Mathematics and Statistics Vol. 12(1), pp. 48 - 54
DOI: 10.13189/ms.2024.120107
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On Intuitionistic Hesitancy Fuzzy Graphs

Sunil M.P. ^*, J. Suresh Kumar
PG and Research Department of Mathematics, N.S.S. Hindu College, Changanacherry, Kottayam, Kerala, India

ABSTRACT

A graph is a basic representation of relationship between vertices and edges. This can be used when the relationships are normal and straight forward. But most of the real life situations are rather complex and it calls for advance development in graph theory. The concept of fuzzy graph addresses uncertainity to a certain extent. But, situations arise when we have to address complex hesitant situations such as taking major decisions regarding merging of companies. Intuitionistic fuzzy graph (IFG) and Hesitancy fuzzy graph (HFG) were developed to resolve this uncertainity. But it also fell short in resolving problems related to hesitant situations. In this paper, we present the concepts of IFG and HFG, which serve as the foundation for introducing, defining and analysing Intuitionistic hesitancy fuzzy graph (IHFG). We explore the concepts such as λ-strong, δ-strong and ρ-strong IHFGs. Also, we make a detailed comparative study on the cartesian product and composition of HFGs and IHFGs, establishing essential theorems related to the properties of such products. We prove that the cartesian product and composition of two strong HFGs need not be a strong HFG, but the cartesian product and composition of two strong IHFGs is a strong IHFG. Also we prove that if the cartesian product of two IHFGs is strong, then, at least one of the IHFG will be strong and if the composition of two IHFGs is strong, then at least one of the IHFG will be strong. IHFG models provide exact and accurate results for taking apt decisions in problems involving hesitant situations.

KEYWORDS
HFG, IHFG, Strong IHFG, Cartesian Product, Composition

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Sunil M.P. , J. Suresh Kumar , "On Intuitionistic Hesitancy Fuzzy Graphs," Mathematics and Statistics, Vol. 12, No. 1, pp. 48 - 54, 2024. DOI: 10.13189/ms.2024.120107.

(b). APA Format:
Sunil M.P. , J. Suresh Kumar (2024). On Intuitionistic Hesitancy Fuzzy Graphs. Mathematics and Statistics, 12(1), 48 - 54. DOI: 10.13189/ms.2024.120107.