โ Scribed by Kabekode V.S. Bhat
No coin nor oath required. For personal study only.
In this paper, we present a consistent theory for the minimization of fuzzy functions given in disjunctive normal form by studying the structure of such functions. An O(N*) time algorithm is given for minimization of a fuzzy function consisting entirely of elementary phrases. The minimal form in this case is shown to be unique (i.e., the minimal form consists of a unique set of phrases). By introducing the notion of standard complex minterms and standard minterrns a tabular method is presented and illustrated for the minimization of a disjunctive normal form consisting of entirely complex phrases. The method resembles the well-known Quine-McCluskey tabular procedure for Boolean function minimization.
The minimal form in this case may not be unique in general. Finally, the approach is extended for the case of minimization of an arbitrary disjunctive normal form consisting of both elementary as well as complex phrases.
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