Abstract
The generalized trapezoidal fuzzy numbers and generalized trapezoidal interval-valued fuzzy numbers cannot handle the complex situation, although individually they are having their own worth in the particular environment. So, we combined both the generalized trapezoidal fuzzy numbers and generalized trapezoidal interval-valued fuzzy numbers and define a hybrid structure named as generalized trapezoidal cubic numbers (GTCNs) which can capture the complex situation in a better way. For utilizing generalized trapezoidal cubic numbers (GTCNs) in real-life problems, we discuss their basic arithmetic operations. Then, we proposed different types of similarity measures between the generalized trapezoidal cubic numbers (GTCNs) so that one can easily handle problems where similarities often exits. We discuss Chen's similarity measure, Hsieh and Chen's similarity measures, Lee's similarity measures, Chen and Chen's similarity measures, Yong et al. similarity measures, Wei and Chen's similarity measures, Xu et al.'s similarity measures, Hejazi et al.'s similarity measures, Patra and Mondal's similarity measure, Khorshidi and Nikfalazar's similarity measures and Chutia's similarity measures. Finally, we discuss the application of generalized trapezoidal cubic numbers (GTCNs) in risk analysis using proposed similarity measures.