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The role a fuzzy implication plays in a multi-criteria decision algorithm

Yun Shi (UGent) , Bart Van Gasse (UGent) and Etienne Kerre (UGent)
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Abstract
We introduce a similarity measure between fuzzy sets using a fuzzy implication. We investigate for the eight most important potential properties of fuzzy implications, which ones should be taken into consideration to measure the similarity, and thereafter choose a suitable fuzzy implication which satisfies these potential properties. Simple examples are given to illustrate the application of the chosen fuzzy implication in a partition algorithm used for multi-criteria decision making.
Keywords
fuzzy inclusion, similarity measure, multi-criteria decision making, fuzzy relation, fuzzy implication, fuzzy set

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Citation

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Chicago
Shi, Yun, Bart Van Gasse, and Etienne Kerre. 2013. “The Role a Fuzzy Implication Plays in a Multi-criteria Decision Algorithm.” International Journal of General Systems 42 (1): 111–120.
APA
Shi, Yun, Van Gasse, B., & Kerre, E. (2013). The role a fuzzy implication plays in a multi-criteria decision algorithm. INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 42(1), 111–120.
Vancouver
1.
Shi Y, Van Gasse B, Kerre E. The role a fuzzy implication plays in a multi-criteria decision algorithm. INTERNATIONAL JOURNAL OF GENERAL SYSTEMS. 2013;42(1):111–20.
MLA
Shi, Yun, Bart Van Gasse, and Etienne Kerre. “The Role a Fuzzy Implication Plays in a Multi-criteria Decision Algorithm.” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 42.1 (2013): 111–120. Print.
@article{3117449,
  abstract     = {We introduce a similarity measure between fuzzy sets using a fuzzy implication. We investigate for the eight most important potential properties of fuzzy implications, which ones should be taken into consideration to measure the similarity, and thereafter choose a suitable fuzzy implication which satisfies these potential properties. Simple examples are given to illustrate the application of the chosen fuzzy implication in a partition algorithm used for multi-criteria decision making.},
  author       = {Shi, Yun and Van Gasse, Bart and Kerre, Etienne},
  issn         = {0308-1079},
  journal      = {INTERNATIONAL JOURNAL OF GENERAL SYSTEMS},
  keyword      = {fuzzy inclusion,similarity measure,multi-criteria decision making,fuzzy relation,fuzzy implication,fuzzy set},
  language     = {eng},
  number       = {1},
  pages        = {111--120},
  title        = {The role a fuzzy implication plays in a multi-criteria decision algorithm},
  url          = {http://dx.doi.org/10.1080/03081079.2012.710441},
  volume       = {42},
  year         = {2013},
}

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