On measures of fuzziness

@article{Knopfmacher1975OnMO,
  title={On measures of fuzziness},
  author={John Knopfmacher},
  journal={Journal of Mathematical Analysis and Applications},
  year={1975},
  volume={49},
  pages={529-534}
}
  • J. Knopfmacher
  • Published 1 March 1975
  • Mathematics
  • Journal of Mathematical Analysis and Applications
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145 Citations
Highly Influential Citations
4
Background Citations
33
Methods Citations
12

145 Citations

Opérateurs d'agrégation pour la mesure de similarité. Application à l'ambiguïté en reconnaissance de formes. (Aggregation operators for similarity measures. Application to ambiguity in pattern recognition)
Dans cette these, nous nous interessons a deux problemes de reconnaissance de formes : l'option de rejet en classification supervisee, et la determination du nombre de classes en classification non…
Divergence Measures: From Uncertainty to Imprecision
TLDR
Following a path similar to the one considered to obtain fuzziness measures from uncertainty measures, the concept of divergence measures is defined, which was proposed as a tool for comparing two fuzzy sets and some possible generalizations are considered.
On the Use of Fuzzy Constraints in Semisupervised Clustering
This paper introduces Fuzzy HSS, a semisupervised hierarchical clustering approach that uses fuzzy instance-level constraints. These constraints are external information on the shape of fuzzy…
FILTER METHOD FOR FEATURE SELECTION USING FUZZINESS INDEX NUMBER WITH FUZZY K-NEAREST NEIGHBOR CLASSIFIER
TLDR
Lappeenranta-Lahti University of Technology LUT School of Engineering Science Computational Engineering and Technical Physics Techno-mathematics is teaching a new generation of scientists and engineers to tackle the challenge of “smart grids”.
On modeling ambiguity through entropy
ANew Fuzzy Information Inequalities and its Applications in Establishing Relation among Fuzzy f -DivergenceMeasures
TLDR
New information inequalities on fuzzy measures and their applications in pattern recognition are introduced and relations between new and well known fuzzy divergence measures are established with help of the fuzzy f -divergence measures and jensen’s inequality.
Measures of inclusion and entropy based on the φ-index of inclusion
Redefining fuzzy entropy with a general framework
Fine-Tuning the Fuzziness of Strong Fuzzy Partitions through PSO
TLDR
This paper proposes a formulation of the parameter space that enables the exploration of all possible levels of fuzziness in a SFP and develops a particular representation of the trapezoidal fuzzy sets that is based on the concept of cuts.
Shadowed sets with higher approximation regions
TLDR
Five-region shadowed set, which effectively deals with the issue of uncertainty balance, is introduced and a closed-form formula for determining its optimum partition thresholds is provided and generalized to n ( ≥ 5) - region shadowed sets.
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References

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Abstraction and pattern classification
L-fuzzy sets
Probability measures of Fuzzy events
  • L. Zadeh
  • Mathematics, Computer Science
  • 1968
A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory