Enumerating fuzzy switching functions and free Kleene algebras
type: Item
instance of: scholarly article
title: Enumerating fuzzy switching functions and free Kleene algebras
zbMATH Open document ID: 0543.94029
DOI: 10.1016/0898-1221(84)90083-X
author: Masao Mukaidono
author: Joel Berman
publication date: 1984-01-01T00:00:00Z
review text: As Boolean algebras are related to two-valued logic and to switching functions, Kleene algebras are related to a three-valued logic and to fuzzy switching functions. The authors consider the free Kleene algebra FK(n) of n generators and determine the cardinality of FK(4) as 160,297,985,276. For general n, lower and upper bounds are given for the cardinality of FK(n), i.e. for the number of n-variable fuzzy switching functions. The methods are applied to determine also the numbers of regular (ternary) functions in 1, 2, 3, and 4 variables.
Mathematics Subject Classification ID: 94C10
Mathematics Subject Classification ID: 94D05
Mathematics Subject Classification ID: 03G10
Mathematics Subject Classification ID: 08B20
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03B52
zbMATH DE Number: 3865167
zbMATH Keywords: regular ternary functions
zbMATH Keywords: three-valued logic
zbMATH Keywords: fuzzy switching functions
zbMATH Keywords: free Kleene algebra
reviewed by: Siegfried J. Gottwald
MaRDI profile type: Publication
cites work: Lattices With Involution
cites work: Q4083730
cites work: On constructible falsity in the constructive logic with strong negation
cites work: Injective de Morgan and Kleene Algebras
cites work: Q4187871
cites work: On Kleene algebras
cites work: Q3328542
cites work: Q4165427
cites work: Q5515373
cites work: Q5812175
cites work: An algebraic approach to non-classical logics
cites work: Fuzzy sets
cites work: Some properties of fuzzy logic
cites work: Continuously valued logic
cites work: Q4166695
cites work: Q4193404
cites work: Q5640746
cites work: Quasi‐Boolean Algebras, Empirical Continuity and Three‐Valued Logic J. P. Cleave in Bristol (Great Britain)
cites work: On the Properties of Fuzzy Switching Functions
cites work: Q4126378
cites work: Q5331549
cites work: Q5593643
cites work: Q5655273
cites work: Q5535953
cites work: Q3331149
cites work: Testing and Realization of Threshold Functions with Don't Cares
cites work: Q4140834
cites work: Fuzzy Maps
cites work: Q3332943
cites work: A generalization of Sperner's lemma
cites work: A decomposition theorem for partially ordered sets
cites work: Lattice Theoretic Properties of Frontal Switching Functions
cites work: On the counting problem for monotone boolean functions
cites work: Free lattices in some small varieties
cites work: Q4200260
cites work: On Minimization of Fuzzy Functions
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 3865167