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New Ranking Approach for Solving Hexagonal Type Fuzzy Assignment Problems Using Branch and Bound Technique.

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Title: New Ranking Approach for Solving Hexagonal Type Fuzzy Assignment Problems Using Branch and Bound Technique.
Authors: Singh, Guman1 guman.202505033@muj.manipal.edu, Rizwanullah, Mohammad2 mohd.rizwanullah@jaipur.manipal.edu, Yadav, Jay Chandra1 jayc.yadav@gmail.com
Source: IAENG International Journal of Applied Mathematics. Feb2026, Vol. 56 Issue 2, p491-495. 5p.
Subjects: Assignment problems (Programming), Fuzzy numbers, Optimization algorithms, Resource allocation, Scheduling
Abstract: The assignment problem (AP) appears in various forms within optimization and graph theory. By modifying certain constraints and incorporating additional ones, the problem can be transformed into routing, distribution, or scheduling challenges. This study applies the branch and bound (BB) method to two types of fuzzy assignment problems (FAP). The first problem deals with costs represented by hexagonal fuzzy numbers, while the second focuses on time, using pentagonal fuzzy numbers. A new ranking approach is introduced to rank these fuzzy numbers. After converting the fuzzy assignment problems into crisp form, they are solved using branch and bound approach. To handle fuzzy assignment problems with qualitative data, linguistic variables are used to translate qualitative information into quantitative data. This approach can apply to practical scenarios like task scheduling, resource allocation and routing problems where uncertainty in costs or times is prevalent. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics 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: New Ranking Approach for Solving Hexagonal Type Fuzzy Assignment Problems Using Branch and Bound Technique.
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Feb2026, Vol. 56 Issue 2, p491-495. 5p.
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  Data: <searchLink fieldCode="DE" term="%22Assignment+problems+%28Programming%29%22">Assignment problems (Programming)</searchLink><br /><searchLink fieldCode="DE" term="%22Fuzzy+numbers%22">Fuzzy numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Resource+allocation%22">Resource allocation</searchLink><br /><searchLink fieldCode="DE" term="%22Scheduling%22">Scheduling</searchLink>
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  Label: Abstract
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  Data: The assignment problem (AP) appears in various forms within optimization and graph theory. By modifying certain constraints and incorporating additional ones, the problem can be transformed into routing, distribution, or scheduling challenges. This study applies the branch and bound (BB) method to two types of fuzzy assignment problems (FAP). The first problem deals with costs represented by hexagonal fuzzy numbers, while the second focuses on time, using pentagonal fuzzy numbers. A new ranking approach is introduced to rank these fuzzy numbers. After converting the fuzzy assignment problems into crisp form, they are solved using branch and bound approach. To handle fuzzy assignment problems with qualitative data, linguistic variables are used to translate qualitative information into quantitative data. This approach can apply to practical scenarios like task scheduling, resource allocation and routing problems where uncertainty in costs or times is prevalent. [ABSTRACT FROM AUTHOR]
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  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics 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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        StartPage: 491
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      – SubjectFull: Assignment problems (Programming)
        Type: general
      – SubjectFull: Fuzzy numbers
        Type: general
      – SubjectFull: Optimization algorithms
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      – SubjectFull: Resource allocation
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      – SubjectFull: Scheduling
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      – TitleFull: New Ranking Approach for Solving Hexagonal Type Fuzzy Assignment Problems Using Branch and Bound Technique.
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              Text: Feb2026
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              Y: 2026
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