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This article proposes a novel asymmetric dual-regression model that combines the principles of twin-support vector machine theory with the possibilistic regression analysis. Using the principle of a twin-support vector machine, the proposed approach solves four smaller quadratic programming problems, each of which constructs the lower and upper bound functions of the possibility and necessity models, rather than a single large one. This strategy significantly reduces the time that is required for training. The output from the obtained dual-regression model is characterized by an asymmetric trapezoidal fuzzy number. The obtained asymmetric dual-regression model is more flexible and models the data distribution better than a symmetric model. The proposed approach provides a unified framework that accepts various types of crisp and fuzzy input variables by using radial kernels. The proposed dual model also indicates a degree of confidence to the predicted outputs. The explicable characteristic for the degree of confidence also means that the proposed approach is more suitable for decision-making task. The experimental results demonstrate that the proposed approach has a more efficient training procedure and better describes the inherent ambiguity in the observed phenomena.