Paper Info
Title
The set of fuzzy points of a fuzzy vector lattice is not a vector lattice
Abstract
Samuel introduced the notions of fuzzy vector lattices and fuzzy points of fuzzy vector lattices. He considered unique extensions of fuzzy Daniell integrals (i.e. positive linear σ-order continuous maps) defined on sets of fuzzy points to spaces that behave like L1-spaces. His arguments hinge on the fact that sets of fuzzy points of a fuzzy vector lattice form vector lattices. We show, by means of a counter example, that the set of fuzzy points of a fuzzy vector lattice does not form a vector lattice. Consequently, Samuel's fuzzy Daniell integrals need not be linear.
Year
DOI
Venue
2006
10.1016/j.fss.2006.07.002
Fuzzy Sets and Systems
Keywords
Field
DocType
03E72,46A40
Discrete mathematics,Fuzzy classification,Defuzzification,Fuzzy set operations,Fuzzy measure theory,Fuzzy set,Fuzzy subalgebra,Fuzzy associative matrix,Fuzzy number,Mathematics
Journal
Volume
Issue
ISSN
157
20
0165-0114
Citations 
PageRank 
References 
0
0.34
1
Authors
2
Name
Order
Citations
PageRank
C.C.A. Labuschagne100.34
A.L. Pinchuck200.34