Types of degrees in bipolar fuzzy graphs

Mohideen, Basheer Ahamed; Arabia, Saudi

doi:10.12988/ams.2013.37389

Cited by 4 publications

(1 citation statement)

References 8 publications

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“…In 1994, Zhang [ 5 ] incorporated the idea of bipolar fuzzy sets as a generalization of fuzzy sets to overcome the double-sided thinking nature of humans in decision making. As explored in [ 6 ], a bipolar fuzzy set is an extension of Zadeh’s fuzzy set theory whose membership degree range is [− 1, 1]. In a bipolar fuzzy set, the membership degree of 0 of an element means that the element is irrelevant to the corresponding property, the membership degree (0, 1] of an element represents what is considered possible to the corresponding property, and the membership degree [− 1, 0) represents what is considered impossible or somewhat satisfies the implicit counter property corresponding to a BFS [ 7 ].…”

Section: Introductionmentioning

confidence: 99%

Interval-valued bipolar fuzzy line graphs

2023

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Objectives The notion of Bipolarity based on positive and negative outcomes. It is well known that bipolar models give more precision, flexibility, and compatibility to the system as compared to the classical models and fuzzy models. A bipolar fuzzy graph(BFG) provides more flexibility while modeling human thinking as compared with a fuzzy graph, and an interval valued bipolar fuzzy graph(IVBFG) has numerous applications where the real-life problem are time dependent and there is a network structure complexity. The aim of this paper is to introduce an interval-valued bipolar line fuzzy graph(IVBFLG). Result In this paper, we have proposed the notion of an IVBFLG and some of its characterizations. Also, some propositions and theorems related to an IVIFLGs are developed and proved. Furthermore, isomorphism between two IVIFLGs toward their IVIFGs was determined and verified. As a result, we derive a necessary and sufficient condition for an IVBFG to be isomorphic to its corresponding IVBFLG and some remarkable properties like degree, size, order, regularity, strength, and completeness of an IVBFLGs have been investigated, and the proposed concepts are illustrated with the examples.

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Section: Introductionmentioning

confidence: 99%

Interval-valued bipolar fuzzy line graphs

2023

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Product of bipolar anti fuzzy graph and their degree of vertex

Rahayu

Sulandra

Kusumasari

2021

J. Phys.: Conf. Ser.

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Based on complete bipolar anti fuzzy graphs and on strong bipolar anti fuzzy graphs we can define a new graph through union, join, Cartesian product, and composition of such two graphs. We call the new graph as a product of graphs. In this article we investigate properties of product of bipolar anti fuzzy graphs and product of strong bipolar anti fuzzy graphs. We also construct the degree of a vertex in such the product, namely, the degree of a vertex in the graph which are obtained from product of two given bipolar anti fuzzy graph.

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