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Square and triangle: reflections on two prominent mathematical structures for the representation of imprecision

Chris Cornelis (UGent) , Glad Deschrijver (UGent) and Etienne Kerre (UGent)
Author
Organization
Abstract
In this paper, Ginsberg's/Fitting's theory of bilattices, and in particular the associated constructs of bilattice-based squares and triangles, is invoked as a natural accommodation and powerful generalization to both intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IVFSs), serving on one hand to clarify the exact nature of the relationship between these two common extensions of fuzzy sets, while on the other hand providing a general framework for the representation of uncertain and potentially conflicting information. Close attention is also paid to the definition of adequate graded versions of basic logical connectives in this setting.
Keywords
graded logical connectives, bilattices, interval-valued fuzzy sets, intuitionistic fuzzy sets

Citation

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Chicago
Cornelis, Chris, Glad Deschrijver, and Etienne Kerre. 2003. “Square and Triangle: Reflections on Two Prominent Mathematical Structures for the Representation of Imprecision.” Notes on Intuitionistic Fuzzy Sets 9 (3): 11–21.
APA
Cornelis, Chris, Deschrijver, G., & Kerre, E. (2003). Square and triangle: reflections on two prominent mathematical structures for the representation of imprecision. Notes on Intuitionistic Fuzzy Sets, 9(3), 11–21.
Vancouver
1.
Cornelis C, Deschrijver G, Kerre E. Square and triangle: reflections on two prominent mathematical structures for the representation of imprecision. Notes on Intuitionistic Fuzzy Sets. 2003;9(3):11–21.
MLA
Cornelis, Chris, Glad Deschrijver, and Etienne Kerre. “Square and Triangle: Reflections on Two Prominent Mathematical Structures for the Representation of Imprecision.” Notes on Intuitionistic Fuzzy Sets 9.3 (2003): 11–21. Print.
@article{208231,
  abstract     = {In this paper, Ginsberg's/Fitting's theory of bilattices, and in particular the associated constructs of bilattice-based squares and triangles, is invoked as a natural accommodation and powerful generalization to both intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IVFSs), serving on one hand to clarify the exact nature of the relationship between these two common extensions of fuzzy sets, while on the other hand providing a general framework for the representation of uncertain and potentially conflicting information. Close attention is also paid to the definition of adequate graded versions of basic logical connectives in this setting.},
  author       = {Cornelis, Chris and Deschrijver, Glad and Kerre, Etienne},
  issn         = {1310-4926},
  journal      = {Notes on Intuitionistic Fuzzy Sets},
  keyword      = {graded logical connectives,bilattices,interval-valued fuzzy sets,intuitionistic fuzzy sets},
  language     = {eng},
  number       = {3},
  pages        = {11--21},
  title        = {Square and triangle: reflections on two prominent mathematical structures for the representation of imprecision},
  volume       = {9},
  year         = {2003},
}