Research Article
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Year 2022, Volume: 71 Issue: 1, 165 - 187, 30.03.2022
https://doi.org/10.31801/cfsuasmas.900312

Abstract

References

  • 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.

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

Year 2022, Volume: 71 Issue: 1, 165 - 187, 30.03.2022
https://doi.org/10.31801/cfsuasmas.900312

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.

References

  • 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.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Tahsin Öner 0000-0002-6514-4027

Tugce Katican 0000-0003-1186-6750

Arsham Borumand Saeıd 0000-0001-9495-6027

Publication Date March 30, 2022
Submission Date March 20, 2021
Acceptance Date July 29, 2021
Published in Issue Year 2022 Volume: 71 Issue: 1

Cite

APA Öner, T., Katican, T., & Saeıd, A. B. (2022). Study strong Sheffer stroke non-associative MV-algebras by fuzzy filters. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(1), 165-187. https://doi.org/10.31801/cfsuasmas.900312
AMA Öner T, Katican T, Saeıd AB. Study strong Sheffer stroke non-associative MV-algebras by fuzzy filters. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2022;71(1):165-187. doi:10.31801/cfsuasmas.900312
Chicago Öner, Tahsin, Tugce Katican, and Arsham Borumand Saeıd. “Study Strong Sheffer Stroke Non-Associative MV-Algebras by Fuzzy Filters”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 1 (March 2022): 165-87. https://doi.org/10.31801/cfsuasmas.900312.
EndNote Öner T, Katican T, Saeıd AB (March 1, 2022) Study strong Sheffer stroke non-associative MV-algebras by fuzzy filters. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 1 165–187.
IEEE T. Öner, T. Katican, and A. B. Saeıd, “Study strong Sheffer stroke non-associative MV-algebras by fuzzy filters”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 1, pp. 165–187, 2022, doi: 10.31801/cfsuasmas.900312.
ISNAD Öner, Tahsin et al. “Study Strong Sheffer Stroke Non-Associative MV-Algebras by Fuzzy Filters”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/1 (March 2022), 165-187. https://doi.org/10.31801/cfsuasmas.900312.
JAMA Öner T, Katican T, Saeıd AB. Study strong Sheffer stroke non-associative MV-algebras by fuzzy filters. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:165–187.
MLA Öner, Tahsin et al. “Study Strong Sheffer Stroke Non-Associative MV-Algebras by Fuzzy Filters”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 1, 2022, pp. 165-87, doi:10.31801/cfsuasmas.900312.
Vancouver Öner T, Katican T, Saeıd AB. Study strong Sheffer stroke non-associative MV-algebras by fuzzy filters. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(1):165-87.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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