Paper Info
Title
Lattices of fuzzy sets and bipolar fuzzy sets, and mathematical morphology
Abstract
Mathematical morphology is based on the algebraic framework of complete lattices and adjunctions, which endows it with strong properties and allows for multiple extensions. In particular, extensions to fuzzy sets of the main morphological operators, such as dilation and erosion, can be done while preserving all properties of these operators. Another extension concerns bipolar fuzzy sets, where both positive information and negative information are handled, along with their imprecision. We detail these extensions from the point of view of the underlying lattice structure. In the case of bipolarity, its two-components nature raises the question of defining a proper partial ordering. In this paper, we consider Pareto (component-wise) and lexicographic orderings.
Year
DOI
Venue
2011
10.1016/j.ins.2010.03.019
Inf. Sci.
Keywords
Field
DocType
extension concern,negative information,complete lattice,fuzzy set,lexicographic ordering,multiple extension,algebraic framework,bipolar fuzzy set,positive information,mathematical morphology,main morphological operator,partial ordering,partial order,lexicographic order
Discrete mathematics,Dilation (morphology),Mathematical morphology,Lexicographic preferences,Fuzzy set,Operator (computer programming),Fuzzy number,Partially ordered set,Mathematics,Pareto principle
Journal
Volume
Issue
ISSN
181
10
0020-0255
Citations 
PageRank 
References 
36
0.95
46
Authors
1
Name
Order
Citations
PageRank
Isabelle Bloch12123170.75