On the representation of cardinalities of interval-valued fuzzy sets: The valuation property

Fuzzy Sets and Systems

Volumn 211, Issue , 2013, Pages 99-119

  Deschrijver, Glad ^a   Král', Pavol ^b  

^a GHENT UNIVERSITY   (Belgium)

^b MATEJ BEL UNIVERSITY   (Slovakia)

Author keywords

Cardinality; Cardinality pattern; Interval valued fuzzy set; Valuation property

Indexed keywords

AXIOMATIC THEORY; BASIC CONDITIONS; CARDINALITIES; CARTESIAN PRODUCTS; FINITE SUPPORTS; INTERVAL-VALUED FUZZY SET THEORY; INTERVAL-VALUED FUZZY SETS; SUBADDITIVITY; SUBINTERVALS; T - NORM; T-CONORMS;

FUZZY SET THEORY; MATHEMATICAL OPERATORS;

FUZZY SETS;

EID: 84867916938     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2012.03.017     Document Type: Article

References (21)

1. K.T. Atanassov, Intuitionistic fuzzy sets, in: VII ITKRs Session, Sofia, 1983 (deposed in Central Science-Technical Library of the Bulgarian Academy of Sciences, 1697/84) (in Bulgarian).
2. K.T. Atanassov Intuitionistic Fuzzy Sets 1999 Physica-Verlag Heidelberg, New York
3. B. De Baets, S. Janssens, and H. De Meyer Meta-theorems on inequalities for scalar fuzzy set cardinalities Fuzzy Sets Syst. 157 11 2006 1463 1476
4. J. Casasnovas, and J. Torrens Scalar cardinalities of finite fuzzy sets for t-norms and t-conorms Int. J. Uncertainty Fuzziness Knowl. Based Syst. 11 5 2003 599 614
5. M. Casasnovas, and J. Torrens An axiomatic approach to fuzzy cardinalities of finite fuzzy sets Fuzzy Sets Syst. 133 2 2003 193 209
6. A. De Luca, and S. Termini A definition of non-probabilistic entropy in the setting of fuzzy sets theory Inf. Control 20 1972 301 312
7. G. Deschrijver, A Thorough Study of the Basic Operators in Intuitionistic Fuzzy Set Theory, Ph.D. Thesis, Ghent University, Belgium, 2004 (in Dutch).
8. G. Deschrijver Arithmetic operators in interval-valued fuzzy set theory Inf. Sci. 177 14 2007 2906 2924
9. G. Deschrijver, C. Cornelis, and E.E. Kerre On the representation of intuitionistic fuzzy t-norms and t-conorms IEEE Trans. Fuzzy Syst. 12 1 2004 45 61
10. G. Deschrijver, and E.E. Kerre On the relationship between some extensions of fuzzy set theory Fuzzy Sets Syst. 133 2 2003 227 235
11. G. Deschrijver, and P. Král' On the cardinalities of interval-valued fuzzy sets Fuzzy Sets Syst. 158 15 2007 1728 1750
12. D. Dubois, and H. Prade Fuzzy cardinality and the modeling of imprecise quantification Fuzzy Sets Syst. 16 3 1985 199 230
13. J.A. Goguen L-fuzzy sets J. Math. Anal. Appl. 18 1 1967 145 174
14. S. Gottwald A note on fuzzy cardinals Kybernetika 16 1980 156 158
15. A. Kaufmann Introduction to the Theory of Fuzzy Subsets 1975 Academic Press New York
16. D. Ralescu Cardinality, quantifiers, and the aggregation of fuzzy criteria Fuzzy Sets Syst. 69 3 1995 355 365
17. D. Rocacher, and P. Bosc The set of fuzzy rational numbers and flexible querying Fuzzy Sets Syst. 155 3 2005 317 339
18. E. Szmidt, and J. Kacprzyk Entropy for intuitionistic fuzzy sets Fuzzy Sets Syst. 118 3 2001 467 477
19. M. Wygralak, Cardinalities of fuzzy sets evaluated by single cardinals, in: Proceedings of the IFSA Congress, Praha, 1997, pp. 73-77.
20. M. Wygralak An axiomatic approach to scalar cardinalities of a fuzzy set Fuzzy Sets Syst. 110 2 2000 175 176
21. M. Wygralak Cardinalities of Fuzzy Sets 2003 Springer-Verlag Berlin, Heidelberg, New York