Study On Similarity-based Fuzzy Reasoning

Fuzzy inference is one of the methods for uncertainty reasoning, which is based on fuzzy set theory. Fuzzy reasoning algorithm is the theoretical foundation and an important tool for designing and analyzing fuzzy expert systems, fuzzy control systems and fuzzy intelligent decision-making systems. At present, many of the fuzzy reasoning algorithms are developed based on the compositional rule of inference approach. However, from the logical semantic implication point of view, the compositional rule of inference algorithm is the lack of sound grounds. But the similarity-based reasoning algorithms do not need to establish the fuzzy relations between two fuzzy sets, which come to certainty factor of the classification of the input sample and thus to determine the appropriate output by calculating the similarity between the input and the antecedent of the rules. The studies of such reasoning algorithms in theory and practical applications have made considerable progress, but there are still many topics that should be discussed in greater depth.In this paper, the main work and contributions are described as follows:1. A new similarity-based reasoning algorithm is proposed. In addition, the continuity and approximation property of the similarity-based reasoning algorithm were discussed and the error estimation in the similarity-based reasoning algorithm under the conditions of perturbations of inputs and rules were also taken into consideration.2. The application of fuzzy Petri nets for fuzzy reasoning is in favor of knowledge representation structured, reasoning process sharpen, and it has strong parallel processing capacity. Therefore, the similarity-based inference algorithm is combined with Petri nets to solve the problem that the token values determined by experts or assumed, also avoid the shortcomings of the computational complexity using the fuzzy statistical method. Then the rules which closed to relatively high degree are synthesized, that avoid the screening of change priority. In accordance with the rules of transition firing in marked fuzzy Petri net, the reasoning process is graphical, then the fuzzy Petri nets is further analyzed from the perspective of Petri nets.3. The fuzzy reasoning algorithms are applied to the fuzzy control systems, through the simulation experiment of fuzzy control system, from the point of reasoning results, reasoning computation speed and the results of control simulation, to analysis the advantages of various algorithms. The experimental results show that similarity-based reasoning algorithms have fast processing speed, time-saving. However, as the threshold of the rules increased, the output of the system fluctuated, therefore, in the actual applications, the threshold of the rules should be reasonable selected to avoid volatility.4. Through the universe self-adaptation algorithm can eliminate the steady-state error of the system, which could make the system's actual output approximation to the desired output. This will make more ideal control efficiency of the fuzzy control systems.