Arithmetic operations of intuitionistic Z numbers using horizontal membership functions
An intuitionistic Z-number (IZN) is an integration of an intuitionistic fuzzy number with a Z-number. The IZN composes of two components; restriction and reliability components, which are represented by the membership and non-membership degrees to indicate the hesitancy. The objective of this paper...
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| Format: | Conference or Workshop Item |
| Language: | English |
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Springer Nature
2022
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| Online Access: | http://umpir.ump.edu.my/id/eprint/35926/ http://umpir.ump.edu.my/id/eprint/35926/1/14.Arithmetic%20Operations%20of%20Intuitionistic%20Z%20Numbers%20Using%20Horizontal%20Membership%20Functions.pdf |
| _version_ | 1848824906118070272 |
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| author | Nik Muhammad Farhan Hakim, Nik Badrul Alam Ku Muhammad Naim, Ku Khalif Nor Izzati, Jaini |
| author_facet | Nik Muhammad Farhan Hakim, Nik Badrul Alam Ku Muhammad Naim, Ku Khalif Nor Izzati, Jaini |
| author_sort | Nik Muhammad Farhan Hakim, Nik Badrul Alam |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | An intuitionistic Z-number (IZN) is an integration of an intuitionistic fuzzy number with a Z-number. The IZN composes of two components; restriction and reliability components, which are represented by the membership and non-membership degrees to indicate the hesitancy. The objective of this paper is to propose new arithmetic operations of IZN using the horizontal membership functions, which are closely related the concept of the relative distance measure. For that reason, the addition, subtraction, multiplication and division on normal trapezoidal IZNs are considered. The proposed operations preserve the arithmetic operations over real numbers and the original IZN-based information, avoiding any significant loss of information. The implementation of the bandwidth method in deriving the operations has reduced the computational complexity on IZN. In the future, aggregation operators of IZN can be derived using the proposed arithmetic operations. |
| first_indexed | 2025-11-15T03:20:28Z |
| format | Conference or Workshop Item |
| id | ump-35926 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T03:20:28Z |
| publishDate | 2022 |
| publisher | Springer Nature |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-359262022-12-15T03:54:44Z http://umpir.ump.edu.my/id/eprint/35926/ Arithmetic operations of intuitionistic Z numbers using horizontal membership functions Nik Muhammad Farhan Hakim, Nik Badrul Alam Ku Muhammad Naim, Ku Khalif Nor Izzati, Jaini QA Mathematics An intuitionistic Z-number (IZN) is an integration of an intuitionistic fuzzy number with a Z-number. The IZN composes of two components; restriction and reliability components, which are represented by the membership and non-membership degrees to indicate the hesitancy. The objective of this paper is to propose new arithmetic operations of IZN using the horizontal membership functions, which are closely related the concept of the relative distance measure. For that reason, the addition, subtraction, multiplication and division on normal trapezoidal IZNs are considered. The proposed operations preserve the arithmetic operations over real numbers and the original IZN-based information, avoiding any significant loss of information. The implementation of the bandwidth method in deriving the operations has reduced the computational complexity on IZN. In the future, aggregation operators of IZN can be derived using the proposed arithmetic operations. Springer Nature 2022-05-04 Conference or Workshop Item PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/35926/1/14.Arithmetic%20Operations%20of%20Intuitionistic%20Z%20Numbers%20Using%20Horizontal%20Membership%20Functions.pdf Nik Muhammad Farhan Hakim, Nik Badrul Alam and Ku Muhammad Naim, Ku Khalif and Nor Izzati, Jaini (2022) Arithmetic operations of intuitionistic Z numbers using horizontal membership functions. In: International Conference on Soft Computing and Data Mining; Fifth International Conference on Soft Computing and Data Mining (SCDM-2022) , May 30-31, 2022 . pp. 25-34., 1. ISBN 978-3-031-00827-6 (Published) https://link.springer.com/book/10.1007/978-3-031-00828-3 |
| spellingShingle | QA Mathematics Nik Muhammad Farhan Hakim, Nik Badrul Alam Ku Muhammad Naim, Ku Khalif Nor Izzati, Jaini Arithmetic operations of intuitionistic Z numbers using horizontal membership functions |
| title | Arithmetic operations of intuitionistic Z numbers using horizontal membership functions |
| title_full | Arithmetic operations of intuitionistic Z numbers using horizontal membership functions |
| title_fullStr | Arithmetic operations of intuitionistic Z numbers using horizontal membership functions |
| title_full_unstemmed | Arithmetic operations of intuitionistic Z numbers using horizontal membership functions |
| title_short | Arithmetic operations of intuitionistic Z numbers using horizontal membership functions |
| title_sort | arithmetic operations of intuitionistic z numbers using horizontal membership functions |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/35926/ http://umpir.ump.edu.my/id/eprint/35926/ http://umpir.ump.edu.my/id/eprint/35926/1/14.Arithmetic%20Operations%20of%20Intuitionistic%20Z%20Numbers%20Using%20Horizontal%20Membership%20Functions.pdf |