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...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/38326/ http://psasir.upm.edu.my/id/eprint/38326/1/38326.pdf |
| _version_ | 1848848848912384000 |
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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. |
| first_indexed | 2025-11-15T09:41:02Z |
| format | Article |
| id | upm-38326 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:41:02Z |
| publishDate | 2019 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |