Korean J. Math.  Vol 27, No 3 (2019)  pp.595-612
DOI: https://doi.org/10.11568/kjm.2019.27.3.595

$\beta$-fuzzy filters in MS-algebras

Berhanu Assaye Alaba, Teferi Getachew Alemayehu


In this paper, we introduce the concept of $ \beta $-fuzzy filters in MS-algebras and $ \beta $-fuzzy filters are characterized in terms of boosters. It is proved that the lattice of  $ \beta $-fuzzy filters is isomorphic to the fuzzy ideal lattice of boosters.


MS-algebras, boosters, $ \beta $-fuzzy filter, maximal $\beta $- fuzzy filter, prime $ \beta $-fuzzy filter.

Subject classification

06D99, 06D05, 06D30


Full Text:



N. Ajmal, Fuzzy lattice, Inform. Sci. 79 (1994), 271–291. (Google Scholar)

M. Attallah, Completely fuzzy prime ideals of distributive lattices, The Journal of Fuzzy Mathematics 8 (1) (2000), 151–156. (Google Scholar)

B. A. Alaba and T. G. Alemayehu, Clousure fuzzy ideals of MS-algebras, Ann. Fuzzy Math. Inform. 16 (2) (2018), 247–260. (Google Scholar)

B. A. Alaba, M. A. Taye and T. G. Alemayehu, δ-fuzzy ideals in MS-algebras, Int. J. Math. and Appl. 6 (2-B) (2018), 273–280. (Google Scholar)

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)

T. S. Blyth and J. C. Varlet, Subvarieties of the class of MS-algebras, Proc.Roy. Soc. Edinburgh Sect. A (1983), 94A, 301–308. (Google Scholar)

B. A. Davey and H. A. Priestley, Introduction to Lattices and order, Second edition Cambrige (2002). (Google Scholar)

A. Kadji, C. Lele and M. Tonga, Fuzzy prime and maximal filters of residual lattice, Soft Comput, Springer-Verlag Berlin Heidelberg (2016) DOI 10.1007/s00500-016-2113-2. (Google Scholar)

B. B. N. Koguep , C. Nkuimi and C. Lele, On Fuzzy prime ideals of lattice, SJPAM 3 (2008), 1–11. (Google Scholar)

A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512–517. (Google Scholar)

M. Sambasiva Rao, β-Filters of MS-algebras, Asian-Eur. J. Math. 5 (2) (2012), 1250023(8 pages). (Google Scholar)

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

U. M. Swamy and D. V. Raju, Irreducibility in algebraic fuzzy systems, Fuzzy Sets and Systems 41 (1991), 233–241. (Google Scholar)

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

L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338–353. (Google Scholar)


  • There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr