Paper Info
Title
K-operators: An approach to the generation of interval-valued fuzzy implications from fuzzy implications and vice versa
Abstract
This paper introduces the interval-valued fuzzy implications generated from fuzzy implications and from K-operators showing that this construction generalizes the canonical representation of fuzzy implications. Such generalization allows to recover the usual fuzzy implication properties when dealing with interval-valued fuzzy implications. In addition, the condition under which the converse construction, i.e. the generation of fuzzy implications by action of K-operators and interval-valued fuzzy implications, is discussed. Moreover, we analysed their conjugate construction obtained by action of interval automorphisms. Through commutative diagrams, the associativity related to compositions of conjugate, dual and K-operators performed over fuzzy implications is shown, also preserving their main properties.
Year
DOI
Venue
2014
10.1016/j.ins.2012.12.047
Inf. Sci.
Keywords
Field
DocType
canonical representation,usual fuzzy implication property,interval-valued fuzzy implication,fuzzy implication,main property,commutative diagram,interval automorphisms,converse construction,conjugate construction
Discrete mathematics,Defuzzification,Fuzzy classification,Fuzzy set operations,Fuzzy mathematics,Fuzzy subalgebra,Type-2 fuzzy sets and systems,Fuzzy associative matrix,Fuzzy number,Mathematics
Journal
Volume
ISSN
Citations 
257,
0020-0255
3
PageRank 
References 
Authors
0.39
28
2
Name
Order
Citations
PageRank
Renata Hax Sander Reiser111010.90
Benjamín C. Bedregal275551.96