Fuzzy Reasoning Mathematical Structure And Its Application

This thesis mainly studies the algebra structure and applications of fuzzy inferenceo The chief research : one is R0 algebra structure of WnxWm, the other is some ways of fuzzy - possible reasoning . It consists of two parts: part I is on the structure of R0 algebra , and par on the undeterministic reasoning. In order to study R0 algebra structure algebra, where R0 algebra is two-dimensional, we introduce middle point concept. Based on it , we find the sufficient and necessary conditions about middle point which is additive (unadditive) or removeable (unremoveable) . Then we give constructive ways of non-total order R0 algebra whose element numbers are odd. This part has the important theory meaning, it points out some direction for people who study the most general R0 algebra structure. In part II, we discuss fuzzy-possible inference ways. Since reasoning in AI and Expert Systems involves a large number of fuzzy phenomenons, fuzzy reasoning has become main direction of undeterministic reasoning. In this part, we mainly discuss production systems whose left part is a fuzzy phenomenon, but right part is a state or proposition. Especially , right with certain factor. A t last we build up some reasoning ways. These wayes aim for different conditions, They have some practical values in AI and expert systems.