Research Article

### Shift Filter of Quasi-ordered Residuated Systems

Year 2022, Volume 5, Issue 3, 124 - 130, 30.09.2022

### 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

### 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 Mathematics Articles Daniel A. ROMANO> (Primary Author) International Mathematical virtual institute Bosnia and Herzegovina - - - September 30, 2022 March 17, 2022 September 12, 2022 Year 2022, Volume 5, Issue 3