A note on rule representation in expert systems
Information Sciences: an International Journal
Twofold fuzzy sets and rough sets—Some issues in knowledge representation
Fuzzy Sets and Systems
The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
Why mathematical morphology needs complete lattices
Signal Processing
The algebraic basis of mathematical morphology
CVGIP: Image Understanding
Fuzzification of set inclusion: theory and applications
Fuzzy Sets and Systems
Cardinality, quantifiers, and the aggregation of fuzzy criteria
Fuzzy Sets and Systems - Special issue on fuzzy information processing
Vague sets are intuitionistic fuzzy sets
Fuzzy Sets and Systems
The applications of interval-valued fuzzy numbers and interval-distribution numbers
Fuzzy Sets and Systems
Complete ordering and multivariate mathematical morphology
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Mathematical morphology on complete semilattices and its applications to image processing
Fundamenta Informaticae - Special issue on mathematical morphology
Distances between intuitionistic fuzzy sets
Fuzzy Sets and Systems
Cardinality concepts for type-two fuzzy sets
Fuzzy Sets and Systems
Grey-Scale Morphology Based on Fuzzy Logic
Journal of Mathematical Imaging and Vision
Some algebraic properties and a distance measure for interval-valued fuzzy numbers
Information Sciences—Applications: An International Journal
Artificial Intelligence - Special issue: Fuzzy set and possibility theory-based methods in artificial intelligence
Artificial Intelligence - Special issue: Fuzzy set and possibility theory-based methods in artificial intelligence
Yin Yang bipolar logic and bipolar fuzzy logic
Information Sciences—Informatics and Computer Science: An International Journal - Special issue: Informatics and computer science intelligent systems applications
Lattice Image Processing: A Unification of Morphological and Fuzzy Algebraic Systems
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Information Sciences: an International Journal
Intuitionistic fuzzy information - Applications to pattern recognition
Pattern Recognition Letters
Computer Vision and Image Understanding
A comparative study on multivariate mathematical morphology
Pattern Recognition
On lexicographical ordering in multivariate mathematical morphology
Pattern Recognition Letters
A new measure using intuitionistic fuzzy set theory and its application to edge detection
Applied Soft Computing
Fuzzy spatial relation ontology for image interpretation
Fuzzy Sets and Systems
An introduction to bipolar representations of information and preference
International Journal of Intelligent Systems
An evolutionist approach to information bipolarity: Representations and affects in human cognition
International Journal of Intelligent Systems
Bipolarity in human reasoning and affective decision making
International Journal of Intelligent Systems
Theoretical Foundations of Spatially-Variant Mathematical Morphology Part I: Binary Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Two routes for bipolar information processing, and a blind spot in between
International Journal of Intelligent Systems
International Journal of Intelligent Systems
Bipolar preference modeling and aggregation in decision support
International Journal of Intelligent Systems
Logical formalisms for representing bipolar preferences
International Journal of Intelligent Systems
Accepting-rejecting propositions from accepted-rejected propositions: A unifying overview
International Journal of Intelligent Systems - Bipolar Representations of Information and Preference Part 2: Reasoning and Learning
Bipolarity in bilattice logics
International Journal of Intelligent Systems - Bipolar Representations of Information and Preference Part 2: Reasoning and Learning
On bipolarity in argumentation frameworks
International Journal of Intelligent Systems - Bipolar Representations of Information and Preference Part 2: Reasoning and Learning
Modeling positive and negative information in possibility theory
International Journal of Intelligent Systems - Bipolar Representations of Information and Preference Part 2: Reasoning and Learning
Intuitionistic Fuzzy Spatial Relationships in Mobile GIS Environment
WILF '07 Proceedings of the 7th international workshop on Fuzzy Logic and Applications: Applications of Fuzzy Sets Theory
Dilation and Erosion of Spatial Bipolar Fuzzy Sets
WILF '07 Proceedings of the 7th international workshop on Fuzzy Logic and Applications: Applications of Fuzzy Sets Theory
A Twofold Fuzzy Region Model for Imprecise Quality Control of Geographic Information
ICCSA '08 Proceeding sof the international conference on Computational Science and Its Applications, Part I
Unifying practical uncertainty representations. II: Clouds
International Journal of Approximate Reasoning
Algebraic Structures for Bipolar Constraint-Based Reasoning
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Interval-valued fuzzy sets constructed from matrices: Application to edge detection
Fuzzy Sets and Systems
A Unified Algebraic Framework for Fuzzy Image Compression and Mathematical Morphology
WILF '09 Proceedings of the 8th International Workshop on Fuzzy Logic and Applications
Bipolar Fuzzy Mathematical Morphology for Spatial Reasoning
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
On the qualitative comparison of decisions having positive and negative features
Journal of Artificial Intelligence Research
Fuzzy filter based on interval-valued fuzzy sets for image filtering
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Fuzzy spatial relationships for image processing and interpretation: a review
Image and Vision Computing
On the Decomposition of Interval-Valued Fuzzy Morphological Operators
Journal of Mathematical Imaging and Vision
Integrating Bipolar Fuzzy Mathematical Morphology in Description Logics for Spatial Reasoning
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
On the role of complete lattices in mathematical morphology: From tool to uncertainty model
Information Sciences: an International Journal
Lattices of fuzzy sets and bipolar fuzzy sets, and mathematical morphology
Information Sciences: an International Journal
New axiomatizations of the Shapley interaction index for bi-capacities
Fuzzy Sets and Systems
On the construction of interval-valued fuzzy morphological operators
Fuzzy Sets and Systems
Triangular norms which are meet-morphisms in interval-valued fuzzy set theory
Fuzzy Sets and Systems
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Orders on partial partitions and maximal partitioning of sets
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Journal of Mathematical Imaging and Vision
On the representation of intuitionistic fuzzy t-norms and t-conorms
IEEE Transactions on Fuzzy Systems
Interval-Valued Fuzzy Sets Applied to Stereo Matching of Color Images
IEEE Transactions on Image Processing
Hi-index | 0.00 |
In many domains of information processing, bipolarity is a core feature to be considered: positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false. If the information is moreover endowed with vagueness and imprecision, as is the case for instance in spatial information processing, then bipolar fuzzy sets constitute an appropriate knowledge representation framework. In this paper, we focus on mathematical morphology as a tool to handle such information and reason on it. Applying mathematical morphology to bipolar fuzzy sets requires defining an appropriate lattice. We extend previous work based on specific partial orderings to any partial ordering leading to a complete lattice. We address the case of algebraic operations and of operations based on a structuring element, and show that they have good properties for any partial ordering, and that they can be useful for processing in particular spatial information, but also other types of bipolar information such as preferences and constraints. Particular cases using Pareto and lexicographic orderings are illustrated. Operations derived from fuzzy bipolar erosion and dilation are proposed as well.