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Bipolar Fuzzy Sets and Bipolar Fuzzy Graphs
2020In this chapter, we first review the notion of bipolar fuzzy sets and present several basic concepts concerning bipolar fuzzy graphs and bipolar fuzzy digraphs. We discuss different methods of construction of bipolar fuzzy graphs and their isomorphism properties.
Muhammad Akram +2 more
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Note on “Bipolar fuzzy graphs with applications”
Knowledge-Based Systems, 2020Abstract In the paper, “Bipolar fuzzy graphs with applications” by Akram (2013), Definitions 3.2, 3.3, 3.4, 3.5, 4.3 and Theorem 3.16 contain some flaws. In this note, we show by examples that these definitions and theorem are not correct. The updated version of these definitions and theorem have been established in this paper with numerical examples.
Soumitra Poulik, Ganesh Ghorai
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f-morphism on bipolar fuzzy graphs
Journal of Intelligent & Fuzzy Systems, 2015The main purpose of this paper is to introduce the notion of bipolar f -morphism on bipolar fuzzy graphs and regular bipolar fuzzy graphs. We study the action of bipolar f -morphism on bipolar fuzzy graphs and derive some elegant results on weak and co ...
A. Tahmasbpour +2 more
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Product of bipolar fuzzy graphs and their degree
International Journal of General Systems, 2016The concepts of graph theory are applied in many areas of computer science including data mining, image segmentation, clustering, image capturing and networking. It is also known that lots of uncertainties occur in these areas. To handle the uncertainty that occurs in graph theory, fuzzy graph theory is successfully used in many problems.
Hossein Rashmanlou +3 more
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Information Sciences, 2011
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Cubic bipolar fuzzy graphs with applications
Journal of Intelligent & Fuzzy Systems, 2019Recently, Jun et al. have introduced the concept of cubic set as a generalization of the concept of fuzzy set and that of the interval valued fuzzy set. This concept has been widely applied in many circumstances like pattern recognition, decision making etc.
Naeem Jan +3 more
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2017
In 1994, Zhang (Proceedings of FUZZ-IEEE, 1998) [195], (Proceedings of IEEE conference, 1994) [71] introduced the concept of bipolar fuzzy sets as a generalization of the notion of Zadeh’s fuzzy sets. A bipolar fuzzy subset of a set is a pair of functions one from the set into the interval [0, 1] and the other into the interval \([-1,0].\) In a bipolar
Sunil Mathew +2 more
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In 1994, Zhang (Proceedings of FUZZ-IEEE, 1998) [195], (Proceedings of IEEE conference, 1994) [71] introduced the concept of bipolar fuzzy sets as a generalization of the notion of Zadeh’s fuzzy sets. A bipolar fuzzy subset of a set is a pair of functions one from the set into the interval [0, 1] and the other into the interval \([-1,0].\) In a bipolar
Sunil Mathew +2 more
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Inverse domination in bipolar fuzzy graphs
Materials Today: Proceedings, 2021Abstract In this paper, we bring together the idea of an inverse domination in bipolar fuzzy graphs (BFG). A set I ⊆ V is supposed to be an inverse dominating set IDS in BFG’s G ( V , E ) if D ⊆ V is a dominating set of G and I ⊆ ( V - D ) is a dominating set of V - D .
S. Kalaiselvan +2 more
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2020
In this chapter, we study the concepts of bipolar fuzzy multisets, bipolar fuzzy multigraphs, strong and complete bipolar fuzzy multigraphs, bipolar fuzzy planar graphs, and bipolar fuzzy dual graphs. We discuss different types of bipolar fuzzy edges, intersection value and planarity value of bipolar fuzzy graphs, strong and weak bipolar fuzzy faces ...
Muhammad Akram +2 more
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In this chapter, we study the concepts of bipolar fuzzy multisets, bipolar fuzzy multigraphs, strong and complete bipolar fuzzy multigraphs, bipolar fuzzy planar graphs, and bipolar fuzzy dual graphs. We discuss different types of bipolar fuzzy edges, intersection value and planarity value of bipolar fuzzy graphs, strong and weak bipolar fuzzy faces ...
Muhammad Akram +2 more
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Bipolar Fuzzy Competition Graphs
2020In this chapter, we discuss the concept of bipolar fuzzy competition graphs and present several notions concerning bipolar fuzzy out neighborhoods, bipolar fuzzy in neighborhoods, bipolar fuzzy open neighborhood graphs, bipolar fuzzy closed neighborhood graphs, bipolar fuzzy \(\textit{\textbf{k}}-\)competition graphs, and underlying bipolar fuzzy ...
Muhammad Akram +2 more
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