Due to rapid urbanization, more cities are having severe issues. These include rising pollution, inadequate transportation, and high traffic. Local governments are building ecologically friendly transportation networks to address these issues. This program aims to create ecologically friendly, innovative cities while solving urban concerns. However, deciding on such a significant endeavor takes time and effort. Smart city planners must consider several criteria to choose a sustainable transportation system that meets the city’s needs. Multi-criteria decision-making (MCDM) is an advanced method that assists in analyzing and solving complex decision-making problems like this. It uses a structured process to evaluate multiple criteria. In recent years, Q-rung orthopair fuzzy sets (Q-ROFS) have become widely used in solving multi-criteria decision-making (MCDM) problems, particularly due to their ability to accurately reflect the perspectives of decision-makers (DMs). Recently, the development of Q-Rung orthopair Z-numbers has further simplified the resolution of MCDM problems. This study introduces innovative m, n-rung orthopair Z-numbers (m, n-ROZN) to tackle these problems. Additionally, we have specifically designed foundational operations to assimilate these fuzzy sets into the new framework effectively. Further, a novel scoring and accuracy mechanism has been implemented to rank the defined m, n-ROZN. To address MCDM problems using the m, n-ROZN, we have developed a series of averaging and geometric operators, namely the m, n-orthopair weighted averaging operator (m, n-WA operator), the m, n-orthopair ordered weighted averaging operator (m, n-OWA operator), the m, n-orthopair weighted geometric operator (m, n-WG operator), and the m, n-orthopair ordered weighted geometric operator (m, n-OWG operator). Furthermore, we have proved the basic desired properties for any aggregation operator, such as idempotency, monotonicity, and boundedness. We also propose a novel MCDM approach that leverages the advantageous features of these Z-numbers. To illustrate the efficacy of the suggested MCDM approach, we executed a case study involving the selection of a transit system that effectively mitigates the issue of traffic pollution. Furthermore, sensitivity and comparative analyses have been conducted on the relevant parameters to validate the stability of the acquired results.

On m, n-rung orthopair Z-numbers and its application to design a transport system for a smart city

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发表日期：

2025年9月23日

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Manish Kumar,
S. K. Gupta

摘要

Due to rapid urbanization, more cities are having severe issues. These include rising pollution, inadequate transportation, and high traffic. Local governments are building ecologically friendly transportation networks to address these issues. This program aims to create ecologically friendly, innovative cities while solving urban concerns. However, deciding on such a significant endeavor takes time and effort. Smart city planners must consider several criteria to choose a sustainable transportation system that meets the city’s needs. Multi-criteria decision-making (MCDM) is an advanced method that assists in analyzing and solving complex decision-making problems like this. It uses a structured process to evaluate multiple criteria. In recent years, Q-rung orthopair fuzzy sets (Q-ROFS) have become widely used in solving multi-criteria decision-making (MCDM) problems, particularly due to their ability to accurately reflect the perspectives of decision-makers (DMs). Recently, the development of Q-Rung orthopair Z-numbers has further simplified the resolution of MCDM problems. This study introduces innovative m, n-rung orthopair Z-numbers (m, n-ROZN) to tackle these problems. Additionally, we have specifically designed foundational operations to assimilate these fuzzy sets into the new framework effectively. Further, a novel scoring and accuracy mechanism has been implemented to rank the defined m, n-ROZN. To address MCDM problems using the m, n-ROZN, we have developed a series of averaging and geometric operators, namely the m, n-orthopair weighted averaging operator (m, n-WA operator), the m, n-orthopair ordered weighted averaging operator (m, n-OWA operator), the m, n-orthopair weighted geometric operator (m, n-WG operator), and the m, n-orthopair ordered weighted geometric operator (m, n-OWG operator). Furthermore, we have proved the basic desired properties for any aggregation operator, such as idempotency, monotonicity, and boundedness. We also propose a novel MCDM approach that leverages the advantageous features of these Z-numbers. To illustrate the efficacy of the suggested MCDM approach, we executed a case study involving the selection of a transit system that effectively mitigates the issue of traffic pollution. Furthermore, sensitivity and comparative analyses have been conducted on the relevant parameters to validate the stability of the acquired results.