Disjunctive representation of triangular bipolar neutrosophic numbers, de-bipolarization technique and application in multi-criteria decision-making problems

This research paper adds to the theory of the generalized neutrosophic number from a distinctive frame of reference. It is universally known that the concept of a neutrosophic number is generally associated with and strongly related to the concept of positive, indeterminacy and non-belongingness mem...

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Main Authors: Chakraborty, Avishek, Mondal, Sankar Prasad, Alam, Shariful, Hosseini, Seyedali Ahmadian, Senu, Norazak, De, Debashis, Salahshour, Soheil
Format: Article
Language:English
Published: MDPI 2019
Online Access:http://psasir.upm.edu.my/id/eprint/38326/
http://psasir.upm.edu.my/id/eprint/38326/1/38326.pdf
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author Chakraborty, Avishek
Mondal, Sankar Prasad
Alam, Shariful
Hosseini, Seyedali Ahmadian
Senu, Norazak
De, Debashis
Salahshour, Soheil
author_facet Chakraborty, Avishek
Mondal, Sankar Prasad
Alam, Shariful
Hosseini, Seyedali Ahmadian
Senu, Norazak
De, Debashis
Salahshour, Soheil
author_sort Chakraborty, Avishek
building UPM Institutional Repository
collection Online Access
description This research paper adds to the theory of the generalized neutrosophic number from a distinctive frame of reference. It is universally known that the concept of a neutrosophic number is generally associated with and strongly related to the concept of positive, indeterminacy and non-belongingness membership functions. Currently, all membership functions always lie within the range of 0 to 1. However, we have generated bipolar concept in this paper where the membership contains both positive and negative parts within the range −1 to 0 and 0 to 1. We describe different structures of generalized triangular bipolar neutrosophic numbers, such as category-1, category-2, and category-3, in relation to the membership functions containing dependency or independency with each other. Researchers from different fields always want to observe the co-relationship and interdependence between fuzzy numbers and crisp numbers. In this platform, we also created the perception of de-bipolarization for a triangular bipolar rneutrosophic number with the help of well-known techniques so that any bipolar neutrosophic fuzzy number of any type can be smoothly converted into a real number instantly. Creating a problem using bipolar neutrosophic perception is a more reliable, accurate, and trustworthy method than others. In this paper, we have also taken into account a multi-criteria decision-making problem (MCDM) for different users in the bipolar neutrosophic domain.
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institution Universiti Putra Malaysia
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spelling upm-383262020-05-04T16:17:40Z http://psasir.upm.edu.my/id/eprint/38326/ Disjunctive representation of triangular bipolar neutrosophic numbers, de-bipolarization technique and application in multi-criteria decision-making problems Chakraborty, Avishek Mondal, Sankar Prasad Alam, Shariful Hosseini, Seyedali Ahmadian Senu, Norazak De, Debashis Salahshour, Soheil This research paper adds to the theory of the generalized neutrosophic number from a distinctive frame of reference. It is universally known that the concept of a neutrosophic number is generally associated with and strongly related to the concept of positive, indeterminacy and non-belongingness membership functions. Currently, all membership functions always lie within the range of 0 to 1. However, we have generated bipolar concept in this paper where the membership contains both positive and negative parts within the range −1 to 0 and 0 to 1. We describe different structures of generalized triangular bipolar neutrosophic numbers, such as category-1, category-2, and category-3, in relation to the membership functions containing dependency or independency with each other. Researchers from different fields always want to observe the co-relationship and interdependence between fuzzy numbers and crisp numbers. In this platform, we also created the perception of de-bipolarization for a triangular bipolar rneutrosophic number with the help of well-known techniques so that any bipolar neutrosophic fuzzy number of any type can be smoothly converted into a real number instantly. Creating a problem using bipolar neutrosophic perception is a more reliable, accurate, and trustworthy method than others. In this paper, we have also taken into account a multi-criteria decision-making problem (MCDM) for different users in the bipolar neutrosophic domain. MDPI 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/38326/1/38326.pdf Chakraborty, Avishek and Mondal, Sankar Prasad and Alam, Shariful and Hosseini, Seyedali Ahmadian and Senu, Norazak and De, Debashis and Salahshour, Soheil (2019) Disjunctive representation of triangular bipolar neutrosophic numbers, de-bipolarization technique and application in multi-criteria decision-making problems. Symmetry, 11 (7). art. no. 932. pp. 1-20. ISSN 2073-8994 https://www.mdpi.com/2073-8994/11/7/932 10.3390/sym11070932
spellingShingle Chakraborty, Avishek
Mondal, Sankar Prasad
Alam, Shariful
Hosseini, Seyedali Ahmadian
Senu, Norazak
De, Debashis
Salahshour, Soheil
Disjunctive representation of triangular bipolar neutrosophic numbers, de-bipolarization technique and application in multi-criteria decision-making problems
title Disjunctive representation of triangular bipolar neutrosophic numbers, de-bipolarization technique and application in multi-criteria decision-making problems
title_full Disjunctive representation of triangular bipolar neutrosophic numbers, de-bipolarization technique and application in multi-criteria decision-making problems
title_fullStr Disjunctive representation of triangular bipolar neutrosophic numbers, de-bipolarization technique and application in multi-criteria decision-making problems
title_full_unstemmed Disjunctive representation of triangular bipolar neutrosophic numbers, de-bipolarization technique and application in multi-criteria decision-making problems
title_short Disjunctive representation of triangular bipolar neutrosophic numbers, de-bipolarization technique and application in multi-criteria decision-making problems
title_sort disjunctive representation of triangular bipolar neutrosophic numbers, de-bipolarization technique and application in multi-criteria decision-making problems
url http://psasir.upm.edu.my/id/eprint/38326/
http://psasir.upm.edu.my/id/eprint/38326/
http://psasir.upm.edu.my/id/eprint/38326/
http://psasir.upm.edu.my/id/eprint/38326/1/38326.pdf