Inclusion grade and fuzzy implication operators

Fuzzy Sets and Systems

Volumn 114, Issue 3, 2000, Pages 417-429

  Burillo, P ^a   Frago, N ^a   Fuentes, R ^a  

^a PUBLIC UNIVERSITY OF NAVARRE   (Spain)

Author keywords

Fuzzy relations; Implication operators; Inclusion grades

Indexed keywords

EID: 0000055572     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(98)00128-6     Document Type: Article

References (19)

1. C. Alsina, E. Trillas, On almost distributive Lukasiewicz triplets, Fuzzy Sets and Systems 50 (1992) 175-178.
2. W. Bandler, L. Kohout, Fuzzy power sets and fuzzy implication operator, Fuzzy Sets and Systems 4 (1980) 13-30.
3. S. Divyendu, E.R. Dougherty, Fuzzification of set inclusion, SPIE 1708 (Applications of Artificial Intelligence X: Machine Vision and Robotics) (1992) 440-449.
4. S. Divyendu, E.R. Dougherty, Fuzzification of set inclusion: theory and applications, Fuzzy Sets and Systems 55 (1993) 15-42.
5. D. Dubois, H. Prade, Fuzzy logic and the generalised modus ponens revised, Cybernet. Systems Internat. J. 15 (1984) 293-331.
6. D. Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Applications, Mathematics in Science and Engineering, Academic Press, New York, 1980.
7. D. Dubois, H. Prade, Fuzzy sets in approximate reasoning, Part 1: inference with possibility distributions, Fuzzy Sets and Systems 40 (1991) 143-202.
8. D. Dubois, L. Jérôme, H. Prade, Fuzzy sets in approximate reasoning, Part 2: logical approaches, Fuzzy Sets and Systems 40 (1991) 203-244.
9. N. Frago, Morfología Matemática Borrosa basada en operadores generalizados de Lukasiewicz: Procesamiento de imágenes, Ph.D. Thesis, Universidad Pública de Navarra, 1996.
10. E. Kerre, A comparative study of the behaviour of some popular fuzzy implication operators on the generalised modus ponens, in: L.A. Zadeh, J. Kacprzyk (Eds.), Fuzzy Logic for the Management of Uncertainty, Wiley, New York, 1992, pp. 281-295.
11. B. Kosko, Neural Networks and Fuzzy Systems: A Dynamical Approach to Machine Intelligence, Prentice-Hall, Englewood Cliffs, NJ, 1992.
12. N.N. Morsi, Hyperspace fuzzy binary relations, Fuzzy Sets and Systems 67 (1994) 221-237.
13. D. Ruan, E.E. Kerre, Fuzzy implication operators and generalised fuzzy method of cases, Fuzzy Sets and Systems 54 (1993) 23-27.
14. D. Ruan, E.E. Kerre, G. De Cooman, B. Capelle, F. Vanmassenhove, Influence of the fuzzy implication operator on the method of cases inference regla, Int. J. Approx. Reasoning 4 (1990) 307-318.
15. P. Smets, P. Magrez, Implications in fuzzy logic, Internat. J. Approx. Reasoning 1 (1987) 327-347.
16. E. Trillas, L. Valverde, On implication and indistinguishability in the setting of fuzzy logic, in: J. Kacprzyk, R.R. Yager (Eds.), Management Decision Support Systems Using Fuzzy Sets and Possibility Theory, TÜV Rheinland, Köln, 1985, pp. 198-212.
17. E. Trillas, L. Valverde, On inference in fuzzy logic, Proc. 2nd IFSA Congress, Tokyo, Japan, 1987, pp. 294-297.
18. E. Trillas, L. Valverde, On mode and implication approximate reasoning, in: M.M. Gupta et al. (Eds.), Approximate Reasoning in Expert System, North-Holland, Amsterdam, 1985, pp. 157-166.
19. R. Willmott, On the transitivity of containment and equivalence in fuzzy power set theory, J. Math. Anal. Appl. 120 (1986) 384-396.