Research Article
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Shift Filter of Quasi-ordered Residuated Systems

Year 2022, Volume 5, Issue 3, 124 - 130, 30.09.2022
https://doi.org/10.33434/cams.1089222

Abstract

The concept of residuated relational systems ordered under a quasi-order relation was introduced in 2018 by S. Bonzio and I. Chajda as a structure $\mathfrak{A} = \langle A, \cdot, \rightarrow, 1, \preccurlyeq \rangle$, where $(A,\cdot)$ is a commutative semigroup with the identity $1$ as the top element in this ordered monoid under a quasi-order $\preccurlyeq$. In 2020, the author introduced and analyzed the concepts of filters in this type of algebraic structures. In addition to the previous, the author continued to investigate some of the types of filters in quasi-ordered residuated systems such as, for example, implicative and comparative filters. In this article, as a continuation of previous author's research, the author introduced and analyzed the concepts of shift filters of quasi-ordered residuated systems and then compared it with other types of filters.

References

  • [1] S. Bonzio, Algebraic structures from quantum and fuzzy logics, Ph.D Thesis, Cagliari: Universit‘a degli studi di Cagliari, 2015.
  • [2] S. Bonzio, I. Chajda, Residuated relational systems, Asian-European J. Math., 11(2) (2018), 1850024
  • [3] D. A. Romano, Filters in residuated relational system ordered under quasi-order, Bull. Int. Math. Virtual Inst., 10(3) (2020), 529-534.
  • [4] D. A. Romano, Implicative filters in quasi-ordered residuated dystem, Proyecciones J. Math., 40(2) (2021), 417-424.
  • [5] D. A. Romano, Associated filters in quasi-ordered residuated systems, Contributions to Mathematics, 1 (2020), 22-26.
  • [6] D. A. Romano, Comparative filter in quasi-ordered residuated sysyem, Bull. Int. Math. Virtual Inst., 11(1) (2021), 177-184.
  • [7] D. A. Romano, Ideals in quasi-ordered residuated system, Contrib. Math., 3 (2021), 68-76.
  • [8] D. A. Romano, Strong quasi-ordered residuated system, Open J. Math. Sci., 5 (2021), 73-79.
  • [9] D. A. Romano, Prime and irreducible filters in strong quasi-ordered residuated systems, Open J. Math. Sci., 5 (2021), 172-181.
  • [10] D. A. Romano, Three types of prime filters in strong quasi-ordered residuated systems, An. Univ. Craiova, Ser. Mat. Inf., 49(1) (2022), 135-145.

Year 2022, Volume 5, Issue 3, 124 - 130, 30.09.2022
https://doi.org/10.33434/cams.1089222

Abstract

References

  • [1] S. Bonzio, Algebraic structures from quantum and fuzzy logics, Ph.D Thesis, Cagliari: Universit‘a degli studi di Cagliari, 2015.
  • [2] S. Bonzio, I. Chajda, Residuated relational systems, Asian-European J. Math., 11(2) (2018), 1850024
  • [3] D. A. Romano, Filters in residuated relational system ordered under quasi-order, Bull. Int. Math. Virtual Inst., 10(3) (2020), 529-534.
  • [4] D. A. Romano, Implicative filters in quasi-ordered residuated dystem, Proyecciones J. Math., 40(2) (2021), 417-424.
  • [5] D. A. Romano, Associated filters in quasi-ordered residuated systems, Contributions to Mathematics, 1 (2020), 22-26.
  • [6] D. A. Romano, Comparative filter in quasi-ordered residuated sysyem, Bull. Int. Math. Virtual Inst., 11(1) (2021), 177-184.
  • [7] D. A. Romano, Ideals in quasi-ordered residuated system, Contrib. Math., 3 (2021), 68-76.
  • [8] D. A. Romano, Strong quasi-ordered residuated system, Open J. Math. Sci., 5 (2021), 73-79.
  • [9] D. A. Romano, Prime and irreducible filters in strong quasi-ordered residuated systems, Open J. Math. Sci., 5 (2021), 172-181.
  • [10] D. A. Romano, Three types of prime filters in strong quasi-ordered residuated systems, An. Univ. Craiova, Ser. Mat. Inf., 49(1) (2022), 135-145.

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

Daniel A. ROMANO> (Primary Author)
International Mathematical virtual institute
Bosnia and Herzegovina

Supporting Institution -
Project Number -
Thanks -
Publication Date September 30, 2022
Submission Date March 17, 2022
Acceptance Date September 12, 2022
Published in Issue Year 2022, Volume 5, Issue 3

Cite

Bibtex @research article { cams1089222, journal = {Communications in Advanced Mathematical Sciences}, issn = {2651-4001}, address = {}, publisher = {Emrah Evren KARA}, year = {2022}, volume = {5}, number = {3}, pages = {124 - 130}, doi = {10.33434/cams.1089222}, title = {Shift Filter of Quasi-ordered Residuated Systems}, key = {cite}, author = {Romano, Daniel A.} }
APA Romano, D. A. (2022). Shift Filter of Quasi-ordered Residuated Systems . Communications in Advanced Mathematical Sciences , 5 (3) , 124-130 . DOI: 10.33434/cams.1089222
MLA Romano, D. A. "Shift Filter of Quasi-ordered Residuated Systems" . Communications in Advanced Mathematical Sciences 5 (2022 ): 124-130 <https://dergipark.org.tr/en/pub/cams/issue/72815/1089222>
Chicago Romano, D. A. "Shift Filter of Quasi-ordered Residuated Systems". Communications in Advanced Mathematical Sciences 5 (2022 ): 124-130
RIS TY - JOUR T1 - Shift Filter of Quasi-ordered Residuated Systems AU - Daniel A.Romano Y1 - 2022 PY - 2022 N1 - doi: 10.33434/cams.1089222 DO - 10.33434/cams.1089222 T2 - Communications in Advanced Mathematical Sciences JF - Journal JO - JOR SP - 124 EP - 130 VL - 5 IS - 3 SN - 2651-4001- M3 - doi: 10.33434/cams.1089222 UR - https://doi.org/10.33434/cams.1089222 Y2 - 2022 ER -
EndNote %0 Communications in Advanced Mathematical Sciences Shift Filter of Quasi-ordered Residuated Systems %A Daniel A. Romano %T Shift Filter of Quasi-ordered Residuated Systems %D 2022 %J Communications in Advanced Mathematical Sciences %P 2651-4001- %V 5 %N 3 %R doi: 10.33434/cams.1089222 %U 10.33434/cams.1089222
ISNAD Romano, Daniel A. . "Shift Filter of Quasi-ordered Residuated Systems". Communications in Advanced Mathematical Sciences 5 / 3 (September 2022): 124-130 . https://doi.org/10.33434/cams.1089222
AMA Romano D. A. Shift Filter of Quasi-ordered Residuated Systems. Communications in Advanced Mathematical Sciences. 2022; 5(3): 124-130.
Vancouver Romano D. A. Shift Filter of Quasi-ordered Residuated Systems. Communications in Advanced Mathematical Sciences. 2022; 5(3): 124-130.
IEEE D. A. Romano , "Shift Filter of Quasi-ordered Residuated Systems", Communications in Advanced Mathematical Sciences, vol. 5, no. 3, pp. 124-130, Sep. 2022, doi:10.33434/cams.1089222
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