On the complexity of growth of the number of distinct fuzzy switching functions |
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Authors: | Michael Thum Abraham Kandel |
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Institution: | Computer Science Department, Florida State University, Tallahassee, FL 32306, USA |
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Abstract: | Several attempts have been made to enumerate fuzzy switching (FSF's) and to develop upper and lower bounds for the number of FSF's of n variables in an effort to better understand the properties and the complexity of FSF's. Previous upper bounds are 24n 9] and 22–3n—2n—1 7].It has also been shown that the exact numbers of FSF's of n variables for n = 0, 1, 2, 3, and 4 are 2, 6, 8, 84, 43 918 and 160 297 985 276 respectively.This paper will give a brief overview of previous approaches to the problem, study some of the properties of fuzzy switching functions and give improved upper and lower bounds for a general n. |
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Keywords: | Fuzzy switching functions Enumerations Minimization Lower and upper bounds |
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