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

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.

___

  • 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
  • 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
  • Chajda, I., Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis Facultas Rerum Naturalium Mathematica, (44)(1) (2005) 19–23. http://dml.cz/dmlcz/133381
  • 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
  • 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
  • Chajda, I., Langer, H., Properties of non-associative MV-algebras, Mathematica Slovaca, 67 (2017), 1095–1104. https://doi.org/10.1515/ms-2017-0035
  • 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
  • Hajek, P., Metamathematics of Fuzzy Logic, Trends in Logic, vol. 4, Kluwer Academic Publishers, 1998.
  • 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
  • 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
  • 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
  • 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
  • Oner, T., Katican, T., Borumand Saeid, A., Fuzzy filters of Sheffer stroke BL-algebras, Kragujevac Journal of Mathematics, 47(1) (2023), 39–55.
  • 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
  • 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
  • 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
  • Wang, G.-J., Non-classical Mathematical Logic and Approximate Reasoning, Science Press, 2000.
  • Zadeh, L. A., Fuzzy sets, Information and Control, 8 (1965), 338–353.