From uncertainty to approximate reasoning: part 3: reasoning with conditional rules

Abstract

This is the third part of a three-part paper. In part 1 (C/V Eng Syst. 1986, 3(3), 143-1 54), different models of uncertainties such as intervals, fuzzy sets, Dempster-Shafer evidence, and random numbers were compared. Then, in part 2 (Civ Eng Syst. 1986, 3(4), 192-202) reasoning based on an inference network of algorithmic rules was described. Algorithmic rules are the simplest inference rules in reasoning, but constitute only one extreme of the rule spectrum. Conditional rules are more general and correspond to less well-defined inference relations. The propagation and combination of uncertainties in a network of conditional rules are described in this part of the paper. Treatment of probabilistic uncertainties is described in detail, and the associated difficulties delineated. Finally, uncertain inference with other forms of uncertainties is presented to provide contrast, and to complete the discussion on the impact of uncertainty models on approximate reasoning.

Keywords:

• conditional rule
• uncertainty propagation
• approximate reasoning
• interval analysis
• fuzzy set
• probability
• evidence