Transportation Problems Using Triangular Type-2 Intuitionistic Fuzzy Numbers

Amr Yousef; Muhammad Naveed Jafar; Zaffar Ahmed Shaikh

doi:10.48084/etasr.17041

Authors

Amr Yousef Electrical Engineering Department, University of Business and Technology, Jeddah, Saudi Arabia | Engineering Mathematics Department, Alexandria University, Alexandria, Egypt https://orcid.org/0000-0003-0875-6462
Muhammad Naveed Jafar Turon University, Karshi, Uzbekistan | International Engineering and Technology Institute, Hong Kong, China | Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Zaffar Ahmed Shaikh Department of Computer Science and Information Technology, Benazir Bhutto Shaheed University Lyari, Karachi, Pakistan | School of Engineering, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland https://orcid.org/0000-0003-0323-2061

Volume: 16 | Issue: 3 | Pages: 34907-34913 | June 2026 | https://doi.org/10.48084/etasr.17041

Received: 18 December 2025 | Revised: 2 March 2026 | Accepted: 19 March 2026 | Online: 4 April 2026

Corresponding author: Amr Yousef

Abstract

This study introduces the structure of normalized Triangular Type-2 Intuitionistic Fuzzy Numbers (TrT2IFNs), a relatively recent concept with strong potential to enhance the modeling and analysis of uncertainty. The study also presents basic arithmetic operations and ranking functions for these fuzzy parameters. The arithmetic operations are defined using the (α, β)-cut technique, where fuzzy numbers are decomposed into α- and β-level sets to enable systematic computation. In addition, a new ranking function is developed based on a mean interval approach, enabling effective comparison of these fuzzy numbers. To validate the proposed methods, a Transportation Problem (TP) is formulated, where cost parameters are represented by TrT2IFNs. The model is illustrated through numerical examples, and the results are analyzed. The findings show that the proposed approach addresses uncertainty in transportation problems more effectively than existing methods. Applying TrT2IFNs improves the representation of cost uncertainty, supporting better decision-making in logistics and supply chain optimization. The numerical results indicate reduced transportation costs compared to current approaches, demonstrating the practical value of the proposed framework in operations research under real-world uncertainty.

Keywords:

Intuitionistic Fuzzy Set (IFS), Triangular Type-2 Intuitionistic Fuzzy Number (TrT2IFN), Arithmetic Operations (AO), Ranking Function (RF), Transportation problem (TP)

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