Theoretical Research And Applications Of Fuzzy Entropy Based On Fuzzy Optimization

The fuzzy information is commonly found in structural optimization. In order to effectively combine fuzzy theory and structural optimization, it needs to relate fuzzy set theory to the fuzzy information of structural optimization and apply theory to practice. In this paper, theoretical research and applications of fuzzy entropy based on fuzzy optimization is the main research.In view of structural optimization problems with discrete variable which often appear in optimal design of complex mechanical structures, round method and other methods which are used to solve this kind of problem have poor precision and simple models with lacking of the description of working conditions. Combined with quantitative characteristics of discrete variable structural optimization, a new discrete variable structural optimization model is established by defining a parameterized fuzzy entropy, and a multidirectional searching algorithm with discrete variable structure is introduced. In order to obtain numerical solution of discrete variable structural optimization problems, traditional genetic algorithm is improved and combined with parameterized fuzzy clustering analysis to form a hybrid genetic algorithm with powerful global searching capability and efficient local searching capability. The design of a high pressure bypass-valve is used as an example to optimize. It shows that, with better operability, the improved discrete variable structural optimization model and solving method is more suitable to establish models and obtain the solution for problems arising from the situation with complex working conditions. The research result provides a new approach and theoretical basis for discrete variable structure optimization problem.In addition, the concepts of distance measure and similarity measure are given to describe the relationship between classical sets and fuzzy sets in this paper. The internal relations between two measures and parameterized fuzzy entropy are discussed. The calculating formulas, induced by parameterized fuzzy entropy, of distance measure and similarity measure of fuzzy sets are constructed with a proof. They are induced by the parameterized fuzzy entropy and the proof is also given. Finally, the application of distance measure in a belt drive design is given. It shows that parameterized fuzzy entropy can be applied to multi-objective optimization decision, which enlarges the applications of parameterized fuzzy entropy.