A representation of t-norms in interval-valued L-fuzzy set theory

Fuzzy Sets and Systems

Volumn 159, Issue 13, 2008, Pages 1597-1618

  Deschrijver, Glad ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Interval valued fuzzy set; Join morphism; Lattice of closed intervals; Representation; Residuation principle; Triangular norm

Indexed keywords

BOUNDARY CONDITIONS; FUZZY LOGIC; NUMERICAL METHODS; THEOREM PROVING;

LATTICE OF CLOSED INTERVALS; RESIDUATION PRINCIPLE; TRIANGULAR NORMS;

FUZZY SETS;

EID: 43449124397     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2007.09.017     Document Type: Article

References (30)

1. Abramsky S., and Jung A. Domain theory. In: Abramsky S., Gabbay D.M., and Maibaum T.S.B. (Eds). Handbook of Logic in Computer Science Vol. III (1994), Oxford University Press, Oxford 1-168
2. Atanassov K.T., and Ban A. Triangular norm-based intuitionistic fuzzy propositional calculus. Notes on Intuitionistic Fuzzy Sets 7 2 (2001) 37-43
3. Bedregal B.R.C., and Takahashi A. The best interval representations of t-norms and automorphisms. Fuzzy Sets and Systems 157 24 (2006) 3220-3230
4. Cornelis C., Arieli O., Deschrijver G., and Kerre E.E. Uncertainty modeling by bilattice-based squares and triangles. IEEE Trans. Fuzzy Systems 15 2 (2007) 161-175
5. De Baets B., and Mesiar R. Triangular norms on product lattices. Fuzzy Sets and Systems 104 1 (1999) 61-75
6. Deschrijver G., Arieli O., Cornelis C., and Kerre E.E. A bilattice-based framework for handling graded truth and imprecision. Internat. J. Uncertainty Fuzziness Knowledge-Based Systems 15 1 (2007) 13-41
7. Deschrijver G., Cornelis C., and Kerre E.E. On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Trans. Fuzzy Systems 12 1 (2004) 45-61
8. Deschrijver G., and Kerre E.E. Classes of intuitionistic fuzzy t-norms satisfying the residuation principle. Internat. J. Uncertainty Fuzziness Knowledge-Based Systems 11 6 (2003) 691-709
9. Deschrijver G., and Kerre E.E. On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems 133 2 (2003) 227-235
10. Fodor J.C. Fuzzy Preference Modelling and Multicriteria Decision Support (1994), Kluwer Academic Publishers, Dordrecht
11. Fodor J.C. Contrapositive symmetry of fuzzy implications. Fuzzy Sets and Systems 69 2 (1995) 141-156
12. Gehrke M., Walker C.L., and Walker E.A. Some comments on interval valued fuzzy sets. Internat. J. Intelligent Systems 11 10 (1996) 751-759
13. Goguen J.A. L-fuzzy sets. J. Math. Anal. Appl. 18 1 (1967) 145-174
14. Gorzałczany M.B. A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems 21 1 (1987) 1-17
15. Hájek P. Metamathematics of Fuzzy Logic (1998), Kluwer Academic Publishers, Dordrecht
16. Jenei S. A more efficient method for defining fuzzy connectives. Fuzzy Sets and Systems 90 1 (1997) 25-35
17. Jenei S., and De Baets B. On the direct decomposability of t-norms on product lattices. Fuzzy Sets and Systems 139 3 (2003) 699-707
18. Klement E.P., Mesiar R., and Pap E. Triangular Norms (2000), Kluwer Academic Publishers, Dordrecht
19. Mayor G., and Torrens J. Triangular norms on discrete settings. In: Klement E.P., and Mesiar R. (Eds). Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms (2005), Elsevier, Amsterdam 189-230 (Chapter 7)
20. Moore R.E. Methods and Applications of Interval Analysis (1979), Society for Industrial and Applied Mathematics, Philadelphia
21. Nguyen H.T., and Kreinovich V. From [0, 1]-based logic to interval logic (from known description of all possible [0, 1]-based logical operations to a description of all possible interval-based logical operations). Notes on Intuitionistic Fuzzy Sets 8 3 (2002) 75-94
22. Novák V., Perfilieva I., and Močkoř J. Mathematical Principles of Fuzzy Logic (1999), Kluwer Academic Publisher, Dordrecht
23. S. Ray, Representation of a Boolean algebra by its triangular norms, Mathware and Soft Comput. 4 (1).
24. R. Sambuc, Fonctions Φ-floues. Application à l'aide au diagnostic en pathologie thyroidienne, Ph.D. Thesis, Université de Marseille, France, 1975.
25. Saminger S. On ordinal sums of triangular norms on bounded lattices. Fuzzy Sets and Systems 157 10 (2006) 1403-1416
26. Schweizer B., and Sklar A. Probabilistic Metric Spaces (1983), Elsevier, North-Holland, New York
27. Turunen E. Mathematics Behind Fuzzy Logic (1999), Physica-Verlag, Wurzburg
28. Zadeh L.A. Fuzzy sets. Inform. and Control 8 3 (1965) 338-353
29. Zherui M., and Wangming W. Logical operators on complete lattices. Inform. Sci. 55 (1991) 77-97
30. Zuo Q. Description of strictly monotonic interval AND/OR operations. Proc. Internat. Workshop on Applications of Interval Computations. El Paso, TX (1995)