Generation of threshold functions of high-order satisfying monotonicities

This paper presents a generation procedure for high-order threshold functions, considering the high-order neighbor vector and the monotonic property. Specifically, it is first shown that the high-order neighbor vector can be derived from an input vector which is noncomparable by the high-order threshold function. Then, it is shown that a monotonic function of a high-order variable can easily be generated from the given monotonic function. Based on the generation process for the monotonic function, the generation procedure for high-order threshold functions is derived. It is also shown that if a given high-order threshold function preserves monotonicity, the generated high-order threshold function also preserves monotonicity, and also the high-order terms. © 2007 Wiley Periodicals, Inc.