Abstract
We propose certain types of interval-valued fuzzy graphs including balanced interval-valued fuzzy graphs, neighbourly irregular interval-valued fuzzy graphs, neighbourly total irregular interval-valued fuzzy graphs, highly irregular interval-valued fuzzy graphs, and highly total irregular interval-valued fuzzy graphs. Some interesting properties associated with these new interval-valued fuzzy graphs are investigated, and necessary and sufficient conditions under which neighbourly irregular and highly irregular interval-valued fuzzy graphs are equivalent are obtained. We also describe the relationship between intuitionistic fuzzy graphs and interval-valued fuzzy graphs.
Highlights
The major role of graph theory in computer applications is the development of graph algorithms
Since most of the time the aspects of graph problems are uncertain, it is nice to deal with these aspects via the methods of fuzzy systems
It is known that fuzzy graph theory has numerous applications in modern science and engineering, especially in the field of information theory, neural networks, expert systems, cluster analysis, medical diagnosis, traffic engineering, network routing, town planning, and control theory
Summary
The major role of graph theory in computer applications is the development of graph algorithms. A number of algorithms are used to solve problems that are modeled in the form of graphs These algorithms are used to solve the graph theoretical concepts, which in turn are used to solve the corresponding computer science application problems. Interval-valued fuzzy set theory reflects the uncertainty by the length of the interval membership degree [μ1, μ2]. In intuitionistic fuzzy set theory for every membership degree (μ1, μ2), the value π = 1 − μ1 − μ2 denotes a measure of nondeterminacy (or undecidedness). It is important to use interval-valued fuzzy sets in applications, such as fuzzy control. Fuzzy graph theory has been finding an increasing number of applications in modeling real time systems where the level of information inherent in the system varies with differences levels of precision. Terminologies and applications are not mentioned in the paper; the readers are referred to [13, 14, 21,22,23,24,25,26,27,28,29]
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