fuzzy rules are used to describe how fuzzy systems process different types of inputs and make decisions based on outputs; fuzzy reasoning is used to characterize the response of fuzzy systems to specific input patterns.
With these basic concepts and terms, combined with some algorithms and formulas, different fuzzy system models can be constructed. Let's take a fuzzy decision analysis model—Maximum Entropy Method (MEM) as an example to describe the basic principles and characteristics of MEM, and how to implement a fuzzy decision analysis model based on MEM.
2. Explanation of basic concepts and terms
2.1 Sequence of events
In the process of fuzzy system modeling, it is first necessary to give the definition of the problem studied by the fuzzy system, that is, which fuzzy decision-making problems to solve. Fuzzy decision-making problems are generally composed of event sequences, that is, under certain conditions, the system needs to generate a series of events in a time sequence, and then the final decision result can be obtained by analyzing the correlation and sequence of these events. A sequence of events can be of two types y