Tree Decompositions in Fuzzy Graphs: Foundations and Structural Insights

Takaaki Fujita; Iqbal M. Batiha; Muhammad Gulistan; Belal Batiha; Essa Lafi Al Smadi; Iqbal Jebril

doi:10.19139/soic-2310-5070-3117

Tree Decompositions in Fuzzy Graphs: Foundations and Structural Insights

Takaaki Fujita
, Iqbal M. Batiha
, Muhammad Gulistan
, Belal Batiha
, Essa Lafi Al Smadi
, Iqbal Jebril

Nonlinear Dynamic Research Centre (NDRC)

Al-Zaytoonah University of Jordan
University of Alberta
Hazara University
Jadara University
Ajloun National University

Research output: Contribution to journal › Article › peer-review

Abstract

A Fuzzy Graph extends classical graph theory by incorporating uncertainty, assigning a membership degree to each edge. Tree-width is a basic metric that assesses how much a graph resembles a tree [31, 32], making it an essential tool in algorithm design and combinatorial optimization. Path-width quantifies how much a graph resembles a path, using smallest bag size minus one in path-decomposition of the graph. The main aim of this work is to present the Fuzzy Tree-Decomposition and Fuzzy Path-Decomposition, extending the classical notions of tree- and path-decompositions to the realm of fuzzy graphs. We anticipate that these novel ideas will expand the possible uses of fuzzy graphs and encourage more investigation into the mathematical structure of graph-width parameters.

Original language	English
Pages (from-to)	312-326
Number of pages	15
Journal	Statistics, Optimization and Information Computing
Volume	16
Issue number	1
DOIs	https://doi.org/10.19139/soic-2310-5070-3117
State	Published - 9 Jun 2026

Keywords

Fuzzy Graph
Graph Width Parameters
Path-width
Tree-width

Access to Document

10.19139/soic-2310-5070-3117

Cite this

@article{04c925ca0dd04c909e0a1467403a3219,

title = "Tree Decompositions in Fuzzy Graphs: Foundations and Structural Insights",

abstract = "A Fuzzy Graph extends classical graph theory by incorporating uncertainty, assigning a membership degree to each edge. Tree-width is a basic metric that assesses how much a graph resembles a tree [31, 32], making it an essential tool in algorithm design and combinatorial optimization. Path-width quantifies how much a graph resembles a path, using smallest bag size minus one in path-decomposition of the graph. The main aim of this work is to present the Fuzzy Tree-Decomposition and Fuzzy Path-Decomposition, extending the classical notions of tree- and path-decompositions to the realm of fuzzy graphs. We anticipate that these novel ideas will expand the possible uses of fuzzy graphs and encourage more investigation into the mathematical structure of graph-width parameters.",

keywords = "Fuzzy Graph, Graph Width Parameters, Path-width, Tree-width",

author = "Takaaki Fujita and Batiha, \{Iqbal M.\} and Muhammad Gulistan and Belal Batiha and \{Al Smadi\}, \{Essa Lafi\} and Iqbal Jebril",

note = "Publisher Copyright: Copyright {\textcopyright} 2026 International Academic Press",

year = "2026",

month = jun,

day = "9",

doi = "10.19139/soic-2310-5070-3117",

language = "English",

volume = "16",

pages = "312--326",

journal = "Statistics, Optimization and Information Computing",

issn = "2311-004X",

publisher = "International Academic Press",

number = "1",

}

TY - JOUR

T1 - Tree Decompositions in Fuzzy Graphs

T2 - Foundations and Structural Insights

AU - Fujita, Takaaki

AU - Batiha, Iqbal M.

AU - Gulistan, Muhammad

AU - Batiha, Belal

AU - Al Smadi, Essa Lafi

AU - Jebril, Iqbal

PY - 2026/6/9

Y1 - 2026/6/9

N2 - A Fuzzy Graph extends classical graph theory by incorporating uncertainty, assigning a membership degree to each edge. Tree-width is a basic metric that assesses how much a graph resembles a tree [31, 32], making it an essential tool in algorithm design and combinatorial optimization. Path-width quantifies how much a graph resembles a path, using smallest bag size minus one in path-decomposition of the graph. The main aim of this work is to present the Fuzzy Tree-Decomposition and Fuzzy Path-Decomposition, extending the classical notions of tree- and path-decompositions to the realm of fuzzy graphs. We anticipate that these novel ideas will expand the possible uses of fuzzy graphs and encourage more investigation into the mathematical structure of graph-width parameters.

AB - A Fuzzy Graph extends classical graph theory by incorporating uncertainty, assigning a membership degree to each edge. Tree-width is a basic metric that assesses how much a graph resembles a tree [31, 32], making it an essential tool in algorithm design and combinatorial optimization. Path-width quantifies how much a graph resembles a path, using smallest bag size minus one in path-decomposition of the graph. The main aim of this work is to present the Fuzzy Tree-Decomposition and Fuzzy Path-Decomposition, extending the classical notions of tree- and path-decompositions to the realm of fuzzy graphs. We anticipate that these novel ideas will expand the possible uses of fuzzy graphs and encourage more investigation into the mathematical structure of graph-width parameters.

KW - Fuzzy Graph

KW - Graph Width Parameters

KW - Path-width

KW - Tree-width

UR - https://www.scopus.com/pages/publications/105041284231

U2 - 10.19139/soic-2310-5070-3117

DO - 10.19139/soic-2310-5070-3117

M3 - Article

AN - SCOPUS:105041284231

SN - 2311-004X

VL - 16

SP - 312

EP - 326

JO - Statistics, Optimization and Information Computing

JF - Statistics, Optimization and Information Computing

IS - 1

ER -

Tree Decompositions in Fuzzy Graphs: Foundations and Structural Insights

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this