Triangular norms on product lattices

Fuzzy Sets and Systems

Volumn 104, Issue 1, 1999, Pages 61-75

  De Baets, Bernard ^a   Mesiar, Radko ^b,c  

^a GHENT UNIVERSITY   (Belgium)

^b SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

^c INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

Author keywords

(pseudo )Archimedean property; Cancellation law; Cartesian product; Direct product; Idempotent element; Lattice; Nilpotent element; Partially ordered set; T norm; Zero divisor

Indexed keywords

EID: 0003004173     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(98)00259-0     Document Type: Article

References (18)

1. J. Agustí, F. Esteva, P. Garcia, L. Godo, R. Lopez de Mantaras, C. Sierra, Local multi-valued logics in modular expert systems, J. Expt. Theor. Artificial Intell. 6 (1994) 303-321.
2. G. Birkhoff, Lattice Theory, vol. XXV, AMS Colloquium Publications, Providence, Rhode Island, 1967.
3. B. De Baets, Oplossen van vaagrelationele vergelijkingen: een ordetheoretisch benadering, Ph.D. Dissertation, University of Gent, 1995, 389 p.
4. B. De Baets, An order-theoretic approach to solving sup-script T equations, in: D. Ruan (Ed. ), Fuzzy Set Theory and Advanced Mathematical Applications, Kluwer Academic Publishers, Dordrecht, 1995, pp. 67-87.
5. B. De Baets, Database entry A030453, Sloane's On-Line Encyclopedia of Integer Sequences, URL: http://www.research.att.com/~njas/sequences/index.html.
6. G. De Cooman, E. Kerre, Order norms on bounded partially ordered sets, J. Fuzzy Math. 2 (1994) 281-310.
7. C. Drossos, M. Navara, Generalized t-conorms and closure operators, in: H.-J. Zimmermann (Ed.), Proc. 4th Eur. Congr. on Intelligent Techniques and Soft Computing, vol. 1, ELITE, Aachen, Germany, 1996, pp. 22-26.
8. L. Godo, C. Sierra, A new approach to connective generation in the framework of expert systems using fuzzy logic, Proc. 18th Internat. Symp. on Multiple-Valued Logic, Palma de Mallorca, Spain, IEEE Computer Society Press, 1988, pp. 157-162.
9. J. Goguen, L-Fuzzy sets, J. Math. Anal. Appl. 18 (1967) 145-174.
10. S. Jenei, A more efficient method for defining fuzzy connectives, Fuzzy Sets and Systems 90 (1997) 25-35.
11. E.-P. Klement, R. Mesiar, E. Pap, Triangular Norms, in preparation.
12. C. Ling, Representation of associative functions, Publ. Math. Debrecen 12 (1965) 189-212.
13. G. Mayor, J. Torrens, On a class of operators for expert systems, Internat. J. Intell. Systems 8 (1993) 771-778.
14. K. Menger, Statistical metrics, Proc. Nat. Acad. Sci., USA, 28 (1942) 535-537.
15. H. Nguyen, E. Walker, A First Course in Fuzzy Logic, CRC Press, Boca Raton, 1997.
16. S. Ray, Representation of a Boolean algebra by its triangular norms, Mathware Soft Comput. 4 (1997) 63-68.
17. B. Schweizer, A. Sklar, Probabilistic Metric Spaces, Elsevier, Amsterdam, 1983.
18. D. Smutná, On a peculiar t-norm, BUSEFAL 75 (1998), in press.