Generalized Properties of Generalized Fuzzy Sets GFScom and Its Application

Negative information plays an essential role in knowledge representation and commonsense inference. We further continually develop the theory of a generalized fuzzy set with contradictory, opposite and medium negation (GFScom). The t-norm, s-norm, convexity and concavity properties of GFScom are discussed. By introducing GFScom to Mamdani fuzzy systems, we propose new constructive approaches from any (infinite) input-output data pairs to approximate any continuous function on a compact set to a desired degree of accuracy, and study the first-order and the second-order approximation error bounds for the classes of the constructed fuzzy systems from mathematical viewpoints in details. Furthermore, the new better sufficient conditions for this class of fuzzy systems to be universal approximators are investigated thoroughly. Finally, we illustrate several examples and compare the new results to published error bounds through numerical examples.