Lattices of fuzzy sets and bipolar fuzzy sets, and mathematical morphology

Information Sciences

Volumn 181, Issue 10, 2011, Pages 2002-2015

  Bloch, Isabelle ^a  

^a INSTITUT TELECOM   (France)

Author keywords

Bipolar mathematical morphology; Complete lattices and mathematical morphology; Fuzzy mathematical morphology; Partial ordering

Indexed keywords

ADJUNCTIONS; ALGEBRAIC FRAMEWORK; BIPOLAR MATHEMATICAL MORPHOLOGY; COMPLETE LATTICES; COMPONENTWISE; FUZZY MATHEMATICAL MORPHOLOGY; LATTICE STRUCTURES; LEXICOGRAPHIC ORDERING; MORPHOLOGICAL OPERATOR; NEGATIVE INFORMATION; PARTIAL ORDERING;

FUZZY SETS; MATHEMATICAL OPERATORS; MORPHOLOGY;

MATHEMATICAL MORPHOLOGY;

EID: 77958494865     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2010.03.019     Document Type: Article

References (74)

1. L. Amgoud, C. Cayrol, M.C. Lagasquie-Schiez, and P. Livet On bipolarity in argumentation frameworks International Journal of Intelligent Systems 23 10 2008 1062 1093
2. J. Angulo Morphological colour operators in totally ordered lattices based on distance: application to image filtering, enhancement and analysis Computer Vision and Image Understanding 107 2007 56 73 (Pubitemid 46829952)
3. E. Aptoula, and S. Lefvre A comparative study in multivariate mathematical morphology Pattern Recognition 40 2007 2914 2929 (Pubitemid 46990424)
4. E. Aptoula, and S. Lefvre On lexicographic ordering in multivariate mathematical morphology Pattern Recognition Letters 29 2008 109 118 (Pubitemid 350116990)
5. K.T. Atanassov Intuitionistic fuzzy sets Fuzzy Sets and Systems 20 1986 87 96
6. K.T. Atanassov Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper "terminology difficulties in fuzzy set theory - the case of "intuitionistic fuzzy sets"" Fuzzy Sets and Systems 156 2005 496 499
7. H. Bandemer, and W. Näther Fuzzy Data Analysis. Theory and Decision Library, Series B: Mathematical and Statistical Methods 1992 Kluwer Academic Publisher Dordrecht
8. S. Benferhat, D. Dubois, S. Kaci, and H. Prade Bipolar possibility theory in preference modeling: representation, fusion and optimal solutions Information Fusion 7 2006 135 150 (Pubitemid 43133036)
9. S. Benferhat, D. Dubois, and H. Prade Modeling positive and negative information in possibility theory International Journal of Intelligent Systems 23 10 2008 1094 1118
10. I. Bloch, Triangular norms as a tool for constructing fuzzy mathematical morphologies, in: International Workshop on Mathematical Morphology and its Applications to Signal Processing, Barcelona, Spain, 1993, pp. 157-161.
11. I. Bloch On links between mathematical morphology and rough sets Pattern Recognition 33 9 2000 1487 1496
12. I. Bloch Modal logics based on mathematical morphology for spatial reasoning Journal of Applied Non Classical Logics 12 3-4 2002 399 424
13. I. Bloch, Duality vs adjunction and general form for fuzzy mathematical morphology, in: WILF, LNCS, vol. 3849, Crema, Italy, 2005, pp. 354-361.
14. I. Bloch Spatial reasoning under imprecision using fuzzy set theory, formal logics and mathematical morphology International Journal of Approximate Reasoning 41 2006 77 95
15. I. Bloch, Dilation and erosion of spatial bipolar fuzzy sets, in: International Workshop on Fuzzy Logic and Applications WILF 2007, LNAI, vol. 4578, Genova, Italy, 2007, pp. 385-393. (Pubitemid 350270304)
16. I. Bloch, A contribution to the representation and manipulation of fuzzy bipolar spatial information: geometry and morphology, in: Workshop on Soft Methods in Statistical and Fuzzy Spatial Information, Toulouse, France, 2008, pp. 7-25.
17. I. Bloch, Bipolar fuzzy mathematical morphology for spatial reasoning, in: International Symposium on Mathematical Morphology ISMM'09, LNCS, vol. 5720, Groningen, The Netherlands, 2009, pp. 24-34.
18. I. Bloch Bipolar fuzzy spatial information: first operations in the mathematical morphology setting R.K. De, D.P. Mandal, A. Ghosh, Machine Interpretation of Patterns: Image Analysis, Data Mining and Bioinformatics 2009 World Scientific Press
19. I. Bloch Duality vs adjunction for fuzzy mathematical morphology and general form of fuzzy erosions and dilations Fuzzy Sets and Systems 160 2009 1858 1867
20. I. Bloch, Geometry of spatial bipolar fuzzy sets based on bipolar fuzzy numbers and mathematical morphology, in: International Workshop on Fuzzy Logic and Applications WILF, LNAI, vol. 5571, Palermo, Italy, 2009, pp. 237-245.
