As one of the most frequently used methods for fuzzy knowledge representation, the fuzzy production rule system has been widely used. However, this conventional fuzzy production system does not render a systematic description on relationship among fuzzy production rules and does not give an efficient inference mechanism. To alleviate these drawbacks of the conventional fuzzy production system, we propose fuzzy petri net model for the fuzzy production system and its inference engine. The fuzzy Petri nets is used to model the fuzzy procuction system and the inference engine is designed to be capable of handling inexact knowledge. The fuzzy logic is adopted to represent vagueness in the rules and the certainty factor is used to express uncertainty of each rules given by a human expert. Parallel inference schemes are devised by transforming fuzzy Petri nets to matrix formula. Since the proposed inference engine mechanism under some implication methods can be described by a simple algebraic formula, real time inference is possible.
As another useful tool for handling fuzzy human knowledge, the fuzzy relational equations have been widely used since a lot of human knowledges may be viewed as a collection of facts and rules, each of which may be represente as a fuzzy relation having some possibility value. Several forms of fuzzy relational equations and their analytical solution methods have been presented. However, most of these analytical solution methods are based on the assumption that there exists a fuzzy relation for all pairs of input and output fuzzy data simultaneously. However, this assumption is quite difficult to satisfy in real situations since different pairs of input fuzzy data often include inconsistence among them.
To overcome the drawbacks of analytic methods for solving fuzzy relational equation, we present a neurocomputational method to solve a convexly combined fuzzy relational equation with generalized connectives. For this, we propose a neural network whose structure represents the fuzzy relational equation. Then we derive a learning algorithm by using the concept of back-propagation learning. Since the proposed method can be used for a general form of fuzzy relational equations, such fuzzy max-min or min-max relational equations can be treated as its special cases.
Finally, as an alternative to fuzzy relational equation approach in handling human knowledge, we propose an inference network as a tool for bidirectional approximate reasoning. The inference network can be designed directly from the given fuzzy data (knowledge). If a fuzzy input is given for the inference network, then the network renders a reasonable fuzzy output after performing approximate reasoning based on an equality measure. Conversely, due to the bidirectional structure, the network can yield its corresponding reasonable fuzzy input for a given fuzzy output.
