WEAKLY PRIME AND SUPER-MAX FILTERS IN BL-ALGEBRAS

Document Type : Original Manuscript

Authors

1 Department of Mathematics, University of Hormozgan, P.O. Box 3995, Bandar Abbas, Iran.

2 Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran.

Abstract

‎In this paper‎, ‎the concepts of weakly prime filters and super-max filters in $\mathrm{BL}$-algebras are introduced‎, ‎and the relationships between them are discussed‎. ‎Also‎, ‎some properties and relations between these filters and other types of filters in $\mathrm{BL}$-algebras are given‎. ‎With some examples‎, ‎it is shown that these filters have differences‎. ‎After that‎, ‎the notions of weakly linear $\mathrm{BL}$-algebras and weak top $\mathrm{BL}$-algebras are defined and investigated‎. ‎Finally‎, ‎using the notion of a weakly prime filter‎, ‎a new topology on $\mathrm{BL}$-algebras is defined and studied‎.

Keywords

References

 1. J. Abaffy, C. G. Broyden and E. Spedicato, A class of direct methods for linear equations, Numer. Math., 45 (1984), 361–376.
2. J. Abaffy and E. Spedicato, ABS Projection Algorithms: Mathematical Techniques for Linear and Nonlinear Equations, Ellis Horwood, Chichester, 1989.
3. A. Borumand Saeid and S. Motamed, A new filter in BL-algebras, Journal of Intelligent and Fuzzy Systems, 27 (2014), 2949–2957.
4. R. A. Borzooei and A. Paad, Integral filters and integral BL-Algebras, Italian Journal of Pure and Applied Mathematics, 30 (2013), 303–316.
5. D. Busneag and D. Piciu, BL-algebra of fractions relative to an ^-closed system, Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, 11(1) (2003), 31–40.
6. D. Busneag and D. Piciu, On the lattice of deductive systems of a BL-algebra, Central European Journal of Mathematics, 1(2) (2003), 221–237.
7. C. C. Chang, Algebraic analysis of many valued logic, Trans. Amer. Math. Soc., 88 (1958), 467–490.
8. P. Ha´jek, Metamathematics of Fuzzy Logic, Dordrecht: Kluwer Academic Publishers, 1998.
9. M. Haveshki, A. Borumand Saeid and E. Eslami, Some types of filters in BL-algebras, Soft Computing, 10 (2006), 657–664.
10. S. Motamed and J. Moghaderi, On Primary Filters in BL-algebras, New Mathematics and Natural Computation, 15(3) (2019), 447–461.
11. S. Motamed and L. Torkzadeh, A new class of BL-algebras, Soft Computing, 21(3) (2017), 687–698.
12. S. Motamed and L. Torkzadeh, Primary decomposition of filters in BL-algebras, Afr. Mat., 24(4) (2013), 725–737.
13. S. Motamed, L. Torkzadeh, A. Borumand Saeid and N. Mohtashamnia, Radical of filters in BL-algebras, MLQ Math. Log. Q., 57(2) (2011), 166–179.
14. E. Turunen, BL-algebras of basic fuzzy logic, Mathware and Soft Computing, 6 (1999), 49–61.
15. E. Turunen, Boolean deductive system of BL-algebras, Arch. Math. Logic., 40 (2001), 467–473.
16. E. Turunen, Mathematics behind fuzzy logic, Physica-Verlag, 1999.
17. E. Turunen and S. Sessa, Local BL-algebras, Multiple Valued Logic, 6 (2001), 229–249. 
Journal of Algebraic Systems
Volume 12, Issue 2
January 2025
Pages 211-235

Files

Share

How to cite

Statistics