Ordering operations and lexicographical estimates of likelihood in models of reasoning

The article investigates the algebra of ordering operations that generalize the minimum, maximum, and negation operations of Zadeh algebra, and that allow, more completely than in that algebra, for information about the operands. Ordered lists of operands which are compared lexicographically with each other constitute a result of applying the ordering operations. The ordering operations are oriented toward processing of qualitative information in models of reasoning used in intellectual systems for various purposes: expert medical and technical diagnosis systems, intelligent decision making systems, and the design of others.