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https://open.uns.ac.rs/handle/123456789/12797
Title: | Characterization of generalized S-threshold functions by nomura parameters | Authors: | Prokić, Ivan Pantović, Jovanka |
Issue Date: | 1-Jan-2019 | Journal: | Journal of Multiple-Valued Logic and Soft Computing | Abstract: | ©2019 Old City Publishing, Inc. This paper deals with the encoding and enumerating of generalized Sthreshold functions. Such a function performs a partition of its finite domain set, where induced subsets are separable with parallel hypersurfaces. Each hyper-surface is characterized as a linear combination of functions from the fixed tuple S. We show that if the function is a generalized S-threshold then it is uniquely characterized by the encoding presented here. The parameters of the code can be seen as a direct generalization of well known Chow and Nomura parameters. Using this characterization, we obtain upper bounds for the number of functions from three classes of threshold functions: linear, multilinear and polynomial with a restricted degree. We give the correspondence of our encoding with one existing in the literature that uses discrete moments. It is shown that, in some cases, we get a sharper upper bounds for the number of threshold functions than those derived using discrete moments. | URI: | https://open.uns.ac.rs/handle/123456789/12797 | ISSN: | 15423980 |
Appears in Collections: | FTN Publikacije/Publications |
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