Circular Intuitionistic Fuzzy Dombi Aggregation Operators and Their Application to Marine Fuel Selection

Higher-order fuzzy sets have emerged as effective tools for decision-making under uncertainty. Among these, the circular intuitionistic fuzzy set (CIFS) has recently been introduced to better represent uncertain information. In a CIFS, each element is modelled as a circular area defined by a radius,...

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Main Authors: Nuraini Rahim, Binyamin Yusoff, Lazim Abdullah, Dian Pratama
Format: Article
Language:English
Published: IEEE 2025-01-01
Series:IEEE Access
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Online Access:https://ieeexplore.ieee.org/document/11084800/
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author Nuraini Rahim
Binyamin Yusoff
Lazim Abdullah
Dian Pratama
author_facet Nuraini Rahim
Binyamin Yusoff
Lazim Abdullah
Dian Pratama
author_sort Nuraini Rahim
collection DOAJ
description Higher-order fuzzy sets have emerged as effective tools for decision-making under uncertainty. Among these, the circular intuitionistic fuzzy set (CIFS) has recently been introduced to better represent uncertain information. In a CIFS, each element is modelled as a circular area defined by a radius, with membership and non-membership degrees located at its center. Aggregation operators play a crucial role in synthesizing multiple inputs into representative ones. Among the well-known operators, Dombi operators, comprising the Dombi t-norm and t-conorm, offer significant flexibility due to their adjustable parameters. However, existing CIFS-based aggregation operators are typically defined for <inline-formula> <tex-math notation="LaTeX">$r \in [{0,1}]$ </tex-math></inline-formula>, which only partially covers the intuitionistic fuzzy interpretation triangle. This study extends Dombi aggregation operators to the full CIFS domain, <inline-formula> <tex-math notation="LaTeX">$r \in [0,\sqrt {2}]$ </tex-math></inline-formula> and examines their mathematical properties in accordance with fundamental algebraic laws. Specifically, we introduce the CIF Dombi Weighted Averaging, CIF Dombi Ordered Weighted Averaging, CIF Dombi Weighted Geometric, and CIF Dombi Ordered Weighted Geometric operators. In addition, existing score functions for ranking CIFS values do not adequately account for the influence of the radius, which should prioritize smaller r values due to their lower uncertainty. Therefore, we propose an alternative score function to improve the consistency and accuracy of CIFS value ranking. Based on these developments, a multi-criteria decision-making (MCDM) model is constructed within the CIFS environment. The model is applied to a real-world problem of marine fuel selection, demonstrating its practicality and robustness. Comparative and sensitivity analyses further validate the model&#x2019;s performance. The findings highlight the effectiveness of the proposed operators in enhancing decision-making under uncertainty, offering valuable insights for policymakers and stakeholders in the marine fuel sector.
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spelling doaj-art-ca5417f7cdac4bbbbef0339cbbf0db872025-08-20T03:13:55ZengIEEEIEEE Access2169-35362025-01-011312739112741010.1109/ACCESS.2025.359055011084800Circular Intuitionistic Fuzzy Dombi Aggregation Operators and Their Application to Marine Fuel SelectionNuraini Rahim0https://orcid.org/0000-0003-4421-795XBinyamin Yusoff1https://orcid.org/0000-0002-3899-1474Lazim Abdullah2https://orcid.org/0000-0002-6646-4751Dian Pratama3Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, Kuala Nerus, Terengganu, MalaysiaSpecial Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, Kuala Nerus, Terengganu, MalaysiaSpecial Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, Kuala Nerus, Terengganu, MalaysiaSpecial Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, Kuala Nerus, Terengganu, MalaysiaHigher-order fuzzy sets have emerged as effective tools for decision-making under uncertainty. Among these, the circular intuitionistic fuzzy set (CIFS) has recently been introduced to better represent uncertain information. In a CIFS, each element is modelled as a circular area defined by a radius, with membership and non-membership degrees located at its center. Aggregation operators play a crucial role in synthesizing multiple inputs into representative ones. Among the well-known operators, Dombi operators, comprising the Dombi t-norm and t-conorm, offer significant flexibility due to their adjustable parameters. However, existing CIFS-based aggregation operators are typically defined for <inline-formula> <tex-math notation="LaTeX">$r \in [{0,1}]$ </tex-math></inline-formula>, which only partially covers the intuitionistic fuzzy interpretation triangle. This study extends Dombi aggregation operators to the full CIFS domain, <inline-formula> <tex-math notation="LaTeX">$r \in [0,\sqrt {2}]$ </tex-math></inline-formula> and examines their mathematical properties in accordance with fundamental algebraic laws. Specifically, we introduce the CIF Dombi Weighted Averaging, CIF Dombi Ordered Weighted Averaging, CIF Dombi Weighted Geometric, and CIF Dombi Ordered Weighted Geometric operators. In addition, existing score functions for ranking CIFS values do not adequately account for the influence of the radius, which should prioritize smaller r values due to their lower uncertainty. Therefore, we propose an alternative score function to improve the consistency and accuracy of CIFS value ranking. Based on these developments, a multi-criteria decision-making (MCDM) model is constructed within the CIFS environment. The model is applied to a real-world problem of marine fuel selection, demonstrating its practicality and robustness. Comparative and sensitivity analyses further validate the model&#x2019;s performance. The findings highlight the effectiveness of the proposed operators in enhancing decision-making under uncertainty, offering valuable insights for policymakers and stakeholders in the marine fuel sector.https://ieeexplore.ieee.org/document/11084800/Aggregation operatorscircular intuitionistic fuzzy setDombi operationsmarine fuelmulti-criteria decision-making
spellingShingle Nuraini Rahim
Binyamin Yusoff
Lazim Abdullah
Dian Pratama
Circular Intuitionistic Fuzzy Dombi Aggregation Operators and Their Application to Marine Fuel Selection
IEEE Access
Aggregation operators
circular intuitionistic fuzzy set
Dombi operations
marine fuel
multi-criteria decision-making
title Circular Intuitionistic Fuzzy Dombi Aggregation Operators and Their Application to Marine Fuel Selection
title_full Circular Intuitionistic Fuzzy Dombi Aggregation Operators and Their Application to Marine Fuel Selection
title_fullStr Circular Intuitionistic Fuzzy Dombi Aggregation Operators and Their Application to Marine Fuel Selection
title_full_unstemmed Circular Intuitionistic Fuzzy Dombi Aggregation Operators and Their Application to Marine Fuel Selection
title_short Circular Intuitionistic Fuzzy Dombi Aggregation Operators and Their Application to Marine Fuel Selection
title_sort circular intuitionistic fuzzy dombi aggregation operators and their application to marine fuel selection
topic Aggregation operators
circular intuitionistic fuzzy set
Dombi operations
marine fuel
multi-criteria decision-making
url https://ieeexplore.ieee.org/document/11084800/
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AT binyaminyusoff circularintuitionisticfuzzydombiaggregationoperatorsandtheirapplicationtomarinefuelselection
AT lazimabdullah circularintuitionisticfuzzydombiaggregationoperatorsandtheirapplicationtomarinefuelselection
AT dianpratama circularintuitionisticfuzzydombiaggregationoperatorsandtheirapplicationtomarinefuelselection