Incompletely Specified Regular Ternary Logic Functions and Their Minimization

Tomoyuki ARAKI  Masao MUKAIDONO  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E82-D   No.5   pp.910-918
Publication Date: 1999/05/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Issue on Multiple-Valued Logic and Its Applications)
Category: Logic and Logic Functions
Keyword: 
regular ternary logic function,  fuzzy switching function,  incompletely specified,  minimization,  fuzzy PLA,  

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Summary: 
Regular ternary logic functions are one of the most useful special classes of Kleenean functions, and a lot of research has been done on them. However, there has been little work done on incompletely specified regular ternary logic functions. This paper describes the following points: (1) Minimization of incompletely specified regular ternary logic functions. (2) A new definition of incompletely specified fuzzy switching functions and their minimization. (Concretely speaking, minimal disjunctive forms of incompletely specified fuzzy switching functions are represented in formulas of regular ternary logic functions. ) (3) Their application to fuzzy logic circuits such as fuzzy PLAs of AND-OR type.