Hyper MV-Algebras Defined by Bipolar-valued Fuzzy Sets

M. Musa Hasankhani; A. Borumand Saeid

doi:10.2478/v10324-012-0003-6

.blurhash-client-img { display: none !important; }

Hyper MV-Algebras Defined by Bipolar-valued Fuzzy Sets

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 50 (2012): Issue 1 (November 2012)

By: M. Musa Hasankhani and A. Borumand Saeid

Open Access

|Nov 2012

Abstract

In this paper the notion of hyper MV -algebra is ex- tended via bipolar-valued fuzzy set and some theorems about this concept are stated and proved. The concepts of strong positive t-cut and strong negative s-cut of bipolar-valued fuzzy set are defined and some of their properties are studied.

References

[1] A. Borumand Saeid, Bipolar-valued fuzzy BCK=BCI-algebras, World Applied Sci. J. 7, No.11, (2009), 1404-1411.
Search in Google Scholar
[2] R. A. Borzooei, A. Hasankhani, M. M. Zahedi, and Y. B. Jun, On hyper-K- algebras, 52(1), (2000), 113-121.
Search in Google Scholar
[3] Sh. Ghorbani, A. Hasankhani, and E. Eslami, Hyper MV -Algebras, Set-valued Math. and Appl., 1 No.2, (2008), 205-222.
Search in Google Scholar
[4] Y. B. Jun, Min Su Kang, and Hee Sik Kim, Fuzzy structures of hyper-MV - deductive systems in hyper-MV -algebras, Computers and Math. with Appl., 59, (2010), 2982-2989.10.1016/j.camwa.2010.02.016
Search in Google Scholar
[5] K. M. Lee, Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent Technologies, (2000), 307-312.
Search in Google Scholar
[6] K. M. Lee, Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets, J. Fuzzy Logic Intelligent Systems, 14, No. 2, (2004), 125-129.10.5391/JKIIS.2004.14.2.125
Search in Google Scholar
[7] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8, (1965), 338{353.10.1016/S0019-9958(65)90241-X
Search in Google Scholar