Korean J. Math. Vol. 27 No. 4 (2019) pp.1159-1180
DOI: https://doi.org/10.11568/kjm.2019.27.4.1159

$e$-Fuzzy filters of MS-algebras

Main Article Content

Berhanu Assaye Alaba
Teferi Getachew Alemayehu


In this article, we present the notion of $ e$-fuzzy filters in an MS-Algebra and characterize in terms of equivalent conditions. The concept of $ D $-fuzzy filters is studied and the set of equivalent conditions under which every $ e $-fuzzy filter is an $ D $-fuzzy filter are observed. Moreover we study some properties of the space of all prime $ e $-fuzzy filters of an MS-algebra.

Article Details


[1] T. S. Blyth and J. C. Varlet, Ockham Algebras, Oxford University Press, (1994). Google Scholar

[2] T. S. Blyth and J. C. Varlet, On a common abstraction of de Morgan and Stone algebras, Proc Roy Soc Edinburgh, Sect A, 1983, 94A: 301-308. Google Scholar

[3] T. S. Blyth and J. C. Varlet, Subvarieties of the class of MS-algebras, Proc Roy Soc Edinburgh, Sect A, 1983, 95A: 157-169. Google Scholar

[4] H. Hadji-Abadi and M.M. Zahedi, Some results on fuzzy prime spectrum of a ring , Fuzzy sets and systems, 77 (1996), 235-240. Google Scholar

[5] R. Kumar, Fuzzy prime spectrum of a ring, Fuzzy sets and systems, 46 (1992), 147-154. Google Scholar

[6] R. Kumar, Spectrum prime fuzzy ideals, Fuzzy sets and systems, 62 (1994),101-109. Google Scholar

[7] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971),512-517. Google Scholar

[8] M. Sambasiva Roa, e-filters in MS-algebras, Acta Mathematica Scientia,(33B(3)) Google Scholar

[9] (2014), 738-746. Google Scholar

[10] U. M. Swamy and D. V. Raju, Fuzzy ideals and congruences of lattices, Fuzzy sets and systems, 95 (1998), 249-253. Google Scholar

[11] Bo. Yuan and W. Wu, Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems, 35 (1990),231-240 . Google Scholar

[12] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338-353. Google Scholar