Intuitionistic Fuzzy Graphs with Categorical Properties

• Main Authors: Hossein Rashmanlou, Sovan Samanta, Madhumangal Pal, Rajab Ali Borzooei
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2015-09-01
• Series: Fuzzy Information and Engineering
• Subjects: Rationally; Intuitionistic fuzzy graph; Strong intuitionistic fuzzy graph
• Online Access: http://www.sciencedirect.com/science/article/pii/S1616865815000655

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.