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Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images

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Abstract
In this paper, we present a new construction method for interval-valued fuzzy relations (interval-valued fuzzy images) from fuzzy relations (fuzzy images) by vicinity. This construction method is based on the concepts of triangular norm (t-norm) and triangular conorm (t-conorm). We analyze the effect of using different t-norms and t-conorms. Furthermore, we examine the influence of different sizes of the submatrix around each element of a fuzzy relation on the interval-valued fuzzy relation. Finally, we apply our construction method to image processing, and we compare the results of our approach with those obtained by means of other, i.e., fuzzy and nonfuzzy, techniques.
Keywords
fuzzy relation (FR), Fuzzy edge, image processing, interval-valued fuzzy relation (IVFR), triangular norm (t-norm), LOGIC SYSTEMS, HYSTERESIS THRESHOLDS, REAL NUMBERS, CONNECTIVES, OPERATORS, NORMS, SETS

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Chicago
Barrenechea, Edurne, Humberto Bustince, Bernard De Baets, and Carlos López-Molina. 2011. “Construction of Interval-valued Fuzzy Relations with Application to the Generation of Fuzzy Edge Images.” Ieee Transactions on Fuzzy Systems 19 (5): 819–830.
APA
Barrenechea, E., Bustince, H., De Baets, B., & López-Molina, C. (2011). Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 19(5), 819–830.
Vancouver
1.
Barrenechea E, Bustince H, De Baets B, López-Molina C. Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images. IEEE TRANSACTIONS ON FUZZY SYSTEMS. 2011;19(5):819–30.
MLA
Barrenechea, Edurne, Humberto Bustince, Bernard De Baets, et al. “Construction of Interval-valued Fuzzy Relations with Application to the Generation of Fuzzy Edge Images.” IEEE TRANSACTIONS ON FUZZY SYSTEMS 19.5 (2011): 819–830. Print.
@article{2135876,
  abstract     = {In this paper, we present a new construction method for interval-valued fuzzy relations (interval-valued fuzzy images) from fuzzy relations (fuzzy images) by vicinity. This construction method is based on the concepts of triangular norm (t-norm) and triangular conorm (t-conorm). We analyze the effect of using different t-norms and t-conorms. Furthermore, we examine the influence of different sizes of the submatrix around each element of a fuzzy relation on the interval-valued fuzzy relation. Finally, we apply our construction method to image processing, and we compare the results of our approach with those obtained by means of other, i.e., fuzzy and nonfuzzy, techniques.},
  author       = {Barrenechea, Edurne and Bustince, Humberto and De Baets, Bernard and L{\'o}pez-Molina, Carlos},
  issn         = {1063-6706},
  journal      = {IEEE TRANSACTIONS ON FUZZY SYSTEMS},
  language     = {eng},
  number       = {5},
  pages        = {819--830},
  title        = {Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images},
  url          = {http://dx.doi.org/10.1109/TFUZZ.2011.2146260},
  volume       = {19},
  year         = {2011},
}

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