SOME CONSTRUCTION METHODS FOR IMPLICATION OPERATORS ON BOUNDED LATTICES

Öz

In this paper, we focus the construction methods of implications on bounded lattices. We introduce several methods to obtain implication on bounded lattices. We basically base on implication defined on subinterval such as [a,1] or [0,b] of the bounded lattice L which has a,b ∈ L with a ≤ b for these construction methods. We also use fuzzy logic operators such as t-norms, t-conorms, negations and implications on L in some construction methods. In addition, we give some remarks and examples to make the new construction methods.

Anahtar Kelimeler

• Implication
• t-norm
• negation
• bounded lattice
• subinterval

Kaynakça

1. E. P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publishers, Dordrecht ,2000.
2. F. Karacal and Z. Sanlı, Some new construction methods of t-norms and t-conorms on bounded lattices, Fuzzy Sets and Systems, Vol.451, pp.84-93 (2022).
3. F. Karacal, M.N. Kesicioglu, U. Ertugrul, The implications obtained by two given implications on bounded lattices, International Journal of General Systems, Vol.50, N.3, pp.281-299 (2021).
4. F. Karacal, K. Karacair, Some implication operators on bounded lattices, International Journal of General Systems, pp.2335907 (2024).
5. G. Birkhoff, Lattice Theory, American Mathematical Society Colloquium Publishers, Providence, RI, 1967.
6. J.V. Riera, J.Torrens, Residual Implications on the Set of Discrete Fuzzy Numbers, Information Sciences, Vol.247, pp.131–143 (2013).
7. M. N. Kesicioglu, U. Ertugrul, F. Karacal, Generalized convex combination of implications on bounded lattices, Iranian Journal of Fuzzy Systems, Vol.17, N.6, pp.75-91 (2020).
8. M. Baczynski, B. Jayaram, Fuzzy Implications. Studies in Fuzziness and Soft Computing (Vol.231) Berlin, Heidelberg: Springer, (2008).

9. M. Mas, M. Monserrat, J.Torrens, The Law of Importation for Discrete Implications, Information Sciences, Vol.179, pp.4208–4218 (2009).
10. F. Neres, B. Bedregal and R. Santiago, Bi-aggregated contrapositivisation: A new contrapositivisation technique for fuzzy implications, Fuzzy Sets and Systems, Vol.466, pp.108427 (2023).
11. R. Santiago, Bedregal, B., Dimuro, G.P., Fernandez, J., Bustince H., Fardoun, H.M., Abstract Homogeneous Functions and Consistently Influenced/Disturbed Multi-Expert Decision Making, IEEE Transactions on Fuzzy Systems, Vol.30, N.9, pp.3447-3459 (2022).
12. W.Y. Liu, Fuzzy data dependencies and implication of fuzzy data dependencies, Fuzzy Sets and Systems, Vol.92, pp.341-348 (1997).