Abstract
The networks of various problems have competing constituents, and there is a concern to compute the strength of competition among these entities. Competition hypergraphs capture all groups of predators that are competing in a community through their hyperedges. This paper reintroduces competition hypergraphs in the context of Pythagorean fuzzy set theory, thereby producing Pythagorean fuzzy competition hypergraphs. The data of real-world ecological systems posses uncertainty, and the proposed hypergraphs can efficiently deal with such information to model wide range of competing interactions. We suggest several extensions of Pythagorean fuzzy competition hypergraphs, including Pythagorean fuzzy economic competition hypergraphs, Pythagorean fuzzy row as well as column hypergraphs, Pythagorean fuzzy k-competition hypergraphs, m-step Pythagorean fuzzy competition hypergraphs and Pythagorean fuzzy neighborhood hypergraphs. The proposed graphical structures are good tools to measure the strength of direct and indirect competing and non-competing interactions. Their aptness is illustrated through examples, and results support their intrinsic interest. We propose algorithms that help to compose some of the presented graphical structures. We consider predator-prey interactions among organisms of the Bering Sea as an application: Pythagorean fuzzy competition hypergraphs encapsulate the competing relationships among its inhabitants. Specifically, the algorithm which constructs the Pythagorean fuzzy competition hypergraphs can also compute the strength of competing and non-competing relations of this scenario.
Highlights
Graph theory gradually emerged as an autonomous subject after the publication of Euler’s work on the problem of the Seven Bridges of Knigsberg in 1736
The PF hyperedges of Pythagorean fuzzy open neighborhood hypergraph (PFONH) and Pythagorean fuzzy closed neighborhood hypergraph (PFCNH), respectively, represent the relationship among neighbors of a species and how a species interact with its neighbors
An intuitionistic fuzzy set (IFS) permits the expression of truth-membership t as well as falsity-membership f, and it imposes the constraint that 0 t þ f 1 throughout, whereas the Pythagorean fuzzy set (PFS) provides more space to nominate the grades as the limitation relaxes to 0 t2 þ f2 1
Summary
Graph theory gradually emerged as an autonomous subject after the publication of Euler’s work on the problem of the Seven Bridges of Knigsberg in 1736. Naz et al [31] presented a more generalized model of Pythagorean fuzzy graphs (PFGs) together with properties and several applications to decision-making problems. It computes both the competing and non-competing strengths of predators corresponding to each prey. The Bering Sea is well known due to the diversity of its bionetwork as it contains numerous species of mammals and fish This characteristic of Bering Sea urged us to study mutual competition among its organisms with the proposed model of PFCHs. Section 7 provides the comparative analysis, and the last section summarizes the main findings of the paper
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