21. I. Bloch, Morphologie mathématique floue bipolaire pour l'ordre lexicographique, in: LFA 2009, Annecy, France, 2009, pp. 209-216.
22. I. Bloch, H. Heijmans, and C. Ronse Mathematical morphology M. Aiello, I. Pratt-Hartman, J. van Benthem, Handbook of Spatial Logics 2007 Springer 857 947 (Chapter 13)
23. I. Bloch, J. Lang, Towards mathematical morpho-logics, in: Eighth International Conference on Information Processing and Management of Uncertainty in Knowledge Based Systems IPMU 2000, vol. III, Madrid, Spain, 2000, pp. 1405-1412.
24. I. Bloch, and H. Maître Fuzzy mathematical morphologies: a comparative study Pattern Recognition 28 9 1995 1341 1387 (Pubitemid 26442210)
25. I. Bloch, R. Pino-Pérez, C. Uzcátegui, Explanatory relations based on mathematical morphology, in: ECSQARU 2001, Toulouse, France, 2001, pp. 736-747. (Pubitemid 33334719)
26. I. Bloch, R. Pino-Pérez, C. Uzcategui, A unified treatment of knowledge dynamics, in: International Conference on the Principles of Knowledge Representation and Reasoning, KR2004, Canada, 2004, pp. 329-337.
27. I. Bloch, R. Pino-Pérez, C. Uzcategui, Mediation in the framework of morphologic, in: European Conference on Artificial Intelligence ECAI 2006, Riva del Garda, Italy, 2006, pp. 190-194.
28. J.F. Bonnefon Two routes for bipolar information processing, and a blind spot in between International Journal of Intelligent Systems 23 9 2008 923 929
29. D. Bouyssou, D. Dubois, M. Pirlot, and H. Prade Concepts and Methods of Decision-Making 2009 ISTE, Wiley
30. H. Bustince, and P. Burillo Vague sets are intuitionistic fuzzy sets Fuzzy Sets and Systems 79 1996 403 405 (Pubitemid 126667425)
31. R. Caferra, and N. Peltier Accepting/rejecting propositions from accepted/rejected propositions: a unifying overview International Journal of Intelligent Systems 23 10 2008 999 1020
32. O. Colliot, O. Camara, and I. Bloch Integration of fuzzy spatial relations in deformable models - application to brain MRI segmentation Pattern Recognition 39 2006 1401 1414 (Pubitemid 44269319)
33. C. Cornelis, G. Deschrijver, and E. Kerre Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application International Journal of Approximate Reasoning 35 2004 55 95
34. C. Cornelis, E. Kerre, Inclusion measures in intuitionistic fuzzy sets, in: ECSQARU'03, LNAI, vol. 2711, 2003, pp. 345-356. (Pubitemid 36904917)
35. B. De Baets Generalized idempotence in fuzzy mathematical morphology E. Kerre, M. Nachtegael, Fuzzy Techniques in Image Processing Studies in Fuzziness and Soft Computing 52 2000 Physica Verlag, Springer 58 75
36. B. De Baets, E. Kerre, and M. Gupta The fundamentals of fuzzy mathematical morphology part 1: basic concepts International Journal of General Systems 23 2 1995 155 171
37. B. De Baets, E. Kerre, and M. Gupta The fundamentals of fuzzy mathematical morphology part 2: idempotence, convexity and decomposition International Journal of General Systems 23 4 1995 307 322
38. T.-Q. Deng, and H. Heijmans Grey-scale morphology based on fuzzy logic Journal of Mathematical Imaging and Vision 16 2002 155 171 (Pubitemid 34239176)
39. G. Deschrijver, C. Cornelis, and E. Kerre On the representation of intuitionistic fuzzy t-norms and t-conorms IEEE Transactions on Fuzzy Systems 12 1 2004 45 61
40. S. Destercke, D. Dubois, and E. Chojnacki Unifying practical uncertainty representations: II. clouds International Journal of Approximate Reasoning 49 3 2008 664 677
41. D. Dubois, H. Fargier, and P. Perny Qualitative decision theory with preference relations and comparative uncertainty: an axiomatic approach Artificial Intelligence 148 1 2003 219 260
42. D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk, and H. Prade Terminology difficulties in fuzzy set theory - the case of "intuitionistic fuzzy sets" Fuzzy Sets and Systems 156 2005 485 491 (Pubitemid 41475504)
43. D. Dubois, S. Kaci, H. Prade, Bipolarity in reasoning and decision, an introduction, in: International Conference on Information Processing and Management of Uncertainty, IPMU'04, Perugia, Italy, 2004, pp. 959-966.
44. D. Dubois, and H. Prade Fuzzy Sets and Systems: Theory and Applications 1980 Academic Press New-York
45. D. Dubois, H. Prade, Inverse operations for fuzzy numbers, in: E. Sanchez, M. Gupta (Eds.), Fuzzy Information, Knowledge Representation and Decision Analysis, IFAC Symposium, Marseille, France, 1983, pp. 391-396.
46. D. Dubois, H. Prade, A bipolar possibilistic representation of knowledge and preferences and its applications, in: WILF 2005, LNAI, vol. 3849, 2005, pp. 1-10.
