<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The fractional factor implicates the characteristics of fractional flow in network data transmission, and it is a crucial tool for analyzing network information transfer. When there is uncertain information in the network, the corresponding network graph should be characterized by fuzzy graphs, in which the vertex membership function (MF) describes the uncertainty of sites, and the edge membership reveals the uncertainty of channels. The previous work introduced the concept of fuzzy fractional factor (FFF) on fuzzy graphs, but the correlated concepts are still open on other fuzzy graph classes. In order to overcome this defect, in this contribution, the concept of fuzzy fractional factor is extended to intuitionistic fuzzy graph, Pythagorean fuzzy graph, and picture fuzzy graph. Sign-alternating walk and increasing walk are extended to the corresponding settings, and the transformation operations are redefined in light of various situations. By means of constructive approaches, the corresponding theoretical results are further generalized in these settings, which characterize the existence of (resp. maximum) fuzzy fractional factors in different kinds of fuzzy graphs.</p>
</abstract>

The fractional factor implicates the characteristics of fractional flow in network data transmission, and it is a crucial tool for analyzing network information transfer. When there is uncertain information in the network, the corresponding network graph should be characterized by fuzzy graphs, in which the vertex membership function (MF) describes the uncertainty of sites, and the edge membership reveals the uncertainty of channels. The previous work introduced the concept of fuzzy fractional factor (FFF) on fuzzy graphs, but the correlated concepts are still open on other fuzzy graph classes. In order to overcome this defect, in this contribution, the concept of fuzzy fractional factor is extended to intuitionistic fuzzy graph, Pythagorean fuzzy graph, and picture fuzzy graph. Sign-alternating walk and increasing walk are extended to the corresponding settings, and the transformation operations are redefined in light of various situations. By means of constructive approaches, the corresponding theoretical results are further generalized in these settings, which characterize the existence of (resp. maximum) fuzzy fractional factors in different kinds of fuzzy graphs.

Fuzzy fractional factors in fuzzy graphs-II

School of Information Science and Technology

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Fuzzy fractional factors in fuzzy graphs-II"}

The fractional factor implicates the characteristics of fractional flow in network data transmission, and it is a crucial tool for analyzing network...

Fuzzy fractional factors in fuzzy graphs-II

Article Category: Rapid Communication

Published Online: Jan 10, 2024

Page range: 155 - 164

Received: Sep 07, 2023

Accepted: Oct 25, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0012

Keywords
Intuitionistic fuzzy graph, Pythagorean fuzzy graph, picture fuzzy graph, fuzzy fractional factor

© 2024 Hainan Zhang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fuzzy fractional factors in fuzzy graphs-II

Article Category: Rapid Communication

Published Online: Jan 10, 2024

Page range: 155 - 164

Received: Sep 07, 2023

Accepted: Oct 25, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0012

KeywordsIntuitionistic fuzzy graph, Pythagorean fuzzy graph, picture fuzzy graph, fuzzy fractional factor

© 2024 Hainan Zhang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Intuitionistic fuzzy graph, Pythagorean fuzzy graph, picture fuzzy graph, fuzzy fractional factor