Intuitionistic Fuzzy Graphs with Categorical Properties

The main purpose of this paper is to show the rationality of some operations, defined or to be defined, on intuitionistic fuzzy graphs. Firstly, three kinds of new product operations (called direct product, lexicographic product, and strong product) are defined in intuitionistic fuzzy graphs, and so...

Full description

Saved in:
Bibliographic Details
Published in:Fuzzy information and engineering 2015-09, Vol.7 (3), p.317-334
Main Authors: Rashmanlou, Hossein, Samanta, Sovan, Pal, Madhumangal, Borzooei, Rajab Ali
Format: Article
Language:English
Subjects:
Graphical representations
Graphs
Homomorphisms
Intuitionistic fuzzy graph
Rationally
Strong intuitionistic fuzzy graph
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The main purpose of this paper is to show the rationality of some operations, defined or to be defined, on intuitionistic fuzzy graphs. Firstly, three kinds of new product operations (called direct product, lexicographic product, and strong product) are defined in intuitionistic fuzzy graphs, and some important notions on intuitionistic fuzzy graphs are demonstrated by characterizing these notions and their level counterparts graphs such as intuitionistic fuzzy complete graph, cartesian product of intuitionistic fuzzy graphs, composition of intuitionistic fuzzy graphs, union of intuitionistic fuzzy graphs, and join of intuitionistic fuzzy graphs. As a result, a kind of representations of intuitionistic fuzzy graphs and intuitionistic fuzzy complete graphs are given. Next, categorical goodness of intuitionistic fuzzy graphs is illustrated by proving that the category of intuitionistic fuzzy graphs and homomorphisms between them is isomorphic-closed, complete, and co-complete.
ISSN:1616-8658
1616-8666
DOI:10.1016/j.fiae.2015.09.005