Exponential similarity measure of confidence consistency fuzzy cubic sets in fuzzy multiset scenarios and its application in piano performance evaluation

Abstract

A consistency fuzzy set is composed of mean values and consistency degrees of fuzzy sequences in the transformation process of a fuzzy multiset (FM), but lacks confidence intervals in relation to a confidence level of fuzzy sequences, which shows its deficiency. To solve this deficiency, this paper aims to propose an improved transformation approach from FM to a confidence consistency fuzzy cubic set (CCFCS) and to develop an exponential similarity measure of CCFCSs for modeling piano performance evaluation (PPE) in a FM scenario. Consequently, this study includes the following context. First, a transformation approach from FM to CCFCS is proposed in terms of mean values, consistency degrees (the complement of standard deviation), and confidence intervals of fuzzy sequences subject to a confidence level and normal distribution. Second, the exponential similarity measure of CCFCSs is proposed in the scenario of FMs. Third, a PPE model is developed based on the proposed similarity measure of CCFCSs in the FM scenario. Finally, the developed model is applied to a piano performance competition organized by Shaoxing University in China as an actual evaluation example, and then the rationality and validity of the proposed model in the scenario of FMs are verified through sensitivity and comparison analysis.