Valued-inverse Dombi neutrosophic graph and application

Mohammad Hamidi; Florentin Smarandache; Mohammad Hamidi; Florentin Smarandache

doi:10.3934/math.20231361

AIMS Mathematics

2023, Volume 8, Issue 11: 26614-26631. doi: 10.3934/math.20231361

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Valued-inverse Dombi neutrosophic graph and application

Mohammad Hamidi ^{1
,
,},
Florentin Smarandache ²

1.
Department of Mathematics, University of Payame Noor, Tehran, Iran
2.
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA

Received: 24 March 2023 Revised: 07 September 2023 Accepted: 11 September 2023 Published: 18 September 2023
MSC : 03E72, 05C72

Utilizing two ideas of neutrosophic subsets (NS) and triangular norms, we introduce a new type of graph as valued-inverse Dombi neutrosophic graphs. The valued-inverse Dombi neutrosophic graphs are a generalization of inverse neutrosophic graphs and are dual to Dombi neutrosophic graphs. We present the concepts of (complete) strong valued-inverse Dombi neutrosophic graphs and analyze the complement of (complete) strong valued-inverse Dombi neutrosophic graphs and self-valued complemented valued-inverse Dombi neutrosophic graphs. Since the valued-inverse Dombi neutrosophic graphs depend on real values, solving the non-equation and the concept of homomorphism play a prominent role in determining the complete, strong, complementarity and self-complementarity of valued-inverse Dombi neutrosophic graphs. We introduce the truth membership order, indeterminacy membership order, falsity membership order, truth membership size, indeterminacy membership size and indeterminacy membership size of any given valued-inverse Dombi neutrosophic graph, which play a major role in the application of valued inverse Dombi neutrosophic graphs in complex networks. An application of a valued-inverse Dombi neutrosophic graph is also described in this study.
- neutrosophic graph,
- Dombi triangular operator,
- inverse fuzzy graph,
- Dombi fuzzy graph,
- valued-Dombi inverse fuzzy graph
Citation: Mohammad Hamidi, Florentin Smarandache. Valued-inverse Dombi neutrosophic graph and application[J]. AIMS Mathematics, 2023, 8(11): 26614-26631. doi: 10.3934/math.20231361

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Abstract

Utilizing two ideas of neutrosophic subsets (NS) and triangular norms, we introduce a new type of graph as valued-inverse Dombi neutrosophic graphs. The valued-inverse Dombi neutrosophic graphs are a generalization of inverse neutrosophic graphs and are dual to Dombi neutrosophic graphs. We present the concepts of (complete) strong valued-inverse Dombi neutrosophic graphs and analyze the complement of (complete) strong valued-inverse Dombi neutrosophic graphs and self-valued complemented valued-inverse Dombi neutrosophic graphs. Since the valued-inverse Dombi neutrosophic graphs depend on real values, solving the non-equation and the concept of homomorphism play a prominent role in determining the complete, strong, complementarity and self-complementarity of valued-inverse Dombi neutrosophic graphs. We introduce the truth membership order, indeterminacy membership order, falsity membership order, truth membership size, indeterminacy membership size and indeterminacy membership size of any given valued-inverse Dombi neutrosophic graph, which play a major role in the application of valued inverse Dombi neutrosophic graphs in complex networks. An application of a valued-inverse Dombi neutrosophic graph is also described in this study.

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