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Solving Fully Fuzzy Multi-Level Programming Problems using Various Fuzzy Numbers and Ranking Functions.

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Title: Solving Fully Fuzzy Multi-Level Programming Problems using Various Fuzzy Numbers and Ranking Functions.
Authors: Shinde, P. B.1 pandit.shinde@aissmsioit.org, Sen, Asit1 pbs26091988@gmail.com, Shelar, D. S.2 dilipsshelar@gmail.com
Source: IAENG International Journal of Computer Science. May2026, Vol. 53 Issue 5, p1911-1924. 14p.
Subjects: Fuzzy numbers, Decomposition method, Decision making, Fuzzy algorithms
Abstract: Multilevel decision-making problems frequently involve hierarchical decision-makers whose objectives are interdependent and influenced by uncertainty. Traditional deterministic multi-level programming formulations are inadequate for such environments because they fail to capture the imprecision, vagueness, and incomplete information inherent in real-world systems. This paper presents an integrated methodology for solving Fully Fuzzy Multi-Level Linear Programming (FFMLLP) problems using multiple fuzzy number representations and an enhanced ranking-based defuzzification approach. Triangular, trapezoidal, and Gaussian fuzzy numbers were employed to model different degrees of uncertainty across objectives, constraints, and decision variables. A hybrid ranking function combining centroid and spread measures is used to convert fuzzy information into crisp equivalents, enabling systematic comparison among different fuzzy representations. The bound-decomposition technique is applied to decompose the FFMLLP into manageable crisp subproblems while preserving the hierarchical decision relationships. Numerical experiments demonstrate that the proposed framework improves solution reliability, convergence behaviour, and computational efficiency compared with conventional fuzzy optimisation approaches. The proposed model serves as a unified, flexible, and robust decision-support tool that is suitable for complex engineering, economic, and management applications. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Computer Science is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Computer+Science%22">IAENG International Journal of Computer Science</searchLink>. May2026, Vol. 53 Issue 5, p1911-1924. 14p.
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  Data: Multilevel decision-making problems frequently involve hierarchical decision-makers whose objectives are interdependent and influenced by uncertainty. Traditional deterministic multi-level programming formulations are inadequate for such environments because they fail to capture the imprecision, vagueness, and incomplete information inherent in real-world systems. This paper presents an integrated methodology for solving Fully Fuzzy Multi-Level Linear Programming (FFMLLP) problems using multiple fuzzy number representations and an enhanced ranking-based defuzzification approach. Triangular, trapezoidal, and Gaussian fuzzy numbers were employed to model different degrees of uncertainty across objectives, constraints, and decision variables. A hybrid ranking function combining centroid and spread measures is used to convert fuzzy information into crisp equivalents, enabling systematic comparison among different fuzzy representations. The bound-decomposition technique is applied to decompose the FFMLLP into manageable crisp subproblems while preserving the hierarchical decision relationships. Numerical experiments demonstrate that the proposed framework improves solution reliability, convergence behaviour, and computational efficiency compared with conventional fuzzy optimisation approaches. The proposed model serves as a unified, flexible, and robust decision-support tool that is suitable for complex engineering, economic, and management applications. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of IAENG International Journal of Computer Science is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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        PageCount: 14
        StartPage: 1911
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        Type: general
      – SubjectFull: Decomposition method
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      – SubjectFull: Decision making
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              Text: May2026
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              Y: 2026
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