INTERVAL-VALUED FUZZY B-ALGEBRAS

Document Type: Research Paper

Author

Dept. of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran

Abstract

In this note the notion of interval-valued fuzzy B-algebras (briefly,
i-v fuzzy B-algebras), the level and strong level B-subalgebra is introduced.
Then we state and prove some theorems which determine the relationship
between these notions and B-subalgebras. The images and inverse images of
i-v fuzzy B-subalgebras are defined, and how the homomorphic images and
inverse images of i-v fuzzy B-subalgebra becomes i-v fuzzy B-algebras are
studied.

[1] R. Biswas, Rosenfeld’s fuzzy subgroups with interval valued membership function, Fuzzy Sets
and Systems, 63 , 1(1994), 87-90.
[2] A. Borumand Saeid, Fuzzy topological B-algebras, (Submitted ).
[3] S. M. Hong, Y. B. Jun, S. J. Kim and G. I. Kim, Fuzzy BCI-subalgebras with interval-valued
membership functions, IJMMS., 25, 2 (2001), 135-143.
[4] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV Proc. Japan Academy,
42 (1966), 19-22.
[5] Y. B. Jun, E. H. Roh, Chinju and H. S. Kim, On Fuzzy B-algebras, Czechoslovak Math.
Journal, 52 (2002), 375-384.
[6] J. Meng and Y.B. Jun, BCK-algebras, Kyung Moonsa, Seoul, Korea, (1994).
[7] J. Neggers and H. S. Kim, On B-algebras, Math. Vensik, 54 (2002), 21-29.
[8] , On d-algebras, Math. Slovaca, 49 (1999), 19-26.
[9] A. Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl., 35 (1971), 512-517.
[10] L. A. Zadeh, Fuzzy Sets, Inform. Control, 8 (1965), 338-353.
[11] , The concept of a linguistic variable and its application to approximate reasoning. I,
Information Sci., 8 (1975), 199-249.