Residual implications and left-continuous t-norms which are ordinal sums of semigroups

Fuzzy Sets and Systems

Volumn 143, Issue 1, 2004, Pages 47-57

  Mesiar, R ^a,b   Mesiarova A ^c  

^a SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

^b INSTITUTE OF MATHEMATICS   (Czech Republic)

^c INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

Additive generator; Ordinal sum; Residual implications; T norm; T subnorm

Indexed keywords

BOUNDARY CONDITIONS; CONFORMAL MAPPING; MATHEMATICAL MODELS; METRIC SYSTEM; PROBABILISTIC LOGICS; PROBLEM SOLVING; THEOREM PROVING;

ADDITIVE GENERATORS; ORDINAL SUMS; RESIDUAL IMPLICATIONS; T-SUBNORMS; TRIANGULAR NORMS (T-NORMS);

FUZZY SETS;

EID: 1342285539     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2003.06.008     Document Type: Conference Paper

References (20)

1. Aczél J. Lectures on Functional Equations and their Applications. 1966;Academic Press, New York.
2. Clifford A.H. Naturally ordered commutative semigroups. Amer. J. Math. 76:1954;631-646.
3. B. De Baets, R. Mesiar, Residual implicators of continuous t-norms, Proc. EUFIT'96, Aachen, 1996, pp. 37-41.
4. Gottwald S. A Treatise on Many-Valued Logic, Studies in Logic and Computation. 2001;Research Studies Press, Baldock.
5. U. Hohle, Commutative, residuated l-monoids, in: U. Hohle, E.P. Klement, (Eds.) Non-Classical Logics and Their Applications of Fuzzy Subsets, A Handbook of the Mathematical Foundations of Fuzzy Set Theory, Kluwer Academic Publishers, Dordrecht, 1995, pp. 53-106.
6. U. Hohle, E.P. Klement, Non-Classical Logics and Their Applications of Fuzzy Subsets. A Handbook of the Mathematical Foundations of Fuzzy Set Theory, Kluwer Academic Publishers, Dordrecht, 1995.
7. Jenei S. Structure of left-continuous triangular norms with strong induced negations. (I) Rotation construction. J. Appl. Non-Classical Logics. 10:2000;83-92.
8. Jenei S. Structure of left-continuous triangular norms with strong induced negations. (II) Rotation-annihilation construction. J. Appl. Non-Classical Logic. 11:2001;3-4.
9. Jenei S. A note on the ordinal sum theorem and its consequence for the construction of triangular norms. Fuzzy Sets and Systems. 126:2002;199-205.
10. S. Jenei, How to construct left-continuous triangular norms - state of the art, Fuzzy Sets and Systems 143 (2004), this issue.
11. Klement E.P., Mesiar R., Pap E. Quasi- and pseudo-inverse of monotone functions, and the construction of t-norms. Fuzzy Sets and Systems. 104:1999;3-13.
12. E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Trends in Logic, Studia Logica Library, vol. 8, Kluwer Academic Publishers, Dordrecht, 2000.
13. Klement E.P., Mesiar R., Pap E. Triangular norms as ordinal sums of semigroups in the sense of A.H. Clifford. Semigroup Forum. 65:2002;71-82.
14. Kolesárová A. A note on Archimedean triangular norms. BUSEFAL. 80:1999;57-60.
15. Ling C.M. Representation of associative functions. Publ. Math. Debrecen. 12:1965;189-212.
16. A. Mesiarová, Triangular norms and their diagonals, Master Thesis, Comenius University, Bratislava, 2002.
17. Mesiarová A. Continuous triangular subnorms. Fuzzy Sets and Systems. 142:2004;75-83.
18. Schweizer B., Sklar A. Statistical metrics spaces. Pacific J. Math. 10:1960;312-334.
19. Schweizer B., Sklar A. Probabilistic Metric Spaces. 1983;North-Holland, New York.
20. P. Vinceník, Non-continuous additive generators of triangular norms, Ph.D. Thesis, Slovak University of Technology, Bratislava (in Slovak).