Decision-making Framework for Urban Transportation Using Linear Diophantine Fuzzy Z-numbers with Dombi Aggregation, TOPSIS and VIKOR Methods

Rukhshanda Anjum; Muhammad Umar Mirza; Nasreen Kausar; Rabia Ali

doi:10.31181/sor4155

Authors

Rukhshanda Anjum Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan Author https://orcid.org/0000-0001-8736-0006
Muhammad Umar Mirza Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan Author https://orcid.org/0000-0001-9525-7308
Nasreen Kausar Department of Mathematics, Faculty of Arts and Science, Balikesir University, 10145 Balikesir, Turkey Author https://orcid.org/0000-0002-8659-0747
Rabia Ali Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan Author https://orcid.org/0000-0002-6115-1166

DOI:

https://doi.org/10.31181/sor4155

Keywords:

Fuzzy numbers, Z-numbers, Linear Diaphantine fuzzy Z-numbers, Dombi operations, Aggregation operator, Multicriteria decision making algorithm, TOPSIS, VIKOR

Abstract

This study proposes an innovative approach to decision-making under uncertainty, using Pakistan’s urban transportation issues—particularly in cities like Karachi, Lahore, and Islamabad—as a case study. These cities face severe traffic congestion, demanding more effective strategies for infrastructure planning. We introduce a Linear Diophantine Fuzzy Z-Numbers (LDFZN) framework that captures membership and non-membership grades alongside the degree of reliability, addressing key limitations of traditional fuzzy systems by simultaneously considering uncertainty and confidence. Within this framework, we develop three decision-making methods: an LDFZN Dombi Weighted Averaging operator that aggregates expert opinions while accounting for their reliability; an adapted VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method for multi-criteria compromise solutions under LDFZN settings; and a modified Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) tailored for LDFZN-based scenarios. These tools are applied to real-world transportation challenges in Pakistan, demonstrating their effectiveness in managing uncertainty and expert-based confidence levels. The results outperform conventional models in decision robustness and clarity under uncertain conditions. This work contributes significantly to the theoretical and practical advancement of fuzzy mathematics, extending uncertainty modeling and providing practical solutions not only for transportation but also for various fields requiring informed decision-making with imprecise and unreliable data.

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