AbstractThis 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. Syst Comp Jpn, 38(9): 63–73, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20243