An approach for the synthesis of multi-threshold threshold elements

doi:10.1109/TC.1972.5009053

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Title:	An approach for the synthesis of multi-threshold threshold elements
Authors:	盛慶琜;Sheng, Ching-lai;Shinha Roy, P. K.
Contributors:	淡江大學經營決策學系
Date:	1972-08-01
Issue Date:	2011-10-20 16:12:25 (UTC+8)
Abstract:	A new approach for the realization of multithreshold threshold elements is presented. The procedure is based on the fact that the excitations at contradictory vertices of the switching function must be unequal. The weights of the multithreshold element, in general, satisfy simple relations of the form U·W = 0, where U=(u1, u2, ... , un) and W=(w1, w2, ... , wn) such that ui ¿{1,0, ¿1,}, i=1,2, ... n, and W¿In. Comparison of the excitations E(Xi) = W·Xi and E(Xj) = W·XjM at TRUE, and FALSE vertices Xi and Xj, respectively, for all specified vertices reusult in some inequalities of the form U·W¿0. Subsets of the remaining set of weight expressions U·W that are compatible are then determined, i.e., no linear combination of some or all of these expressions results in an expression Ui·W such that Ui·W¿0 and independent of each other. Each expression of each of these subsets is then equated to zero, and simple relations between weights are established. These are then used to find the weights vectors W's. The threshold vector T for each W is next established. From the set of weight-threshold vectors (W, T) the desired solution is determined by some minimality criterion. An example has been worked out by hand and an algorithm is given for systematic synthesis procedure.
Relation:	IEEE transactions on computers21(8), pp.913-920
DOI:	10.1109/TC.1972.5009053
Appears in Collections:	[Department of Management Sciences] Journal Article

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