47. D. Dubois, and H. Prade An introduction to bipolar representations of information and preference International Journal of Intelligent Systems 23 8 2008 865 866
48. H. Fargier, N. Wilson, Algebraic structures for bipolar constraint-based reasoning, in: ECSQARU, LNCS, vol. 4724, 2007, pp. 623-634.
49. M. Grabisch, S. Greco, and M. Pirlot Bipolar and bivariate models in multicriteria decision analysis: descriptive and constructive approaches International Journal of Intelligent Systems 23 9 2008 930 969
50. H.J.A.M. Heijmans, and C. Ronse The algebraic basis of mathematical morphology - part I: dilations and erosions Computer Vision, Graphics and Image Processing 50 1990 245 295 (Pubitemid 20695762)
51. C. Hudelot, J. Atif, and I. Bloch Fuzzy spatial relation ontology for image interpretation Fuzzy Sets and Systems 159 2008 1929 1951
52. S. Kaci Logical formalisms for representing bipolar preferences International Journal of Intelligent Systems 23 8 2008 985 997
53. R. Keshet Mathematical morphology on complete semilattices and its applications to image processing Fundamenta Informaticae 41 2000 33 56
54. S. Konieczny, P. Marquis, and P. Besnard Bipolarity in bilattice logics International Journal of Intelligent Systems 23 10 2008 1046 1061
55. L. Lietard, D. Rocacher, Requêtes bipolaires exprimant des préférences, in: Rencontres francophones sur la logique floue et ses applications, LFA, Lens, France, 2008, pp. 68-75.
56. K. Maes, and B. De Baets Negation and affirmation: the role of involutive negators Soft Computing-A Fusion of Foundations, Methodologies and Applications 11 7 2007 647 654
57. P. Maragos Lattice image processing: a unification of morphological and fuzzy algebraic systems Journal of Mathematical Imaging and Vision 22 2005 333 353
58. H. Moulin Axioms of Cooperative Decision Making 1991 Cambridge University Press
59. M. Nachtegael, and E.E. Kerre Classical and fuzzy approaches towards mathematical morphology E.E. Kerre, M. Nachtegael, Fuzzy Techniques in Image Processing Studies in Fuzziness and Soft Computing 2000 Physica-Verlag, Springer 3 57 (Chapter 1)
60. M. Nachtegael, P. Sussner, T. Mélange, E. Kerre, Some aspects of interval-valued and intuitionistic fuzzy mathematical morphology, in: IPCV 2008, 2008.
61. O. Nempont, J. Atif, E. Angelini, I. Bloch, Structure segmentation and recognition in images guided by structural constraint propagation, in: European Conference on Artificial Intelligence ECAI, Patras, Greece, 2008, pp. 621-625.
62. A. Neumaier Clouds, fuzzy sets, and probability intervals Reliable Computing 10 4 2004 249 272
63. R.D.S. Neves, and P. Livet Bipolarity in human reasoning and affective decision making International Journal of Intelligent Systems 23 8 2008 898 922
64. M. Öztürk, and A. Tsoukias Bipolar preference modeling and aggregation in decision support International Journal of Intelligent Systems 23 9 2008 970 984
65. A.T. Popov, Morphological operations on fuzzy sets, in: IEE Image Processing and its Applications, Edinburgh, UK, 1995, pp. 837-840.
66. E. Raufaste, and S. Vautier An evolutionist approach to information bipolarity: representations and affects in human cognition International Journal of Intelligent Systems 23 8 2008 878 897
67. C. Ronse Why mathematical morphology needs complete lattices Signal Processing 21 2 1990 129 154
68. C. Ronse, and H.J.A.M. Heijmans The algebraic basis of mathematical morphology - part II: openings and closings Computer Vision, Graphics and Image Processing 54 1991 74 97 (Pubitemid 21700322)
69. B. Roy The outranking approach and the foundations of ELECTRE methods Theory and Decision 31 1 1991 49 73
70. J. Serra Image Analysis and Mathematical Morphology 1982 Academic Press London
71. D. Sinha, and E.R. Dougherty Fuzzification of set inclusion: theory and applications Fuzzy Sets and Systems 55 1993 15 42
72. P. Sussner, and M. Valle Classification of fuzzy mathematical morphologies based on concepts of inclusion measure and duality Journal of Mathematical Imaging and Vision 21 2008 139 159
73. H. Talbot, C. Evans, R. Jones, Complete ordering and multivariate mathematical morphology, in: Proceedings of the Fourth International Symposium on Mathematical Morphology and its Applications to Image and Signal Processing, 1998, pp. 27-34.
74. L.A. Zadeh The concept of a linguistic variable and its application to approximate reasoning Information Sciences 8 1975 199 249