Autor:

Praba, Bashyam ; Anto Freeda, Lourdusamy Packiammal

Współtwórca:

Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.

Tytuł:

Generation of Gray codes through the rough identity-summand graph of filters of a rough bi-Heyting algebra

Tytuł publikacji grupowej:

AMCS, volume 35 (2025)

Temat i słowa kluczowe:

Heyting algebra ; filters ; identity-summand graph ; complete bipartite graph ; Gray code

Abstract:

This paper introduces the concept of filters in a rough bi-Heyting algebra. The rough bi-Heyting algebra defined through the rough semiring offers interesting properties. Filters on this rough bi-Heyting algebra are to be described in terms of the R-upset. Then a one-to-one correspondence between the filters, the principle ideal and R-upsets is established. Various filters are characterized on this rough bi-Heyting algebra. For each filter, a rough identity-summand graph is constructed. This rough identity-summand graph is proved to be a complete bipartite graph in certain cases involving pairs of elements. ; When more than two elements are involved, a rough identity-summand graph exists and generates multiple complete bipartite graphs. The number of distinct complete bipartite graphs generated from this graph is defined to be an RBP number. The union of these distinct complete bipartite graphs forms a subgraph of the rough identity-summand graph. Additionally, this study demonstrates how two transition sequences obtained from the distinct complete bipartite graphs of the rough identity-summand graph can be utilized to generate Gray codes, making a substantial contribution.

Wydawca:

Zielona Góra: Uniwersytet Zielonogórski

Data wydania:

2025

Typ zasobu:

artykuł

DOI:

10.61822/amcs-2025-0026

Strony:

371-385

Źródło:

AMCS, volume 35, number 2 (2025) ; kliknij tutaj, żeby przejść

Jezyk:

eng

Licencja CC BY 4.0:

kliknij tutaj, żeby przejść

Prawa do dysponowania publikacją:

Biblioteka Uniwersytetu Zielonogórskiego