Similarity measures of generalized trapezoidal fuzzy numbers for fault diagnosis

In this paper, we propose a new similarity measure between generalized trapezoidal fuzzy numbers and several synthesized similarity measures to solve fault diagnosis problem by merging our proposed measures with Dempster-Shafer evidence theory. Firstly, combining the exponential distance with numerical indexes of generalized trapezoidal fuzzy number, such as the span, the center width and the height, etc, we propose a new similarity measure between generalized trapezoidal fuzzy numbers. Secondly, we introduce an evaluation index, distinguish ability, to evaluate the performance of different similarity measures. The experimental results show that our proposed similarity measure can overcome the drawbacks of the existing similarity measures. Thirdly, to solve fault diagnosis problems, we propose three formulas to integrate several single similarity measures to a synthesized one. Finally, based on Dempster-Shafer evidence theory, we transform each similarity measure between fault model and test model, the synthesized similarity measures to their corresponding basic probability assignments to deal with fault diagnosis problem, the results show that our proposed similarity measure is more effective than some other existing similarity measures.