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Fuzzy relational images in computer science

Mike Nachtegael (UGent) , Martine De Cock (UGent) , Dietrich Van der Weken (UGent) and Etienne Kerre (UGent)
Author
Organization
Abstract
Relations appear in many fields of mathematics and computer science. In classical mathematics these relations are usually crisp, i.e. two objects are related or they are not. However, many relations in real-world applications are intrinsically fuzzy, i.e. objects can be related to each other to a certain degree. With each fuzzy relation, different kinds of fuzzy relational images can be associated, all with a very practical interpretation in a wide range of application areas. In this paper we will explicite the formal link between well known direct and inverse images of fuzzy sets under fuzzy relations on one hand, and different kinds of compositions of fuzzy relations on the other. Continuing from this point of view we are also able to define a new scale of so-called double images. The wide applicability in mathematics and computer science of all these fuzzy relational images is illustrated with several examples.
Keywords
SETS

Citation

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Chicago
Nachtegael, Mike, Martine De Cock, Dietrich Van der Weken, and Etienne Kerre. 2002. “Fuzzy Relational Images in Computer Science.” Ed. HCM De Swart. Lecture Notes in Computer Science 2561: 134–151.
APA
Nachtegael, M., De Cock, M., Van der Weken, D., & Kerre, E. (2002). Fuzzy relational images in computer science. (HCM De Swart, Ed.)LECTURE NOTES IN COMPUTER SCIENCE, 2561, 134–151. Presented at the 6th International Conference on Relational Methods in Computer Science.
Vancouver
1.
Nachtegael M, De Cock M, Van der Weken D, Kerre E. Fuzzy relational images in computer science. De Swart H, editor. LECTURE NOTES IN COMPUTER SCIENCE. Berlin, Germany: Springer; 2002;2561:134–51.
MLA
Nachtegael, Mike, Martine De Cock, Dietrich Van der Weken, et al. “Fuzzy Relational Images in Computer Science.” Ed. HCM De Swart. LECTURE NOTES IN COMPUTER SCIENCE 2561 (2002): 134–151. Print.
@article{161915,
  abstract     = {Relations appear in many fields of mathematics and computer science. In classical mathematics these relations are usually crisp, i.e. two objects are related or they are not. However, many relations in real-world applications are intrinsically fuzzy, i.e. objects can be related to each other to a certain degree.
With each fuzzy relation, different kinds of fuzzy relational images can be associated, all with a very practical interpretation in a wide range of application areas. In this paper we will explicite the formal link between well known direct and inverse images of fuzzy sets under fuzzy relations on one hand, and different kinds of compositions of fuzzy relations on the other. Continuing from this point of view we are also able to define a new scale of so-called double images. The wide applicability in mathematics and computer science of all these fuzzy relational images is illustrated with several examples.},
  author       = {Nachtegael, Mike and De Cock, Martine and Van der Weken, Dietrich and Kerre, Etienne},
  editor       = {De Swart, HCM},
  isbn         = {3-540-00315-0},
  issn         = {0302-9743},
  journal      = {LECTURE NOTES IN COMPUTER SCIENCE},
  keyword      = {SETS},
  language     = {eng},
  location     = {Oisterwijk (Tilburg), The Netherlands},
  pages        = {134--151},
  publisher    = {Springer},
  title        = {Fuzzy relational images in computer science},
  volume       = {2561},
  year         = {2002},
}

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