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On a new class of implications in fuzzy logic

Yun Shi (UGent) , Bart Van Gasse (UGent) , Da Ruan (UGent) and Etienne Kerre (UGent)
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Abstract
We define and study a new class of implications determined only by a negation. We examine under which conditions the most popular eight axioms for implications are satisfied. We obtain the intersection of the new class of implications with the S- and R- implications.
Keywords
fuzzy implication, IMPLICATION OPERATORS, Lukasiewicz implication, R-implication, S-implication, fuzzy implication axiom, negation, Sugeno negation

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Chicago
Shi, Yun, Bart Van Gasse, Da Ruan, and Etienne Kerre. 2010. “On a New Class of Implications in Fuzzy Logic.” In Communications in Computer and Information Science, ed. E Hullermeir, R Kruse, and F Hoffmann, 80:525–534. New York, NY, USA: Springer.
APA
Shi, Yun, Van Gasse, B., Ruan, D., & Kerre, E. (2010). On a new class of implications in fuzzy logic. In E Hullermeir, R. Kruse, & F. Hoffmann (Eds.), Communications in Computer and Information Science (Vol. 80, pp. 525–534). Presented at the 13th International conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, New York, NY, USA: Springer.
Vancouver
1.
Shi Y, Van Gasse B, Ruan D, Kerre E. On a new class of implications in fuzzy logic. In: Hullermeir E, Kruse R, Hoffmann F, editors. Communications in Computer and Information Science. New York, NY, USA: Springer; 2010. p. 525–34.
MLA
Shi, Yun, Bart Van Gasse, Da Ruan, et al. “On a New Class of Implications in Fuzzy Logic.” Communications in Computer and Information Science. Ed. E Hullermeir, R Kruse, & F Hoffmann. Vol. 80. New York, NY, USA: Springer, 2010. 525–534. Print.
@inproceedings{2132602,
  abstract     = {We define and study a new class of implications determined only by a negation. We examine under which conditions the most popular eight axioms for implications are satisfied. We obtain the intersection of the new class of implications with the S- and R- implications.},
  author       = {Shi, Yun and Van Gasse, Bart and Ruan, Da and Kerre, Etienne},
  booktitle    = {Communications in Computer and Information Science},
  editor       = {Hullermeir, E and Kruse, R and Hoffmann, F},
  isbn         = {9783642140549},
  issn         = {1865-0929},
  language     = {eng},
  location     = {Dortmund, Germany},
  pages        = {525--534},
  publisher    = {Springer},
  title        = {On a new class of implications in fuzzy logic},
  url          = {http://dx.doi.org/10.1007/978-3-642-14055-6\_55},
  volume       = {80},
  year         = {2010},
}

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