Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications

Chakraborty, Avishek; Mondal, Sankar Prasad; Ahmadian, Ali; Senu, Norazak; Alam, Shariful; Salahshour, Soheil

doi:10.3390/sym10080327

Open AccessArticle

Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications

by

Avishek Chakraborty

^1,2,

Sankar Prasad Mondal

³

,

Ali Ahmadian

^4,*,

Norazak Senu

⁴,

Shariful Alam

⁵ and

Soheil Salahshour

²

¹

Department of Basic Science, Narula Institute of Technology, Agarpara, Kolkata 700109, India

²

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India

³

Department of Mathematics, Midnapore College (Autonomous), Midnapore, West Midnapore 721101, India

⁴

Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research, University Putra Malaysia, Serdang 43400 UPM, Malaysia

⁵

Young Researchers and Elite Club, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Iran

^*

Author to whom correspondence should be addressed.

Symmetry 2018, 10(8), 327; https://doi.org/10.3390/sym10080327

Submission received: 10 June 2018 / Revised: 28 June 2018 / Accepted: 3 July 2018 / Published: 7 August 2018

(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)

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Abstract

In this paper, we introduce the concept of neutrosophic number from different viewpoints. We define different types of linear and non-linear generalized triangular neutrosophic numbers which are very important for uncertainty theory. We introduced the de-neutrosophication concept for neutrosophic number for triangular neutrosophic numbers. This concept helps us to convert a neutrosophic number into a crisp number. The concepts are followed by two application, namely in imprecise project evaluation review technique and route selection problem.

Keywords: linear and non-linear neutrosophic number; de-neutrosophication methods

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MDPI and ACS Style

Chakraborty, A.; Mondal, S.P.; Ahmadian, A.; Senu, N.; Alam, S.; Salahshour, S. Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications. Symmetry 2018, 10, 327. https://doi.org/10.3390/sym10080327

AMA Style

Chakraborty A, Mondal SP, Ahmadian A, Senu N, Alam S, Salahshour S. Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications. Symmetry. 2018; 10(8):327. https://doi.org/10.3390/sym10080327

Chicago/Turabian Style

Chakraborty, Avishek, Sankar Prasad Mondal, Ali Ahmadian, Norazak Senu, Shariful Alam, and Soheil Salahshour. 2018. "Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications" Symmetry 10, no. 8: 327. https://doi.org/10.3390/sym10080327

APA Style

Chakraborty, A., Mondal, S. P., Ahmadian, A., Senu, N., Alam, S., & Salahshour, S. (2018). Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications. Symmetry, 10(8), 327. https://doi.org/10.3390/sym10080327

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications

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