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Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets pp 603–622Cite as

Multiple Attribute Projection Methods with Neutrosophic Sets

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

Abstract

Projection measure (PM) is an appropriate method for dealing with multiple attribute decision making (MADM) problems since they can contain the distance and included angle between objects evaluated. Then, the simplified neutrosophic set (SNS) includes the information of single-valued neutrosophic set (SVNS) and interval neutrosophic set (INS) as a sub-class of a neutrosophic set, which can be used for real science and engineering fields under incomplete, indeterminate, and inconsistent environments. First, the general PM and bidirectional PM were presented between two SNSs (SVNSs and INSs), and then a harmonic averaging PM of SNSs was further introduced based on two (bidirectional) projections . Further, MADM methods were provided based on the general PM , bidirectional PM, and harmonic averaging PM in the simplified neutrosophic setting. In the introduced multiple attribute projection methods , the ranking order of all alternatives and the best alternative can be efficiently identified by these PMs between the ideal solution (the ideal alternative) and each alternative in MADM problems with simplified neutrosophic information . Finally, the effectiveness and applicability of these multiple attribute PMs were demonstrated by two numerical examples. The contribution of the chapter is that the three kinds of simplified neutrosophic PM methods are proposed and used for simplified neutrosophic MADM problems.

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Author information

Authors and Affiliations

  1. Center of Rock Mechanics and Geohazards, Shaoxing University, 508 Huancheng West Road, Shaoxing, 312000, Zhejiang Province, People’s Republic of China

    Rui Yong & Jun Ye

  2. Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, 312000, Zhejiang Province, People’s Republic of China

    Jun Ye

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  1. Rui Yong
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  2. Jun Ye
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Correspondence to Jun Ye .

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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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Yong, R., Ye, J. (2019). Multiple Attribute Projection Methods with Neutrosophic Sets. 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_23

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