Abstract
A Pythagorean fuzzy set is very effective mathematical framework to represent parameter-wise imprecision which is the property of linguistic communication. A Pythagorean fuzzy soft graph is more potent than the intuitionistic fuzzy soft as well as the fuzzy soft graph as it depicts the interactions among the objects of a system using Pythagorean membership grades with respect to different parameters. This article addresses the content of competition graphs as well as economic competition graphs like k-competition graphs, m-step competition graphs and p-competition graphs in Pythagorean fuzzy soft environment. All these concepts are illustrated with examples and fascinating results. Furthermore, an application which describes the competition among distinct forest trees, that grow together in the mixed conifer forests of California, for plant resources is elaborated graphically. An algorithm is also designed for the construction of Pythagorean fuzzy soft competition graphs. It is worthwhile to express the competing and non-competing interactions in various networks with the help of Pythagorean fuzzy soft competition graphs wherein a variation in competition relative to different attributes is visible.
Highlights
A graph is an effective tool to depict the connectivity and relationship among the objects of a system
We often experience different types of competitions in our daily life that can be modeled as networks or graphs
The Pythagorean fuzzy set (PFS) f theory is a good blend of PFS and S f S, which permits the assignment of Pythagorean membership values with respect to different parameters
Summary
A graph is an effective tool to depict the connectivity and relationship among the objects of a system. FS represents the evidence for x ∈ X , but it lacks the ability to represent the Complex & Intelligent Systems evidence against x ∈ X To address this issue, Atanassov [3], in 1983, put forward the intuitionistic fuzzy set (IFS) by inserting a new component ν : X → [0, 1] that investigates the non-membership grade such that μ + ν ≤ 1. He compared the IFS and PFS and declared that the set of intuitionistic membership values is smaller than that of Pythagorean membership grades All these extensions of crisp sets dealt with many actual-world problems that have fuzziness and uncertainty. Definition 8 A PFS f edge (x, y) is called independent strong in G = (A, B, Q) if the Pythagorean fuzzy edge (x, y) is independent strong in PFG R(q) = (A(q), B(q)) for every q, i.e., following inequalities hold for all q: μB(q)(x, y). Is PFS f edge set for the PFS f digraph G
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