Interval-valued fuzzy planar graphs

• Published in: International journal of machine learning and cybernetics Vol. 7; no. 4; pp. 653 - 664
• Main Authors: Pramanik, Tarasankar, Samanta, Sovan, Pal, Madhumangal
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2016; Springer Nature B.V
• Subjects: Apexes; Artificial Intelligence; Complex Systems; Computational Intelligence; Control; Engineering; Fuzzy sets; Graph theory; Graphs; Mechatronics; Original Article; Pattern Recognition; Robotics; Systems Biology; Urban planning; Interval-valued fuzzy graphs; Interval-valued fuzzy planar graphs; Interval-valued fuzzy multigraphs
• ISSN: 1868-8071; 1868-808X
• DOI: 10.1007/s13042-014-0284-7

In this paper, interval-valued fuzzy planar graphs are defined and several properties are studied. The interval-valued fuzzy graphs are more efficient than fuzzy graphs, since the degree of membership of vertices and edges lie within the interval [0, 1] instead at a point in fuzzy graphs. We also use the term ‘degree of planarity’ to measures the nature of planarity of an interval-valued fuzzy graph. The other relevant terms such as strong edges, interval-valued fuzzy faces, strong interval-valued fuzzy faces are defined here. The interval-valued fuzzy dual graph which is closely associated to the interval-valued fuzzy planar graph is defined. Several properties of interval-valued fuzzy dual graph are also studied. An example of interval-valued fuzzy planar graph is given.