Complex linear Diophantine fuzzy Dombi prioritized operators-based MULTIMOORA approach with applications to sustainable energy planning

Abstract Sustainable energy planning is a critical challenge, particularly in regions with complex decision-making environments and uncertain data. The selection of an optimal energy source requires robust methodologies that can effectively handle multi-criteria decision-making (MCDM) under uncertai...

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Main Authors: Abdul Wahab Mustafa, Zia Bashir, Jawad Ali, Muhammed I. Syam
Format: Article
Language:English
Published: Nature Portfolio 2025-08-01
Series:Scientific Reports
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Online Access:https://doi.org/10.1038/s41598-025-05710-w
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author Abdul Wahab Mustafa
Zia Bashir
Jawad Ali
Muhammed I. Syam
author_facet Abdul Wahab Mustafa
Zia Bashir
Jawad Ali
Muhammed I. Syam
author_sort Abdul Wahab Mustafa
collection DOAJ
description Abstract Sustainable energy planning is a critical challenge, particularly in regions with complex decision-making environments and uncertain data. The selection of an optimal energy source requires robust methodologies that can effectively handle multi-criteria decision-making (MCDM) under uncertainty. This study explores the application of the multiple objective optimization on the basis of ratio analysis plus full multiplicative form (MULTIMOORA) method by incorporating the concept of the complex linear Diophantine fuzzy ( $$C_pLD_yF$$ ) set. The $$C_pLD_yF$$ set extends the conventional linear Diophantine fuzzy set by introducing a phase component, thereby enhancing the system’s adaptability. To examine the interrelationships among multiple $$C_pLD_yF$$ numbers, we develop the $$C_pLD_yF$$ Dombi prioritized averaging ( $$C_pLD_yFDPA$$ ) and the $$C_pLD_yF$$ Dombi prioritized geometric ( $$C_pLD_yFDPG$$ ) aggregation operators, along with their weighted versions, based on the proposed Dombi operational laws. The fundamental properties of these aggregation operators are systematically analyzed. The developed $$C_pLD_yF$$ operators are then integrated into the MULTIMOORA method to address MCDM problems. To illustrate the practical effectiveness of the proposed framework, a case study is conducted to determine a sustainable energy source for Gwadar, Pakistan, utilizing $$C_pLD_yF$$ information. Furthermore, comparative analyses are performed against existing methodologies to validate the applicability and accuracy of the proposed approach.
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spelling doaj-art-3a19948e074c4d2d817e1c2eba8682a12025-08-20T03:45:59ZengNature PortfolioScientific Reports2045-23222025-08-0115113610.1038/s41598-025-05710-wComplex linear Diophantine fuzzy Dombi prioritized operators-based MULTIMOORA approach with applications to sustainable energy planningAbdul Wahab Mustafa0Zia Bashir1Jawad Ali2Muhammed I. Syam3Department of Mathematics, Quaid-i-Azam UniversityDepartment of Mathematics, Quaid-i-Azam UniversityInstitute of Numerical Sciences, Kohat University of Science and TechnologyDepartment of Mathematical Sciences, United Arab Emirates UniversityAbstract Sustainable energy planning is a critical challenge, particularly in regions with complex decision-making environments and uncertain data. The selection of an optimal energy source requires robust methodologies that can effectively handle multi-criteria decision-making (MCDM) under uncertainty. This study explores the application of the multiple objective optimization on the basis of ratio analysis plus full multiplicative form (MULTIMOORA) method by incorporating the concept of the complex linear Diophantine fuzzy ( $$C_pLD_yF$$ ) set. The $$C_pLD_yF$$ set extends the conventional linear Diophantine fuzzy set by introducing a phase component, thereby enhancing the system’s adaptability. To examine the interrelationships among multiple $$C_pLD_yF$$ numbers, we develop the $$C_pLD_yF$$ Dombi prioritized averaging ( $$C_pLD_yFDPA$$ ) and the $$C_pLD_yF$$ Dombi prioritized geometric ( $$C_pLD_yFDPG$$ ) aggregation operators, along with their weighted versions, based on the proposed Dombi operational laws. The fundamental properties of these aggregation operators are systematically analyzed. The developed $$C_pLD_yF$$ operators are then integrated into the MULTIMOORA method to address MCDM problems. To illustrate the practical effectiveness of the proposed framework, a case study is conducted to determine a sustainable energy source for Gwadar, Pakistan, utilizing $$C_pLD_yF$$ information. Furthermore, comparative analyses are performed against existing methodologies to validate the applicability and accuracy of the proposed approach.https://doi.org/10.1038/s41598-025-05710-wComplex linear Diophantine fuzzy setDombi operationsPrioritized operatorsSustainable energy sourceDecision-makingMULTIMOORA method
spellingShingle Abdul Wahab Mustafa
Zia Bashir
Jawad Ali
Muhammed I. Syam
Complex linear Diophantine fuzzy Dombi prioritized operators-based MULTIMOORA approach with applications to sustainable energy planning
Scientific Reports
Complex linear Diophantine fuzzy set
Dombi operations
Prioritized operators
Sustainable energy source
Decision-making
MULTIMOORA method
title Complex linear Diophantine fuzzy Dombi prioritized operators-based MULTIMOORA approach with applications to sustainable energy planning
title_full Complex linear Diophantine fuzzy Dombi prioritized operators-based MULTIMOORA approach with applications to sustainable energy planning
title_fullStr Complex linear Diophantine fuzzy Dombi prioritized operators-based MULTIMOORA approach with applications to sustainable energy planning
title_full_unstemmed Complex linear Diophantine fuzzy Dombi prioritized operators-based MULTIMOORA approach with applications to sustainable energy planning
title_short Complex linear Diophantine fuzzy Dombi prioritized operators-based MULTIMOORA approach with applications to sustainable energy planning
title_sort complex linear diophantine fuzzy dombi prioritized operators based multimoora approach with applications to sustainable energy planning
topic Complex linear Diophantine fuzzy set
Dombi operations
Prioritized operators
Sustainable energy source
Decision-making
MULTIMOORA method
url https://doi.org/10.1038/s41598-025-05710-w
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