Paper Info
Title
Basic intuitionistic principles in fuzzy set theories and its extensions (A terminological debate on Atanassov IFS)
Abstract
In this paper we contribute to the terminological debate about Atanassov's use of the term ''Intuitionistic'' in defining his structure based on ortho-pairs of fuzzy sets. In particular, we stress that it is defined as ''intuitionistic'' a negation which from one side does not satisfy a standard property of the intuitionistic Brouwer negation (contradiction law) and on the contrary asserts some principles rejected by intuitionism (strong double negation law and one of the de Morgan laws). An algebraic Brouwer negation is studied in the context of IFS showing that it can be induced from a Heyting implication. A similar situation occurs in the case of standard fuzzy sets (FS). Some conditions which allow one to distinguish from the algebraic point of view FS from IFS are treated. Finally, a particular subclass of IFS consisting of ortho-pairs of crisp sets (denoted by ICS) is studied, showing that shadowed sets can be algebraically identified with ICSs.
Year
DOI
Venue
2006
10.1016/j.fss.2006.06.003
Fuzzy Sets and Systems
Keywords
Field
DocType
fuzzy set,atanassov ifs,algebraic point,basic intuitionistic principle,de morgan law,contradiction law,terminological debate,standard fuzzy set,fuzzy set theory,particular subclass,intuitionistic brouwer negation,algebraic brouwer negation,standard property,strong double negation law,intuitionism,fuzzy sets,satisfiability
Discrete mathematics,Double negation,Algebraic number,Negation,Fuzzy set operations,Fuzzy set,Intuitionism,De Morgan's laws,Type-2 fuzzy sets and systems,Mathematics
Journal
Volume
Issue
ISSN
157
24
Fuzzy Sets and Systems
Citations 
PageRank 
References 
19
0.92
13
Authors
2
Name
Order
Citations
PageRank
Gianpiero Cattaneo156658.22
Davide Ciucci267253.74