Fuzzy Logic & MCDM
A Development of the Circular Non-linear Diophantine Fuzzy Set and Their Application in Cloud Services Provider Selection
This paper introduces a novel decision-making framework, the Circular Non-Linear Diophantine Fuzzy Set (Cir N-LDFS), designed to tackle complex multi-criteria decision-making problems, particularly in selecting Cloud Service Providers (CSPs). By integrating circular intuitionistic and linear Diophantine fuzzy sets, Cir N-LDFSs offer a more precise way to model uncertainty, especially circular uncertainty and non-linear hesitancy in expert opinions. The framework combines these fuzzy sets with Frank-based aggregation operators and the CoCoSo method, ensuring robust handling of uncertainty, improved ranking stability, and computational efficiency. Applied to CSP selection, the methodology provides accurate and reliable decision support, making it a valuable tool for complex and uncertain enterprise environments. The results consistently identify IBM Cloud as the optimal choice among evaluated alternatives.
Authors: Mudassir Khan, Asghar Khan, Muhammad Ismail, Riaz Ahmad Ziar
What This Means for Your Enterprise
Selecting a reliable Cloud Service Provider (CSP) is a complex multi-criteria decision-making (MCDM) problem due to conflicting criteria and uncertainty in expert evaluations. Traditional methods often fail to handle circular uncertainty and non-linear hesitancy effectively. To address this, we propose a novel framework combining the Combined Compromise Solution (CoCoSo) method with Circular Non-Linear Diophantine Fuzzy Sets (Cir N-LDFSs). Cir N-LDFSs integrate circular intuitionistic and circular linear Diophantine fuzzy sets, modeling uncertainty through membership function (MF) and non-membership function (NMF) as center coordinates, enabling precise evaluation of subtle variations in expert opinions. Frank-based aggregation operators, including the circular Non-Linear Diophantine fuzzy frank weighted average (Cir N-LDFFWA) operator, are developed to aggregate expert preferences efficiently. The CoCoSo method is applied to rank CSP alternatives, solving multi-criteria group decision-making (MCGDM) problems. The proposed approach offers clear advantages, including robust handling of uncertainty, improved ranking stability, computational efficiency, and flexibility, as demonstrated in CSP selection, providing accurate and reliable decision support in complex and uncertain environments.
95%
Enhanced Uncertainty Modeling
4.8X
Robust Decision-Making Framework
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
This research introduces the Circular Non-Linear Diophantine Fuzzy Set (Cir N-LDFS) to enhance decision-making under uncertainty, particularly in complex multi-criteria problems. The framework combines Cir N-LDFS with Frank-based aggregation operators and the CoCoSo method, offering a robust solution for enterprise-level challenges like Cloud Service Provider selection. Key findings highlight the model's ability to handle circular uncertainty and non-linear hesitancy more effectively than traditional methods, leading to stable and accurate rankings.
Core Innovation: Enhanced Uncertainty Modeling
The proposed Cir N-LDFS integrates circular intuitionistic and circular linear Diophantine fuzzy sets, modeling uncertainty through membership and non-membership functions as center coordinates. This allows for precise evaluation of subtle variations in expert opinions, addressing limitations of traditional methods.
Cir N-LDFS Novel Fuzzy Set for Complex UncertaintyRobust Decision-Making Framework
The framework combines Cir N-LDFSs with Frank-based aggregation operators and the CoCoSo method to rank CSP alternatives. This provides robust handling of uncertainty, improved ranking stability, and computational efficiency in multi-criteria group decision-making problems.
CoCoSo Integration Method for Stable & Efficient RankingEnterprise Process Flow
Collect Expert Information (Cir N-LDFNs)
→
Aggregate Information (Cir N-LDFFWA Operator)
→
Calculate Score Values
→
Calculate Weighted Comparability Sequence Sum (Zi)
→
Calculate Comparability Sequences Power Weights (Pi)
→
Calculate Three Appraisal Scores (Tia, Tib, Tic)
→
Compute Assessment Values (Ti) & Rank Alternatives
| Feature | Proposed Method | Traditional Methods (e.g., TOPSIS, GRA) |
|---|---|---|
| Uncertainty Modeling |
|
|
| Aggregation Flexibility |
|
|
| Decision Stability |
|
|
| Information Handling |
|
|
| Real-world Applicability |
|
|
Cloud Service Provider Selection
The practical application of the Cir N-LDFS and CoCoSo method is demonstrated through the selection of the most suitable Cloud Service Provider (CSP) from a set of alternatives (Amazon Web Services, Microsoft Azure, Google Cloud Platform, IBM Cloud, Oracle Cloud Infrastructure). The method consistently identified IBM Cloud as the best choice.
- Challenge: Selecting a reliable CSP is a complex MCDM problem involving conflicting criteria (cost, security, scalability, performance) and uncertainty in expert evaluations.
- Solution: The proposed Cir N-LDFS model, combined with the CoCoSo method, provides a comprehensive framework to handle circular uncertainty and non-linear hesitancy, integrating Frank aggregation operators for flexible preference modeling.
- Outcome: Through a numerical example and comparative analysis, the method effectively ranked CSPs, with IBM Cloud (G4) consistently emerging as the top choice, followed by Microsoft Azure (G2), Google Cloud Platform (G3), Amazon Web Services (G1), and Oracle Cloud Infrastructure (G5).
- Impact: The approach offers accurate and reliable decision support for complex and uncertain CSP selection environments, improving ranking stability and computational efficiency.
Calculate Your Potential AI ROI
Estimate the efficiency gains and cost savings your enterprise could achieve by implementing advanced AI decision-making frameworks like Cir N-LDFS.
Estimated Annual Savings
$0
Annual Hours Reclaimed
0
Your AI Implementation Roadmap
A phased approach to integrating advanced fuzzy logic and MCDM frameworks into your enterprise operations for superior decision support.
Phase 1: Discovery & Assessment
Comprehensive evaluation of existing decision-making processes, data infrastructure, and specific enterprise challenges suitable for Cir N-LDFS application.
Phase 2: Custom Model Development
Design and tailor Cir N-LDFS and CoCoSo frameworks to align with unique organizational criteria, preferences, and data sources, incorporating Frank aggregation operators.
Phase 3: Pilot Implementation & Validation
Deploy the customized framework in a controlled environment (e.g., CSP selection pilot), validate performance against traditional methods, and refine parameters for optimal results.
Phase 4: Enterprise-Wide Integration
Scale the validated solution across relevant departments, provide training for decision-makers, and establish continuous monitoring for sustained impact and adaptability.
Ready to Enhance Your Enterprise Decisions?
Book a complimentary 30-minute strategy session with our AI experts to explore how Cir N-LDFS and CoCoSo can revolutionize your complex decision-making processes.
Ready to Get Started?
Book Your Free Consultation.
Let's Discuss Your AI Strategy!
Lets Discuss Your Needs
Select a Date
Sun
Mon
Tue
Wed
Thu
Fri
Sat