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Properties of Interval-Valued Neutrosophic Graphs

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Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 369))

Abstract

Recently, the properties of neutrosophic graph are introduced for handling uncertainty and vagueness in attributes. In this process a problem arises when the partial ignorance exists in the data sets for the given interval [0, 1]. To deal with this problem, current chapter introduces notion of interval-valued neutrosophic sets as a generalization of intuitionistic fuzzy sets, interval-valued fuzzy sets, interval-valued intuitionistic fuzzy sets and single valued neutrosophic sets. Further, the graphical structure visualization of given interval-valued neutrosophic sets as an instance of neutrosophic sets and graph theory are also established. In addition, certain types of interval-valued neutrosophic graphs (IVNG) and their properties are introduced with the proofs. Each of the established properties is illustrated with an example in this chapter.

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Acknowledgements

Author thanks the anonymous reviewers and the editor for providing useful comments and suggestions to improve the quality of this chapter.

Author information

Authors and Affiliations

  1. Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, B.P 7955, Sidi Othman, Casablanca, Morocco

    Said Broumi & Mohamed Talea

  2. Ecole Royale Navale-Boulevard Sour Jdid, B.P 16303, Casablanca, Morocco

    Assia Bakali

  3. Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM, 87301, USA

    Florentin Smarandache

  4. Amity Institute of Information Technology and Engineering, Amity University, Noida, 201313, Uttar Pradesh, India

    Prem Kumar Singh

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  1. Said Broumi
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  2. Assia Bakali
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  4. Florentin Smarandache
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  5. Prem Kumar Singh
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Correspondence to Said Broumi .

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Editors and Affiliations

  1. Department of Industrial Engineering, Istanbul Technical University, Macka, Istanbul, Turkey

    Cengiz Kahraman

  2. Department of Industrial Engineering, Istanbul Okan University, Akfirat-Tuzla, Istanbul, Turkey

    İrem Otay

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Broumi, S., Bakali, A., Talea, M., Smarandache, F., Singh, P.K. (2019). Properties of Interval-Valued Neutrosophic Graphs. In: Kahraman, C., Otay, İ. (eds) Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets. Studies in Fuzziness and Soft Computing, vol 369. Springer, Cham. https://doi.org/10.1007/978-3-030-00045-5_8

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