In this paper, we develop a method to find the uncertain consequent by fusing the uncertain antecedent and the uncertain implication rule. In particular with Dempster-Shafer theoretic models utilized to capture the uncertainty intervals associated with the antecedent and the rule itself, we derive bounds on the confidence interval associated with the rule consequent. We derive inequalities for the belief and plausibility values of the consequent and with least commitment choice they become equations. We also demonstrate the consistency of our model with probability and classical logic.
@inproceedings{heendenietal14belief,
title={Modelling and Fusion of Imperfect Implication Rules},
author={J. N. Heendeni and K. Premaratne and M. N. Murthi and M. Scheutz},
year={2014},
booktitle={International Conference on Belief Functions},
url={https://hrilab.tufts.edu/publications/heendenietal14belief.pdf}
doi={10.1007/978-3-319-11191-9_34}
}