List all monotonic binary functions

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Joshua Carmichael
Joshua Carmichael 2022년 8월 8일
편집: Walter Roberson 2022년 8월 8일
Is there a simple implemntation of functions in Matlab that can list / output all monotonic binary functions for a given input vector? These are sometimes informally called Dedekind functions. I saw a link on the Mathematica stack exchange, but I don't see a clear equivalency between the solution that appears in the that link, and functions that we can implement in Matlab. Stated simply, there is something lost in translation.
I pasted an example table when N = 2 and there are N = 16 different functions, but only 6 are monotone. The "sensor output" just indicates a decision (0 or 1). The "global fusion rule" is the list of binary functions.
Others (table from reference pasted below) give the number montone functions for a larger "number of sensors", which is just the length of the Boolean vector. The reference for the table that appears below is: "Thomopoulos, S. C. A., Viswanathan, R., & Bougoulias, D. K. (1989). Optimal distributed decision fusion. IEEE Transactions on aerospace and electronic systems, 25(5), 761-765."
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Joshua Carmichael
Joshua Carmichael 2022년 8월 8일
Thanks, Walter. It seems that "Algorithm 5" on page 32 provides the list of fusion rules that I require. I may list your answer "the Answer" if this what I need. I think a "profile" in the CS community is equivalenet to the "fusion rule" in terminology of the EE community. Similarly, I think "sensor input" (data fusion / EE literature) is just a "variable" in CS literature.

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