Arithmetic operations of intuitionistic Z numbers using horizontal membership functions

• Main Authors: Nik Muhammad Farhan Hakim, Nik Badrul Alam, Ku Muhammad Naim, Ku Khalif, Nor Izzati, Jaini
• Format: Conference or Workshop Item
• Language: English
• Published: Springer Nature 2022
• Subjects: QA Mathematics
• Online Access: http://umpir.ump.edu.my/id/eprint/35926/1/14.Arithmetic%20Operations%20of%20Intuitionistic%20Z%20Numbers%20Using%20Horizontal%20Membership%20Functions.pdf; http://umpir.ump.edu.my/id/eprint/35926/; https://link.springer.com/book/10.1007/978-3-031-00828-3
• Institution: Universiti Malaysia Pahang

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.