Study strong Sheffer stroke non-associative MV-algebras by fuzzy filters

Abstract

In this paper, some types of fuzzy filters of a strong Sheffer stroke non-associative MV-algebra (for short, strong Sheffer stroke NMV-algebra) are introduced. By presenting new properties of filters, we define a prime filter in this algebraic structure. Then (prime) fuzzy filters of a strong Sheffer stroke NMV-algebra are determined and some features are proved. Finally, we built quotient strong Sheffer stroke NMV-algebra by a fuzzy filter.

Keywords

• Sheffer operation
• strong Sheffer stroke NMV-algebra
• fuzzy filter

References

1. Abbott, J. C., Implicational algebras, Bulletin Mathematique de la Societe des Sciences Mathematiques de la Republique Socialiste de Roumanie, 11(1) (1967), 3–23. http://www.jstor.org/stable/43679502
2. Botur, M., Halas, R., Commutative basic algebras and non-assocative fuzzy logics, Archive for Mathematical Logic, 48 (2009), 243–255. https://doi.org/10.1007/s00153-009-0125-7
3. Chajda, I., Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis Facultas Rerum Naturalium Mathematica, (44)(1) (2005) 19–23. http://dml.cz/dmlcz/133381
4. Chajda, I., Halas, R., Langer, H., Operations and structures derived from non-associative MV-algebras, Soft Computing, 23(12) (2019), 3935–3944. https://doi.org/10.1007/s00500-018-3309-4
5. Chajda, I., Kuhr, J., A non-associative generalization of MV-algebras, Mathematica Slovaca, 57 (2007), 301–312. https://doi.org/10.2478/s12175-007-0024-5
6. Chajda, I., Langer, H., Properties of non-associative MV-algebras, Mathematica Slovaca, 67 (2017), 1095–1104. https://doi.org/10.1515/ms-2017-0035
7. Esteva, F., Godo, L., Monoidal t-norm based logic: towards a logic for left-continous t-norms, Fuzzy Sets and Systems, 124 (2001), 271–288. https://doi.org/10.1016/S0165-0114(01)00098-7
8. Hajek, P., Metamathematics of Fuzzy Logic, Trends in Logic, vol. 4, Kluwer Academic Publishers, 1998.

9. McCune, W., Veroff, R., Fitelson, B., Harris, K., Feist, A., Wos, L., Short single axioms for Boolean algebra, Journal of Automated Reasoning, 29(1) (2002), 1–16. https://doi.org/10.1023/A:1020542009983
10. Oner, T., Katican, T., Borumand Saeid, A., Terziler, M., Filters of strong Sheffer stroke non-associative MV-algebras, Analele Stiintifice ale Universitatii Ovidius Constanta, 29(1) (2021), 143—164. https://doi.org/10.2478/auom-2021-0010
11. Oner, T., Katican, T. Borumand Saeid, A., Relation between Sheffer stroke operation and Hilbert algebras, Categories and General Algebraic Structures with Applications, 14(1) (2021), 245–268. https://doi.org/10.29252/CGASA.14.1.245
12. Oner, T., Katican, T., Borumand Saeid, A., Fuzzy filters of Sheffer stroke Hilbert algebras, Journal of Intelligent and Fuzzy Systems, 40(1) (2021), 759–772. https://doi.org/10.3233/JIFS-200760
13. Oner, T., Katican, T., Borumand Saeid, A., Fuzzy filters of Sheffer stroke BL-algebras, Kragujevac Journal of Mathematics, 47(1) (2023), 39–55.
14. Oner, T., Katican, T., Borumand Saeid, A., On Sheffer stroke UP-algebras, Discussiones Mathematicae General Algebra and Applications, 41 (2021), 381—394 https://doi.org/10.7151/dmgaa.1368
15. Oner, T., Katican, T., Rezaei, A., Neutrosophic n-structures on strong Sheffer stroke non-associative MV-algebras, Neutrosophic Sets and Systems, 40 (2021), 235–252. https://doi.org/10.5281/zenodo.4549403
16. Sheffer, H. M., A set of five independent postulates for Boolean algebras, with application to logical constants, Transactions of the American Mathematical Society, 14(4) (1913), 481–488. https://doi.org/10.2307/1988701
17. Wang, G.-J., Non-classical Mathematical Logic and Approximate Reasoning, Science Press, 2000.
18. Zadeh, L. A., Fuzzy sets, Information and Control, 8 (1965), 338–353.