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A bilattice-based framework for handling graded truth and imprecision

Glad Deschrijver (UGent) , Ofer Arieli, Chris Cornelis (UGent) and Etienne Kerre (UGent)
Author
Organization
Abstract
We present a family of algebraic structures, called rectangular bilattices, which serve as a natural accommodation and powerful generalization to both intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IVFSs). These structures are useful on one hand to clarify the exact nature of the relationship between the above two common extensions of fuzzy sets, and on the other hand provide an intuitively attractive framework for the representation of uncertain and potentially conflicting information. We also provide these structures with adequately defined graded versions of the basic logical connectives, and study their properties and relationships. Application potential and intuitive appeal of the proposed framework are illustrated in the context of preference modeling.
Keywords
bilattices, interval-valued fuzzy sets, intuitionistic fuzzy sets, graded logical connectives, preference modeling

Citation

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Chicago
Deschrijver, Glad, Ofer Arieli, Chris Cornelis, and Etienne Kerre. 2007. “A Bilattice-based Framework for Handling Graded Truth and Imprecision.” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15 (1): 13–41.
APA
Deschrijver, Glad, Arieli, O., Cornelis, C., & Kerre, E. (2007). A bilattice-based framework for handling graded truth and imprecision. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 15(1), 13–41.
Vancouver
1.
Deschrijver G, Arieli O, Cornelis C, Kerre E. A bilattice-based framework for handling graded truth and imprecision. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. WORLD SCIENTIFIC PUBL CO PTE LTD; 2007;15(1):13–41.
MLA
Deschrijver, Glad, Ofer Arieli, Chris Cornelis, et al. “A Bilattice-based Framework for Handling Graded Truth and Imprecision.” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15.1 (2007): 13–41. Print.
@article{385644,
  abstract     = {We present a family of algebraic structures, called rectangular bilattices, which serve as a natural accommodation and powerful generalization to both intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IVFSs). These structures are useful on one hand to clarify the exact nature of the relationship between the above two common extensions of fuzzy sets, and on the other hand provide an intuitively attractive framework for the representation of uncertain and potentially con\unmatched{fb02}icting information. We also provide these structures with adequately de\unmatched{fb01}ned graded versions of the basic logical connectives, and study their properties and relationships. Application potential and intuitive appeal of the proposed framework are illustrated in the context of preference modeling.},
  author       = {Deschrijver, Glad and Arieli, Ofer and Cornelis, Chris and Kerre, Etienne},
  issn         = {0218-4885},
  journal      = {International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems},
  language     = {eng},
  number       = {1},
  pages        = {13--41},
  publisher    = {WORLD SCIENTIFIC PUBL CO PTE LTD},
  title        = {A bilattice-based framework for handling graded truth and imprecision},
  volume       = {15},
  year         = {2007},
}

Web of Science
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