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The Theory of Fuzzy Logic Based on Family of Implication Operators

Author: HuangAMin
Tutor: PeiDaoWu
School: Zhejiang University of Technology
Course: Basic mathematics
Keywords: Fuzzy Logic Fuzzy Reasoning Family of implication operator Three methods I Fuzzy Control
CLC: O159
Type: Master's thesis
Year: 2010
Downloads: 33
Quote: 0
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Abstract


In recent years, fuzzy control has achieved remarkable success in the application. However, as the core of the mathematical basis of the fuzzy inference is not perfect. Therefore, in order to research the mathematical foundations of fuzzy reasoning as the core of fuzzy logic, as a new field of mathematics, aroused the attention of many scholars in the world, and made a series of important research results. Fuzzy logic is a very wide range of applications. On the one hand, it is enriched and developed the theory of pure mathematics. On the other hand, it is in the field of approximate reasoning and fuzzy control a wide range of applications. Fuzzy Control parameters implication operator fuzzy controller design can be improved through the selection of parameters, the effect of fuzzy control, which has a certain rationality. So the subject of this paper is to study the parameters based implication operator fuzzy logic theory, fuzzy control provides new ways and means (ie family of implication operator). The main research work and results are as follows: 1. Fuzzy Implication Operator Families nature study. By t-norm family of implication operator family and visited the family of implication operator to meet the 16 constraints, further given the relationship between the family of implication operator with several important family of implication operator. Generalized tautologies. Since the RDP logical system in fuzzy logic theory occupy an important position, so we chose the implication operator subfamily R p in the system as the research object, a detailed analysis based on the family of implication operator fuzzy logic system established in generalized tautologies Theory. The results show that the system, only three different generalized tautology type. In addition, we will also be effective in some multi-valued logic and fuzzy logic system upgrade algorithm used in the system, proved that a finite number of non-tautology in the system upgrade algorithm may not be able to get a tautology. 3 Triple I method. Discussion the fuzzy inference R_p based on the family of implication operator full implication triple I method with alpha-triple I method theory, Triple I Method for FMP and FMT problems formula, which will help to improve the flexibility of the fuzzy inference to reduce the fuzzy inference resulting blindness. 4 properties of fuzzy reasoning algorithm. Triple I method consistent continuity problems, the research-based implication Operator Family Triple I method is uniformly continuous, which to some extent illustrate the superiority of the algorithm. 5 simulation. Fuzzy reasoning triple I method is applied to fuzzy control, the rational design of fuzzy controller to guide practice. System simulation experiments show that: the parameters for different values ??of the control target are not the same. Therefore, in the reasoning process by selecting the appropriate parameters, optimize fuzzy control effect.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Fuzzy Mathematics
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