Implicative filters in quasi-ordered residuated system

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2021-02-0025

Keywords:

Quasi-ordered residuated system, Implicative filter in quasi-ordered residuated system

Abstract

The concept of residuated relational systems ordered under a quasiorder relation was introduced in 2018 by S. Bonzio and I. Chajda as a structure ūĚíú = ‚Ć©A, ¬∑,‚Üí, 1, R‚Ć™, where (A, ¬∑) is a commutative monoid with the identity 1 as the top element in this ordered monoid under a quasi-order R. The author introduced and analyzed the concepts of filters in this type of algebraic structures. In this article, as a continuation of previous author‚Äôs research, the author introduced and analyzed the concept of implicative filters in quasi-ordered residuated systems.

References

E. Bonzio, "Algebraic structures from quantum and fuzzy logics", PhD Thesis, Università degli studi di Cagliari, 2016. [On line]. Available: https://bit.ly/3bUmb5N

S. Bonzio and I. Chajda, ‚ÄúResiduated relational systems‚ÄĚ, Asian-European journal of mathematics, vol. 11, no. 2, Art ID. 1850024, 2018, doi: 10.1142/S1793557118500249

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D. A. Romano, ‚ÄúFilters in residuated relational system ordered under quasi-order‚ÄĚ, Bulletin International Mathematics Virtual Institute, vol. 10, no. 3, pp. 529-534, 2020, doi: 10.7251/BIMVI2003529R

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A. Tarski and S. R. Givant, A formalization of set theory without variables. Providence, RI: AMS, 1987.

Published

2021-03-04

How to Cite

[1]
D. Romano, ‚ÄúImplicative filters in quasi-ordered residuated system‚ÄĚ, Proyecciones (Antofagasta, On line), vol. 40, no. 2, pp. 417-424, Mar. 2021.

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Section

Artículos