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Some Results on Interval-Valued Fuzzy BG-Algebras

Authors: Arsham Borumand Saeid

Abstract:

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

Keywords: BG-algebra, fuzzy BG-subalgebra, interval-valued fuzzy set, interval-valued fuzzy BG-subalgebra.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1058279

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References:


[1] S. S. Ahn and h. D. Lee, Fuzzy Subalgebras of BG-algebras, Commun. Korean Math. Soc. 19 (2004) 243-251.
[2] R. Biswas, Rosenfeld-s fuzzy subgroups with interval valued membership function, Fuzzy Sets and Systems 63 (1994), No. 1 87-90.
[3] A. Borumand Saeid, Fuzzy topological BG-algebras, Int. J. Math. (to appear).
[4] 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.
[5] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV Proc. Japan Academy, 42 (1966), 19-22.
[6] C. B. Kim, H. S. Kim, On BG-algebras, (submitted).
[7] J. Meng and Y.B. Jun, BCK-algebras, Kyung Moonsa, Seoul, Korea, (1994).
[8] J. Neggers and H. S. Kim, On B-algebras, Math. Vensik 54 (2002), 21- 29.
[9] , On d-algebras, Math. Slovaca 49 (1999), 19-26.
[10] A Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl. 35 (1971), 512-517.
[11] L. A. Zadeh, Fuzzy Sets, Inform. Control, 8 (1965), 338-353.
[12] , The concept of a linguistic variable and its application to approximate reasoning. I, Information Sci. 8 (1975), 199-249.