Mathematics and Statistics Vol. 11(3), pp. 558 - 565
DOI: 10.13189/ms.2023.110312
Reprint (PDF) (608Kb)

Bounded Autocatalytic Set and Its Basic Properties

Sumarni Abu Bakar ^1,*, Noor Syamsiah Mohd Noor ¹, Tahir Ahmad ², Siti Salwana Mamat ^3
1 College of Computing, Informatics and Media, Universiti Teknologi MARA, 40450, Shah Alam, Selangor, Malaysia
² Faculty of Science, Universiti Teknologi Malaysia, 81310, Skudai, Johor, Malaysia
³ Centre of Foundation Studies, Universiti Teknologi MARA, 43800, Dengkil, Selangor, Malaysia

ABSTRACT

Autocatalytic Set (ACS) is one of the areas of study that can be modelled using graph theory. An Autocatalytic Set (ACS) is defined as a graph, in which there is at least one incoming link for every node in the graph. Past research on ACS tremendously solved many applications including modelling complex systems through integration of ACS with fuzzy theory. Recently, a restricted form of ACS known as Weak Autocatalytic Set (WACS) was established and used to solve multi-criteria decision-making problems (MCDM), in which the related graph is transitive and involves non-cyclic triads. Though, in scenarios that occur in the real world, there exist MCDM problems, in which the related graph is intransitive, involving cyclic triads. Thus, it creates a limitation to used WACS to solve decision-making problems over cyclic triads. This paper introduced another class of ACS known as Bounded Autocatalytic Set (BACS). The concept of BACS provides the ability to represent a relation between one criterion to each other criterion, and the graph involves cyclic triads. Here, the definition of BACS is formed and introduced for the first time, and its basic properties related to edges, paths, and cycles in the form of theorem and propositions are established and presented.

KEYWORDS
Autocatalytic Set, Weak Autocatalytic Set, Graph Theory, Fuzzy Autocatalytic Set, Fuzzy Weak Autocatalytic Set

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Sumarni Abu Bakar , Noor Syamsiah Mohd Noor , Tahir Ahmad , Siti Salwana Mamat , "Bounded Autocatalytic Set and Its Basic Properties," Mathematics and Statistics, Vol. 11, No. 3, pp. 558 - 565, 2023. DOI: 10.13189/ms.2023.110312.

(b). APA Format:
Sumarni Abu Bakar , Noor Syamsiah Mohd Noor , Tahir Ahmad , Siti Salwana Mamat (2023). Bounded Autocatalytic Set and Its Basic Properties. Mathematics and Statistics, 11(3), 558 - 565. DOI: 10.13189/ms.2023.110312.