## 6 Conclusions  
In this paper, based on the fuzzy theory, a novel membership function was constructed and verified through the experimental data. Subsequently, the material properties, dimensions, and loads of welded A-type frame were considered as random variables, and the fatigue limit of the welded A-type frame was taken as a fuzzy variable. By taking advantage of Latin hypercube method, the samples were obtained and fitted to build the fuzzy fatigue reliability performance function. Based on the suggested membership function, the fuzzy fatigue reliability of the welded A-type frame under conditions of downhill and turning braking with full load. When the fuzzy fatigue reliability was found to be less than the engineering requirement, the optimal design for improving the reliability based on genetic algorithm was conducted. Here are some specific conclusions:  
1. Based on the fuzzy theory, a novel membership function was presented to characterize the distribution feature of fuzziness for this welded A-type frame. It was more accurate to obtain the ambiguity that was caused by the fatigue damage.
2. The multi-source uncertainties from the material properties, dimensions, and loads of welded A-type frame were fully taken into account. A fuzzy fatigue reliability calculation method was proposed based on the self-configuring membership function.
3. The fuzzy fatigue reliability of welded A-type frame under conditions of downhill and turning braking with full load was found to be 69.47%. It was far less than the engineering requirement. Based on the genetic algorithm, it was improved to 95.12%.  
Figure 20: Stress contour of welded A-type frame after optimization.  
According to the optimized results, the quality of weld seam had to be ascertained in order to ensure the enough fuzzy fatigue reliability of welded A-type frame. In addition, the driving speed under this severe condition had to be reduced.  
Conceptualization, C.M. and W.L.; Methodology, C.M.; Software, X.X.; Validation, X.X., W.L. and C.M.; Formal Analysis, X.X.; Investigation, J.L.; Resources, X.M.; Data Curation, X.X.; Writing-Original Draft Preparation, C.M.; Writing-Review & Editing, C.M.; Visualization, W.L.; Supervision, X.M.; Project Administration, J.L.; Funding Acquisition, C.M. and X.M.  
This research was funded by [Natural Science Foundation of Hunan Province] grant number [2017J]3059 and [Postdoctoral Science Foundation] grant number [2017M622569], and [State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body] grant number [31715012], and [Outstanding Youth Foundation of Education Department of Hunan Province] grant number [18B301].  
The authors gratefully thank for the support of the Hunan Province Natural Science Foundation (Grant No.: 2017 JJ3059 and 2017J4023) and China Postdoctoral Science Foundation (Grant No.: 2017M622569) and Open Foundation of State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body (Grant No.: 31715012) and Outstanding Youth Foundation of Education Department of Hunan Province (Grant No.: 18B301).  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.